[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: republican
Target surface form: Republican
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the <t>Republican</t> gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=republican%3:01:01:: | definition=relating to or belonging to the Republican Party | examples=a Republican senator; Republican party politics
2. sense_key=republican%5:00:00:democratic:00 | definition=having the supreme power lying in the body of citizens entitled to vote for officers and representatives responsible to them or characteristic of such government; - United States Constitution; ; - Philip Marsh; -Nathaniel Hawthorne | examples=the United States shall guarantee to every state in this union a republican form of government; a very republican notion

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the Target Lemma and Form**: The target lemma is "republican" and the surface form is "Republican" (capitalized). The capitalization is a strong indicator of a proper noun usage, specifically referring to the political party in the US context.

2.  **Analyze the Context**:
    *   The text discusses US politics (Senate, Democrats, GOP, presidential candidates, senatorial candidates, voting, state government).
    *   Phrases like "Republican presidential and senatorial candidates", "GOP candidates", "Republican-governor", "Republican share of the lower state house" appear.
    *   The target instance is "...the <t>Republican</t> gubernatorial candidate...".
    *   The context contrasts Democrats and Republicans as political parties.
    *   "GOP" is used as a synonym for "Republican" in the text ("GOP candidates for president...").

3.  **Analyze the Candidate Senses**:
    *   **Sense 1**: `republican%3:01:01::` | Definition: "relating to or belonging to the Republican Party" | Examples: "a Republican senator", "Republican party politics". This sense specifically refers to the US political party (proper noun sense).
    *   **Sense 2**: `republican%5:00:00:democratic:00` | Definition: "having the supreme power lying in the body of citizens... or characteristic of such government..." | Examples: "...a republican form of government...", "a very republican notion". This sense refers to the political philosophy (lowercase 'r' republican, akin to representative democracy).

4.  **Map Context to Senses**:
    *   The context is about the US Republican Party (GOP).
    *   The target phrase is "Republican gubernatorial candidate" (a candidate belonging to the Republican Party).
    *   Sense 1 matches perfectly ("relating to or belonging to the Republican Party").
    *   Sense 2 refers to a system of government (republicanism), not the specific US political party. It is usually lowercase, whereas the text uses uppercase "Republican".

5.  **Conclusion**: Sense 1 is the correct choice. It refers to the specific political party entity, which fits the capitalization and the context of US elections.

6.  **Format Output**: The user requested a JSON object with the key "sense_index".
    *   Sense 1 is the first option.
    *   JSON: `{"sense_index": 1}`.


attempt_kind: initial

status: success

[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: candidate
Target surface form: candidate
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial <t>candidate</t> and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=candidate%1:18:01:: | definition=a politician who is running for public office | synonyms=campaigner, nominee
2. sense_key=candidate%1:18:00:: | definition=someone who is considered for something (for an office or prize or honor etc.) | synonyms=prospect

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

finish_reason: stop

role: assistant

reasoning_content:
1.  **Analyze the Target Word and Context:**
    *   **Target Lemma:** candidate
    *   **Target Surface Form:** candidate
    *   **Context Sentence:** "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial <t>candidate</t> and the Republican share of the lower state house is a positive function of the state tax rate."
    *   **Broader Context:** The text discusses voting patterns, Senate elections, presidential candidates, gubernatorial candidates, and tax burdens. It compares votes for Republican presidential candidates vs. senatorial candidates, and then gubernatorial candidates vs. state house share.

2.  **Analyze the Candidate Senses:**
    *   **Sense 1:** `candidate%1:18:01::` | Definition: a politician who is running for public office | Synonyms: campaigner, nominee.
    *   **Sense 2:** `candidate%1:18:00::` | Definition: someone who is considered for something (for an office or prize or honor etc.) | Synonyms: prospect.

3.  **Evaluate Sense Fit:**
    *   The specific instance refers to a "Republican gubernatorial <t>candidate</t>".
    *   "Gubernatorial" refers to the office of governor.
    *   The context is about voting behavior, elections, and comparing vote shares.
    *   The text mentions "senatorial candidates" earlier: "votes for Republican presidential and senatorial candidates".
    *   These people are politicians actively running for a specific public office (governor, president, senator).
    *   Sense 1 ("a politician who is running for public office") fits this scenario perfectly. They are campaigning/nominees for an active election.
    *   Sense 2 ("someone who is considered for something") is broader. It could apply to a shortlist for a job, a potential candidate, or someone up for a prize. While an election candidate *is* considered for the office, the specific act of running for office (implied by the voting context and "gubernatorial") is captured more precisely by Sense 1. Sense 1 is the standard definition for a person running in an election. Sense 2 is often used for "candidates for the degree" or "candidates for the job opening" (before the selection process becomes an election/vote). Since this is an election context ("vote going to..."), Sense 1 is the primary and correct meaning.

4.  **Confirm with Synonyms:**
    *   Sense 1 synonyms: campaigner, nominee. A gubernatorial candidate is indeed a nominee of their party and is campaigning.
    *   Sense 2 synonyms: prospect. A candidate in an election is usually not called a "prospect" in this sense (unless talking about potential candidates before they run).

5.  **Final Decision:** Sense 1 matches the context of an active election for public office.

6.  **Formulate Output:**
    *   The prompt asks for a JSON object: `{"sense_index": 1}`.

format: unknown

native_finish_reason: stop

provider: Chutes

currency: USD


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: republican
Target surface form: Republican
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the <t>Republican</t> share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=republican%3:01:01:: | definition=relating to or belonging to the Republican Party | examples=a Republican senator; Republican party politics
2. sense_key=republican%5:00:00:democratic:00 | definition=having the supreme power lying in the body of citizens entitled to vote for officers and representatives responsible to them or characteristic of such government; - United States Constitution; ; - Philip Marsh; -Nathaniel Hawthorne | examples=the United States shall guarantee to every state in this union a republican form of government; a very republican notion

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the Target Word:** The target lemma is "republican" and the surface form is "Republican" (capitalized). This capitalization is a strong hint that it refers to a proper noun or specific political entity, rather than a generic adjective describing a form of government.

2.  **Analyze the Context:**
    *   "An examination of changes in personal staffing decisions in the Senate..."
    *   "...disproportionate control Democrats exercise, due to their majority - party status..."
    *   "...difference between popular votes for Republican presidential and senatorial candidates..."
    *   "...GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate..."
    *   "State government is more typically split along Republican-governor / Democratic-legislature lines..."
    *   "...difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house..."

    The context is heavily focused on US politics, specifically the Republican Party (capitalized) versus the Democratic Party. It mentions "GOP candidates," "senatorial candidates," "presidential candidates," "gubernatorial candidate," and "major-party vote." It contrasts "Republican" with "Democrats."

3.  **Analyze the Candidate Senses:**

    *   **Sense 1:** `republican%3:01:01::`
        *   Definition: "relating to or belonging to the Republican Party"
        *   Examples: "a Republican senator", "Republican party politics"
        *   Fit: This fits perfectly. The text discusses the Republican Party (GOP) in the US political context. The target word is capitalized "Republican" referring to a specific political party affiliation.

    *   **Sense 2:** `republican%5:00:00:democratic:00`
        *   Definition: "having the supreme power lying in the body of citizens entitled to vote for officers and representatives responsible to them or characteristic of such government..."
        *   Examples: "the United States shall guarantee to every state in this union a republican form of government", "a very republican notion"
        *   Fit: This refers to the political philosophy of a republic (representative democracy), usually lowercase "republican" unless at the start of a sentence. The context is clearly about the specific political party organization, not the abstract political theory of republicanism.

4.  **Compare and Decide:**
    *   The text contrasts Republicans with Democrats.
    *   It mentions GOP.
    *   It discusses elections (president, senator, governor).
    *   The surface form is capitalized "Republican".
    *   Sense 1 defines belonging to the Republican Party.
    *   Sense 2 defines a form of government.

    Sense 1 is the correct choice. The target refers to the US political party.

5.  **Format Output:** The user wants a JSON object with "sense_index". Sense 1 is index 1.

    JSON: `{"sense_index": 1}`

provider: Baidu


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: share
Target surface form: share
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican <t>share</t> of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=share%1:21:00:: | definition=assets belonging to or due to or contributed by an individual person or group | synonyms=portion, part, percentage | examples=he wanted his share in cash
2. sense_key=share%1:21:01:: | definition=any of the equal portions into which the capital stock of a corporation is divided and ownership of which is evidenced by a stock certificate | examples=he bought 100 shares of IBM at the market price
3. sense_key=share%1:04:00:: | definition=the allotment of some amount by dividing something | synonyms=parcel, portion | examples=death gets more than its share of attention from theologians
4. sense_key=share%1:04:01:: | definition=the part played by a person in bringing about a result | synonyms=contribution, part | examples=I am proud of my contribution in advancing the project; they all did their share of the work
5. sense_key=share%1:06:00:: | definition=a sharp steel wedge that cuts loose the top layer of soil | synonyms=plowshare, ploughshare

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the target word and context:**
    *   Target lemma: `share`
    *   Target surface form: `share`
    *   Context segment: "...the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican <t>share</t> of the lower state house..."
    *   The sentence is discussing voting results, specifically comparing the percentage of votes for a governor versus the percentage of seats or votes held by Republicans in the lower state house.

2.  **Analyze the candidate senses:**
    *   Sense 1 (`share%1:21:00::`): Definition: "assets belonging to or due to or contributed by an individual person or group". Synonyms: portion, part, percentage. Examples: "he wanted his share in cash". This refers to a portion of a whole, often financial or physical assets, but the synonym "percentage" is very relevant here.
    *   Sense 2 (`share%1:21:01::`): Definition: "any of the equal portions into which the capital stock of a corporation is divided...". Examples: "he bought 100 shares of IBM". This is financial stock market terminology. Not applicable to voting seats.
    *   Sense 3 (`share%1:04:00::`): Definition: "the allotment of some amount by dividing something". Synonyms: parcel, portion. Examples: "death gets more than its share of attention". This refers to the act of allotting or the result of an allotment, often abstract.
    *   Sense 4 (`share%1:04:01::`): Definition: "the part played by a person in bringing about a result". Synonyms: contribution, part. Examples: "they all did their share of the work". This refers to contribution/effort. Not applicable to vote counts.
    *   Sense 5 (`share%1:06:00::`): Definition: "a sharp steel wedge...". Synonyms: plowshare. Agricultural tool. Not applicable.

3.  **Evaluate the best fit:**
    *   The context is "the Republican share of the lower state house".
    *   This refers to the proportion or percentage of the total votes or seats that the Republican party received.
    *   Sense 1 includes "percentage" as a synonym. The definition mentions "assets... or contributed by a group", but broadly in WordNet, sense 1:21:00 covers "portion, part, percentage". It is the general sense of a part of a whole.
    *   Sense 3 is "the allotment of some amount". While a "share" is an allotment, the usage here ("Republican share") refers to the *amount* possessed/received (the percentage), not the action of allotting. Sense 1 fits "amount of a whole" better in this specific quantitative context.
    *   Let's look closer at Sense 1 vs Sense 3.
        *   Sense 1: "assets belonging to... a group". Often used for inheritance, profit, etc. But the synonym list includes "percentage".
        *   Sense 3: "the allotment...". Often used for "share of attention", "share of the work".
    *   However, in political science contexts, "share of the vote" or "share of the seats" is a standard quantitative measure (a portion of the total).
    *   Let's check WordNet hierarchy. Sense 1 is `assets` -> `possession` -> `relation`. Sense 3 is `allotment` -> `apportionment` -> `distribution`.
    *   Actually, Sense 1 is usually defined as "assets belonging to or due to or contributed by an individual person or group". It has synonyms: portion, part, percentage.
    *   Sense 3 is "the allotment of some amount by dividing something". Synonyms: parcel, portion.
    *   Common usage: "market share" usually maps to Sense 1 (percentage/portions of total sales). "Share of the vote" is analogous to market share. It is a specific quantity/percentage of the whole.
    *   Sense 1 is the standard sense for "a part of a whole" when referring to quantities like "market share" or "vote share". The inclusion of "percentage" in the synonyms for Sense 1 strongly supports this. "Republican share of the lower state house" effectively means "Republican percentage of the lower state house".
    *   Sense 4 is "contribution".
    *   Therefore, Sense 1 is the correct choice.

4.  **Double Check:**
    *   Sentence: "...the Republican share of the lower state house..."
    *   Meaning: The portion or percentage of seats/votes held by Republicans.
    *   Sense 1: "assets... part, percentage".
    *   Sense 2: Stock market shares.
    *   Sense 3: Allotment/Assignment (process or result of dividing, but less specific to the quantitative "percentage" aspect compared to Sense 1).
    *   Actually, let's look at the "percentage" synonym in Sense 1. That is the clincher. "Vote share" = "Vote percentage".
    *   Therefore, Sense 1 is the best fit.

5.  **Formatting Output:**
    *   Must be JSON: `{"sense_index": 1}`.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: house
Target surface form: house
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state <t>house</t> is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=house%1:06:00:: | definition=a dwelling that serves as living quarters for one or more families | examples=he has a house on Cape Cod; she felt she had to get out of the house
2. sense_key=house%1:14:01:: | definition=the members of a business organization that owns or operates one or more establishments | synonyms=firm, business firm | examples=he worked for a brokerage house
3. sense_key=house%1:14:04:: | definition=the members of a religious community living together
4. sense_key=house%1:14:03:: | definition=the audience gathered together in a theatre or cinema | examples=the house applauded; he counted the house
5. sense_key=house%1:14:02:: | definition=an official assembly having legislative powers | examples=a bicameral legislature has two houses
6. sense_key=house%1:14:00:: | definition=aristocratic family line | examples=the House of York
7. sense_key=house%1:04:00:: | definition=play in which children take the roles of father or mother or children and pretend to interact like adults | examples=the children were playing house
8. sense_key=house%1:15:00:: | definition=(astrology) one of 12 equal areas into which the zodiac is divided | synonyms=sign of the zodiac, star sign, sign, mansion, planetary house
9. sense_key=house%1:14:06:: | definition=the management of a gambling house or casino | examples=the house gets a percentage of every bet
10. sense_key=house%1:14:05:: | definition=a social unit living together | synonyms=family, household, home, menage | examples=he moved his family to Virginia; It was a good Christian household
11. sense_key=house%1:06:02:: | definition=a building where theatrical performances or motion-picture shows can be presented | synonyms=theater, theatre | examples=the house was full
12. sense_key=house%1:06:01:: | definition=a building in which something is sheltered or located | examples=they had a large carriage house

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the Target Word:** The target word is "house" (noun).
2.  **Analyze the Context:**
    *   Sentence: "A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state <t>house</t> is a positive function of the state tax rate."
    *   The phrase is "lower state house".
    *   The broader context discusses government, legislature, Senate, elections, gubernatorial candidates, and voting.
    *   "Lower state house" refers to one of the chambers of a state legislature (the lower chamber).
    *   "Senate" was mentioned earlier as the upper body.
    *   The text compares votes for a governor vs. the "Republican share of the lower state house".
    *   This clearly refers to a legislative body.

3.  **Evaluate Candidate Senses:**
    *   *Sense 1:* "a dwelling that serves as living quarters..." - Incorrect. Not a building for living.
    *   *Sense 2:* "the members of a business organization..." - Incorrect. Not a business context.
    *   *Sense 3:* "the members of a religious community..." - Incorrect.
    *   *Sense 4:* "the audience gathered together in a theatre..." - Incorrect.
    *   *Sense 5:* "an official assembly having legislative powers" - Examples: "a bicameral legislature has two houses". This fits perfectly. "Lower state house" is a legislative chamber.
    *   *Sense 6:* "aristocratic family line" - Incorrect.
    *   *Sense 7:* "play in which children..." - Incorrect.
    *   *Sense 8:* "astrology..." - Incorrect.
    *   *Sense 9:* "management of a gambling house..." - Incorrect.
    *   *Sense 10:* "a social unit living together..." - Incorrect.
    *   *Sense 11:* "a building where theatrical performances..." - Incorrect.
    *   *Sense 12:* "a building in which something is sheltered..." - Incorrect.

4.  **Confirm Sense 5:**
    *   Definition: "an official assembly having legislative powers".
    *   Example: "a bicameral legislature has two houses".
    *   Context match: The text discusses the "Senate" (upper house) and the "lower state house" (lower house) of the state legislature. This is a legislative sense.

5.  **Format Output:** Return JSON `{"sense_index": 5}`.

provider: DigitalOcean


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: positive
Target surface form: positive
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a <t>positive</t> function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=positive%3:00:01:: | definition=characterized by or displaying affirmation or acceptance or certainty etc. | examples=a positive attitude; the reviews were all positive
2. sense_key=positive%5:00:00:certain:02 | definition=persuaded of; very sure | synonyms=convinced, confident | examples=were convinced that it would be to their advantage to join; I am positive he is lying
3. sense_key=positive%5:00:00:advantageous:00 | definition=involving advantage or good | synonyms=plus | examples=a plus (or positive) factor
4. sense_key=positive%3:00:04:: | definition=indicating existence or presence of a suspected condition or pathogen | synonyms=confirming | examples=a positive pregnancy test
5. sense_key=positive%5:00:00:formal:01 | definition=formally laid down or imposed | synonyms=prescribed | examples=positive laws
6. sense_key=positive%5:00:00:undeniable:00 | definition=impossible to deny or disprove | synonyms=incontrovertible, irrefutable | examples=incontrovertible proof of the defendant's innocence; proof positive
7. sense_key=positive%3:01:00:: | definition=of or relating to positivism | synonyms=positivist, positivistic | examples=positivist thinkers; positivist doctrine
8. sense_key=positive%3:00:05:: | definition=reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion | examples=positive increase in graduating students
9. sense_key=positive%5:00:00:plus:00 | definition=greater than zero | examples=positive numbers
10. sense_key=positive%5:00:00:charged:00 | definition=having a positive charge | synonyms=electropositive, positively charged | examples=protons are positive
11. sense_key=positive%5:00:00:confident:00 | definition=marked by excessive confidence | synonyms=cocksure, overconfident | examples=an arrogant and cocksure materialist; so overconfident and impudent as to speak to the queen

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  phrase "positive function".
    Sentence: "...the difference between popular votes for Republican presidential and senatorial candidates... turns out to be a positive function of how onerous the federal government's tax burden is per state..."
    Later sentence: "...the difference between a state's major - party vote... is a positive function of the state tax rate."

    The context is an academic/political science text discussing statistical relationships (econometric investigation). The phrase "positive function" implies a mathematical or statistical relationship where as one variable increases (tax rate), the other variable increases (vote difference).

2.  **Evaluate the candidate senses against the context:**

    *   **Sense 1:** "characterized by or displaying affirmation..." (attitudinal). Doesn't fit "positive function".
    *   **Sense 2:** "persuaded of; very sure". (Epistemic). Doesn't fit.
    *   **Sense 3:** "involving advantage or good". (Evaluative). A "positive function" here doesn't mean a "good function". It means a specific type of mathematical relationship.
    *   **Sense 4:** "indicating existence or presence...". (Medical). Doesn't fit.
    *   **Sense 5:** "formally laid down or imposed". (Legal). Doesn't fit.
    *   **Sense 6:** "impossible to deny or disprove". (Epistemic strength). Doesn't fit.
    *   **Sense 7:** "of or relating to positivism". (Philosophy). Doesn't fit.
    *   **Sense 8:** "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion". This describes directionality or correlation. Example: "positive increase". This aligns with the concept of a "positive correlation" or "positive function" where variable X goes up as variable Y goes up.
    *   **Sense 9:** "greater than zero" (Arithmetic). While this is the mathematical definition of a positive number, "positive function" in this context usually refers to the *slope* or the relationship (monotonic increase) rather than the function returning a value > 0. However, let's compare Sense 8 and Sense 9.
    *   **Sense 10:** "having a positive charge". (Physics). Doesn't fit.
    *   **Sense 11:** "marked by excessive confidence". Doesn't fit.

3.  **Deep Dive: Sense 8 vs. Sense 9.**
    *   Sense 9 is specific to numbers being greater than zero. A "positive function" *could* mean a function f(x) > 0, but in the context of econometrics (where they are examining changes, differences in votes, and tax rates), the phrase "positive function of" almost certainly means that Y is a function of X where dy/dx > 0 (a positive relationship/correlation).
    *   Sense 8 defines it as "tending in the direction which... is taken to indicate increase". The gloss mentions "increase or progress".
    *   The phrase "positive function of X" implies that as X increases, the result increases.
    *   WordNet sense 8 is often used for this general directional meaning (positive correlation, positive increase). WordNet sense 9 is strictly "greater than zero" for numbers.
    *   Let's look at the gloss for Sense 8 again: "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion".
    *   Let's look at the specific usage in the text: "...turns out to be a positive function of how onerous the federal government's tax burden is..."
    *   Interpretation: Higher tax burden -> Higher vote difference.
    *   This fits the "direction... to indicate increase" definition of Sense 8 perfectly. It captures the sense of "positive correlation" or "positive relationship".

    Let's check if Sense 9 ("greater than zero") applies. If the function value is positive, that's Sense 9. If the relationship is positive (slope), that's Sense 8.
    Context clues: "difference between popular votes... turns out to be a positive function of..."
    Usually, "a positive function of" means "increases with". It describes the *nature of the dependency* (positive relationship), not necessarily just the sign of the output value (though the output value here is a difference, which could be positive or negative, but the *change* is what matters). Actually, usually "Y is a positive function of X" means dY/dX > 0.
    WordNet Sense 8 covers the "direction indicating increase".
    WordNet Sense 9 covers "greater than zero".

    Which is better?
    If I say "temperature is a positive function of heat", I mean it goes up.
    If I say "the result was a positive number", I use Sense 9.
    The text says: "turns out to be a positive function of how onerous...".
    The text is describing the relationship between variables in an econometric model.
    The gloss for Sense 8: "tending in the direction which ... indicates increase".
    This is the definition of a positive relationship/correlation in a scientific/statistical context.

    Let's re-read Sense 8's example: "positive increase in graduating students". This is slightly awkward phrasing but illustrates the concept of directional increase.
    Let's re-read Sense 9's example: "positive numbers".

    In corpus linguistics/semantics, "positive function" in the sense of "Y increases as X increases" is distinct from "f(x) > 0". The text is clearly discussing the former (relationships between voting patterns and tax rates). "Holding other factors constant... turns out to be a positive function of..." refers to the coefficient or slope direction.

    Therefore, Sense 8 is the intended meaning. It captures the directional/relational aspect of "positive" used in statistical analysis (positive association).

4.  **Final Verification:**
    Context: Econometric investigation, "positive function of".
    Meaning: As the tax burden increases, the vote difference increases.
    Sense 8: "reckoned, situated or tending in the direction which... is taken to indicate increase". Matches the concept of positive correlation/slope.
    Sense 9: "greater than zero". Matches numbers.
    The phrase "positive function" refers to the relationship (slope), not just the value being > 0.
    Therefore, Sense 8 is the correct choice.

    Note on indexing:
    The user provided a numbered list.
    1. positive%3:00:01::
    2. positive%5:00:00:certain:02
    3. positive%5:00:00:advantageous:00
    4. positive%3:00:04::
    5. positive%5:00:00:formal:01
    6. positive%5:00:00:undeniable:00
    7. positive%3:01:00::
    8. positive%3:00:05::
    9. positive%5:00:00:plus:00
    10. positive%5:00:00:charged:00
    11. positive%5:00:00:confident:00

    Sense 8 corresponds to "reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion".

    I will select Sense 8.

provider: Amazon Bedrock


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: function
Target surface form: function
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive <t>function</t> of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=function%1:24:00:: | definition=(mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function) | synonyms=mathematical function, single-valued function, map, mapping
2. sense_key=function%1:07:00:: | definition=what something is used for | synonyms=purpose, role, use | examples=the function of an auger is to bore holes; ballet is beautiful but what use is it?
3. sense_key=function%1:04:00:: | definition=the actions and activities assigned to or required or expected of a person or group | synonyms=office, part, role | examples=the function of a teacher; the government must do its part
4. sense_key=function%1:24:01:: | definition=a relation such that one thing is dependent on another | examples=height is a function of age; price is a function of supply and demand
5. sense_key=function%1:14:00:: | definition=a formal or official social gathering or ceremony | examples=it was a black-tie function
6. sense_key=function%1:11:00:: | definition=a vaguely specified social event | synonyms=affair, occasion, social occasion, social function | examples=the party was quite an affair; an occasion arranged to honor the president
7. sense_key=function%1:10:00:: | definition=a set sequence of steps, part of larger computer program | synonyms=routine, subroutine, subprogram, procedure

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
The context is discussing a mathematical/statistical relationship between variables. Specifically:

"the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state"

And later:

"the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate."

This is using "function" in the sense of a relationship where one variable depends on another - specifically, vote differences are dependent on/related to tax rates. This is a causal or correlational relationship.

Looking at the senses:

1. sense_key=function%1:24:00:: - This is the mathematical definition (domain/range), very technical
2. sense_key=function%1:07:00:: - "what something is used for" - purpose/role - doesn't fit
3. sense_key=function%1:04:00:: - "the actions and activities assigned to or required or expected of a person or group" - doesn't fit
4. sense_key=function%1:24:01:: - "a relation such that one thing is dependent on another" with examples "height is a function of age; price is a function of supply and demand" - This fits! The vote difference is a function of the tax rate - one thing depends on another.
5. sense_key=function%1:14:00:: - formal social gathering - doesn't fit
6. sense_key=function%1:11:00:: - vaguely specified social event - doesn't fit
7. sense_key=function%1:10:00:: - computer subroutine - doesn't fit

The context clearly shows that one variable (vote difference) is dependent on another (tax rate). Sense 4 with examples like "height is a function of age; price is a function of supply and demand" matches this usage perfectly. This is the sense where "function" means a relationship of dependency between variables, not the strictly mathematical definition of sets and mappings.

So the answer is sense_index: 4 (the fourth sense inthe list).

provider: Together


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: state
Target surface form: state
Context:
An examination of changes in personal staffing decisions in the Senate between 1986 and 1987 -LRB- when control of that body changed party hands -RRB-, moreover, reveals that the personal staffing differences noted in the table can not be attributed to the disproportionate control Democrats exercise, due to their majority - party status, over other resources such as committee staff. An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the <t>state</t> tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation.

Candidate senses:
1. sense_key=state%1:15:01:: | definition=the territory occupied by one of the constituent administrative districts of a nation | synonyms=province | examples=his state is in the deep south
2. sense_key=state%1:03:00:: | definition=the way something is with respect to its main attributes | examples=the current state of knowledge; his state of health
3. sense_key=state%1:14:01:: | definition=the group of people comprising the government of a sovereign state | examples=the state has lowered its income tax
4. sense_key=state%1:14:00:: | definition=a politically organized body of people under a single government | synonyms=nation, country, land, commonwealth, res publica, body politic | examples=the state has elected a new president; African nations
5. sense_key=state%1:26:02:: | definition=(chemistry) the three traditional states of matter are solids (fixed shape and volume) and liquids (fixed volume and shaped by the container) and gases (filling the container) | synonyms=state of matter | examples=the solid state of water is called ice
6. sense_key=state%1:26:01:: | definition=a state of depression or agitation | examples=he was in such a state you just couldn't reason with him
7. sense_key=state%1:15:00:: | definition=the territory occupied by a nation | synonyms=country, land | examples=he returned to the land of his birth; he visited several European countries
8. sense_key=state%1:14:02:: | definition=the federal department in the United States that sets and maintains foreign policies | synonyms=Department of State, United States Department of State, State Department, DoS | examples=the Department of State was created in 1789

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the target lemma and context:**
    *   Target lemma: `state`
    *   Target surface form: `state`
    *   Context sentence: "...the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the *state* tax rate."

2.  **Analyze the surrounding context:**
    *   The text discusses political science, voting patterns, senate elections, gubernatorial candidates, state legislatures ("lower state house"), and tax rates.
    *   It mentions "states conducting a Senate election", "state government level", "Republican-gubernatorial candidate", "lower state house".
    *   The specific phrase is "state tax rate".
    *   The word "state" here refers to a constituent administrative unit of the United States (one of the 50 states).

3.  **Evaluate the candidate senses:**

    *   **Sense 1 (state%1:15:01::):**
        *   Definition: "the territory occupied by one of the constituent administrative districts of a nation"
        *   Synonyms: province
        *   Examples: "his state is in the deep south"
        *   Analysis: This fits perfectly with the US context. The US is a nation composed of constituent administrative districts called "states". The phrase "state tax rate" refers to the tax rate imposed by one of these specific districts (e.g., Texas, California). The example "his state is in the deep south" aligns with US usage.

    *   **Sense 2 (state%1:03:00::):**
        *   Definition: "the way something is with respect to its main attributes"
        *   Analysis: This is a general condition (e.g., state of mind, state of affairs). It does not fit "state tax rate".

    *   **Sense 3 (state%1:14:01::):**
        *   Definition: "the group of people comprising the government of a sovereign state"
        *   Analysis: While related to government, this usually refers to the abstract entity of the government acting as an agent (e.g., "The State acted arbitrarily"). Here, "state tax rate" implies a geographical/political subdivision, not just the body of government people.

    *   **Sense 4 (state%1:14:00::):**
        *   Definition: "a politically organized body of people under a single government"
        *   Synonyms: nation, country, land, commonwealth, res publica, body politic
        *   Analysis: This refers to a sovereign state/country. While US states have governments, they are not sovereign nations in the international relations sense usually implied by "nation" or "country" synonyms. However, WordNet often blurs the line between sovereign states and federal states. But Sense 1 is much more specific to the "constituent administrative districts of a nation," which exactly describes US states (Texas, New York, etc.) mentioned in the text ("states conducting a Senate election"). The distinction between a sovereign country (Sense 4) and a federal subdivision (Sense 1) is crucial here. The text discusses "states" within the "federal government" context.

    *   **Sense 5 (state%1:26:02::):**
        *   Definition: chemistry/physics states of matter.
        *   Analysis: Irrelevant.

    *   **Sense 6 (state%1:26:01::):**
        *   Definition: emotional state/agitation.
        *   Analysis: Irrelevant.

    *   **Sense 7 (state%1:15:00::):**
        *   Definition: "the territory occupied by a nation"
        *   Synonyms: country, land
        *   Analysis: Similar to Sense 4, refers to a sovereign nation's territory. Not a subdivision.

    *   **Sense 8 (state%1:14:02::):**
        *   Definition: The US Department of State.
        *   Analysis: Irrelevant.

4.  **Compare Sense 1 and Sense 4:**
    *   The text is about US politics ("Senate", "Republican", "gubernatorial", "lower state house").
    *   It refers to the subdivisions of the USA.
    *   Sense 1 definition: "the territory occupied by one of the constituent administrative districts of a nation". This is the technical definition of a state in a federal system like the USA.
    *   Sense 4 definition: "a politically organized body of people under a single government" (synonyms: nation, country). This usually applies to sovereign entities (France, Japan).
    *   "State tax rate" refers to the tax rate of a specific subdivision (e.g., Pennsylvania). Sense 1 is the correct choice for the subdivisions of a nation.

5.  **Final Selection:**
    *   Sense 1 is the specific sense for a constituent state of a federal nation (like the USA).

    Let's check the indices provided in the prompt.
    1. sense_key=state%1:15:01:: ...
    2. sense_key=state%1:03:00:: ...
    3. sense_key=state%1:14:01:: ...
    4. sense_key=state%1:14:00:: ...
    5. sense_key=state%1:26:02:: ...
    6. sense_key=state%1:26:01:: ...
    7. sense_key=state%1:15:00:: ...
    8. sense_key=state%1:14:02:: ...

    I need to choose index 1.

    Context: "...positive function of the state tax rate."
    Refers to one of the 50 US states.
    Sense 1 defines "state" as a constituent administrative district of a nation.

    Result: sense_index 1.

provider: StreamLake


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: federal
Target surface form: federal
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the <t>federal</t> and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=federal%5:00:00:national:01 | definition=national; especially in reference to the government of the United States as distinct from that of its member units | examples=the Federal Bureau of Investigation; federal courts
2. sense_key=federal%3:01:02:: | definition=of or relating to the central government of a federation | examples=a federal district is one set aside as the seat of the national government
3. sense_key=federal%5:00:00:northern:02 | definition=being of or having to do with the northern United States and those loyal to the Union during the American Civil War | synonyms=Union | examples=Union soldiers; Federal forces
4. sense_key=federal%3:00:00:: | definition=characterized by or constituting a form of government in which power is divided between one central and several regional authorities | examples=a federal system like that of the United States; federal governments often evolved out of confederations

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
Let me analyze the context and determine which sense of "federal" best fits the usage in this text.

The context discusses government systems at both the federal and state levels in the United States. It's comparing voting patterns for presidential vs. senatorial candidates, and gubernatorial vs. state legislative candidates. It's specifically talking about the relationship between tax rates and voting behavior, with references to "federal government's tax burden" and comparing federal and state government levels.

Now let's examine each candidate sense:

1. sense_key=federal%5:00:00:national:01 | definition=national; especially in reference to the government of the United States as distinct from that of its member units | examples=the Federal Bureau of Investigation; federal courts

This sense refers to the national government of the United States as distinct from state governments. This seems to match the usage in the text where "federal government" is contrasted with state government.

2. sense_key=federal%3:01:02:: | definition=of or relating to the central government of a federation | examples=a federal district is one set aside as the seat of the national government

This is similar to sense 1, but more generally about any central government of a federation, not specifically the United States. The text is clearly about the U.S. federal government in contrast to state governments.

3. sense_key=federal%5:00:00:northern:02 | definition=being of or having to do with the northern United States and those loyal to the Union during the American Civil War | synonyms=Union | examples=Union soldiers; Federal forces

This historical sense about the Civil War era is clearly not relevant to this modern political science context.

4. sense_key=federal%3:00:00:: | definition=characterized by or constituting a form of government in which power is divided between one central and several regional authorities | examples=a federal system like that of the United States; federal governments often evolved out of confederations

This sense is about the federal system or form of government, rather than the federal government itself. While related, the text is using "federal" to refer to the national level of government rather than describing the type of government system.

Looking at the context, the text is comparing "federal government" with "state government," referring to the national level of government in the United States. This aligns best with sense 1, which specifically refers to the government of the United States as distinct from its member units (states).

The usage in phrases like "the federal government's tax burden" and "at the federal level" refers to the national government of the United States, not just any federal system in general.

Therefore, sense 1 is the best match for this context.

provider: Phala


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: level
Target surface form: levels
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government <t>levels</t> at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=level%1:07:00:: | definition=a position on a scale of intensity or amount or quality | synonyms=degree, grade | examples=a moderate grade of intelligence; a high level of care is required
2. sense_key=level%1:26:01:: | definition=a relative position or degree of value in a graded group | synonyms=grade, tier | examples=lumber of the highest grade
3. sense_key=level%1:26:00:: | definition=a specific identifiable position in a continuum or series or especially in a process | synonyms=degree, stage, point | examples=a remarkable degree of frankness; at what stage are the social sciences?
4. sense_key=level%1:07:01:: | definition=height above ground | examples=the water reached ankle level; the pictures were at the same level
5. sense_key=level%1:06:00:: | definition=indicator that establishes the horizontal when a bubble is centered in a tube of liquid | synonyms=spirit level
6. sense_key=level%1:06:03:: | definition=a flat surface at right angles to a plumb line | synonyms=horizontal surface | examples=park the car on the level
7. sense_key=level%1:09:00:: | definition=an abstract place usually conceived as having depth | synonyms=layer, stratum | examples=a good actor communicates on several levels; a simile has at least two layers of meaning
8. sense_key=level%1:06:01:: | definition=a structure consisting of a room or set of rooms at a single position along a vertical scale | synonyms=floor, storey, story | examples=what level is the office on?

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
Let me analyze the context to determine the correct sense for "levels" in this sentence.

The sentence is: "In sum, at both the federal and state government <t>levels</t> at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation."

The context discusses "federal and state government levels" - referring to different tiers or layers of government organization. The text is discussing how voting patterns and political behavior work similarly at both federal and state government "levels."

Let me examine the candidate senses:

1. sense_key=level%1:07:00:: | definition=a position on a scale of intensity or amount or quality | synonyms=degree, grade | examples=a moderate grade of intelligence; a high level of care is required

2. sense_key=level%1:26:01:: | definition=a relative position or degree of value in a graded group | synonyms=grade, tier | examples=lumber of the highest grade

3. sense_key=level%1:26:00:: | definition=a specific identifiable position in a continuum or series or especially in a process | synonyms=degree, stage, point | examples=a remarkable degree of frankness; at what stage are the social sciences?

4. sense_key=level%1:07:01:: | definition=height above ground | examples=the water reached ankle level; the pictures were at the same level

5. sense_key=level%1:06:00:: | definition=indicator that establishes the horizontal when a bubble is centered in a tube of liquid | synonyms=spirit level

6. sense_key=level%1:06:03:: | definition=a flat surface at right angles to a plumb line | synonyms=horizontal surface | examples=park the car on the level

7. sense_key=level%1:09:00:: | definition=an abstract place usually conceived as having depth | synonyms=layer, stratum | examples=a good actor communicates on several levels; a simile has at least two layers of meaning

8. sense_key=level%1:06:01:: | definition=a structure consisting of a room or set of rooms at a single position along a vertical scale | synonyms=floor, storey, story | examples=what level is the office on?

Looking at the context, "federal and state government levels" refers to different hierarchical tiers or strata of government. This is talking about organizational levels or layers of government.

Sense 7 seems most appropriate: "an abstract place usually conceived as having depth" with synonyms "layer, stratum" - the example "a good actor communicates on several levels" shows this abstract sense of different hierarchical planes or strata of operation. This matches well with "federal and state government levels" - different strata or layers of government organization.

Sense 2 with "a relative position or degree of value in a graded group" with synonyms "grade, tier" could also potentially fit, but the examples about lumber grade suggest it's more about quality rankings.

Sense 3 with "a specific identifiable position in a continuum or series or especially in a process" could also potentially fit, but seems more focused on stages in a process.

The best match appears to be Sense 7 - referring to abstract layers or strata of organization, which matches the notion of different governmental strata (federal vs. state levels).

The answer is {"sense_index": 7}.

provider: Friendli


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: part
Target surface form: part
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least <t>part</t> of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=part%1:24:00:: | definition=something determined in relation to something that includes it | synonyms=portion, component part, component, constituent | examples=he wanted to feel a part of something bigger than himself; I read a portion of the manuscript
2. sense_key=part%1:06:00:: | definition=something less than the whole of a human artifact | synonyms=portion | examples=the rear part of the house; glue the two parts together
3. sense_key=part%1:17:00:: | definition=a portion of a natural object | synonyms=piece | examples=they analyzed the river into three parts; he needed a piece of granite
4. sense_key=part%1:09:02:: | definition=that which concerns a person with regard to a particular role or situation | examples=it requires vigilance on our part; they resisted every effort on his part
5. sense_key=part%1:15:00:: | definition=the extended spatial location of something | synonyms=region | examples=the farming regions of France; religions in all parts of the world
6. sense_key=part%1:04:01:: | definition=the actions and activities assigned to or required or expected of a person or group | synonyms=function, office, role | examples=the function of a teacher; the government must do its part
7. sense_key=part%1:09:01:: | definition=an actor's portrayal of someone in a play | synonyms=character, role, theatrical role, persona | examples=she played the part of Desdemona
8. sense_key=part%1:21:00:: | definition=assets belonging to or due to or contributed by an individual person or group | synonyms=share, portion, percentage | examples=he wanted his share in cash
9. sense_key=part%1:09:00:: | definition=one of the portions into which something is regarded as divided and which together constitute a whole | synonyms=section, division | examples=the written part of the exam; the finance section of the company
10. sense_key=part%1:08:01:: | definition=a line of scalp that can be seen when sections of hair are combed in opposite directions | synonyms=parting | examples=his part was right in the middle
11. sense_key=part%1:10:00:: | definition=the melody carried by a particular voice or instrument in polyphonic music | synonyms=voice | examples=he tried to sing the tenor part
12. sense_key=part%1:04:03:: | definition=the part played by a person in bringing about a result | synonyms=contribution, share | examples=I am proud of my contribution in advancing the project; they all did their share of the work

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

raw_output:
```json
{"sense_index": 1}
```

content:
```json
{"sense_index": 1}
```

reasoning_content:
The target word is "part" in the context: "at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation."

Here, "part" means a portion or fraction of the seemingly irrational behavior. It refers to something determined in relation to something that includes it.

Let's look at the candidate senses:
1. part%1:24:00:: - something determined in relation to something that includes it - synonyms: portion, component part, component, constituent
2. part%1:06:00:: - something less than the whole of a human artifact
3. part%1:17:00:: - a portion of a natural object
4. part%1:09:02:: - that which concerns a person with regard to a particular role or situation
5. part%1:15:00:: - the extended spatial location of something
6. part%1:04:01:: - the actions and activities assigned to or required or expected of a person or group
7. part%1:09:01:: - an actor's portrayal of someone in a play
8. part%1:21:00:: - assets belonging to or due to or contributed by an individual person or group
9. part%1:09:00:: - one of the portions into which something is regarded as divided and which together constitute a whole - synonyms: section, division
10. part%1:08:01:: - a line of scalp that can be seen when sections of hair are combed in opposite directions
11. part%1:10:00:: - the melody carried by a particular voice or instrument in polyphonic music
12. part%1:04:03:: - the part played by a person in bringing about a result

"part of the seemingly irrational behavior" refers to a portion of the behavior.
Sense 1 (something determined in relation to something that includes it - "he wanted to feel a part of something bigger", "I read a portion of the manuscript") fits "part of the seemingly irrational behavior". It is a portion of a whole.
Sense 9 (one of the portions into which something is regarded as divided and which together constitute a whole - "the written part of the exam") usually refers to a distinct division or section.

"At least part of the behavior" means a portion of it. "Portion" is a synonym for Sense 1.
Sense 1 definition: "something determined in relation to something that includes it" applies perfectly to "part of the behavior" (the part is determined in relation to the behavior which includes it).
Wait, Sense 9 definition: "one of the portions into which something is regarded as divided and which together constitute a whole" - this implies a discrete division.
Sense 1 is more general for "a part of something" meaning a portion of a whole without necessarily being a discrete division.
Let's check the examples.
Sense 1 examples: "he wanted to feel a part of something bigger than himself; I read a portion of the manuscript"
Sense 9 examples: "the written part of the exam; the finance section of the company"

"part of the seemingly irrational behavior" is like "a portion of the manuscript" or "a portion of the behavior". It's not a section or division of the behavior. It just means some fraction/portion of it.
So Sense 1 seems the best fit.

Let me double check Sense 1 vs Sense 9.
"part of the behavior" - just a fraction, not a section.
Sense 1 is defined as: something determined in relation to something that includes it. Synonyms: portion, component part, component, constituent.
"part of" in "part of the behavior" is best captured by Sense 1.

Let me confirm index:
1 -> sense_key=part%1:24:00::
2 -> sense_key=part%1:06:00::
3 -> sense_key=part%1:17:00::
4 -> sense_key=part%1:09:02::
5 -> sense_key=part%1:15:00::
6 -> sense_key=part%1:04:01::
7 -> sense_key=part%1:09:01::
8 -> sense_key=part%1:21:00::
9 -> sense_key=part%1:09:00::

Yes, Sense 1 fits best.

provider: SiliconFlow


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: irrational
Target surface form: irrational
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly <t>irrational</t> behavior voters display in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=irrational%3:00:00:: | definition=not consistent with or using reason | examples=irrational fears; irrational animals
2. sense_key=irrational%3:01:00:: | definition=real but not expressible as the quotient of two integers | examples=irrational numbers

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
The user wants me to perform Word Sense Disambiguation for the word "irrational" in a specific context.

**Context Analysis:**
- Sentence: "In sum, at both the federal and state government levels at least part of the seemingly <t>irrational</t> behavior voters display in the voting booth may have an exceedingly rational explanation."
- The text discusses voting behavior (ticket splitting, vote differences between presidential and senate candidates, etc.).
- The behavior is described as "seemingly irrational" but having a "rational explanation."
- "Rational" here refers to logical, reasonable behavior, or behavior guided by reason.
- Therefore, "irrational" in this context means "not rational" or "not consistent with or using reason."

**Candidate Sense Analysis:**
1. `sense_key=irrational%3:00:00::` | Definition: "not consistent with or using reason" | Examples: "irrational fears", "irrational animals".
2. `sense_key=irrational%3:01:00::` | Definition: "real but not expressible as the quotient of two integers" | Examples: "irrational numbers".

**Matching:**
- The context talks about human behavior (voters' behavior) being seemingly irrational but actually having a rational cause.
- Sense 1 deals with reason/logic in behavior or thought.
- Sense 2 deals with mathematics (numbers).
- The context is clearly about human behavior and decision-making, not mathematics.

**Conclusion:**
Sense 1 is the correct match. It refers to the lack of reason in behavior.

**Formatting:**
The user asks for a JSON object: `{"sense_index": X}`.
Sense 1 corresponds to index 1.

provider: Venice


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: behavior
Target surface form: behavior
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational <t>behavior</t> voters display in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=behavior%1:04:00:: | definition=manner of acting or controlling yourself | synonyms=behaviour, conduct, doings
2. sense_key=behavior%1:26:00:: | definition=the action or reaction of something (as a machine or substance) under specified circumstances | synonyms=behaviour | examples=the behavior of small particles can be studied in experiments
3. sense_key=behavior%1:07:00:: | definition=(behavioral attributes) the way a person behaves toward other people | synonyms=demeanor, demeanour, behaviour, conduct, deportment
4. sense_key=behavior%1:04:01:: | definition=(psychology) the aggregate of the responses or reactions or movements made by an organism in any situation | synonyms=behaviour

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
The target word is "behavior" in the context: "In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly rational explanation."

Let me analyze the context:
- The passage discusses voting patterns and voter behavior
- It's about how voters act/make decisions in the voting booth
- The "seemingly irrational behavior voters display" refers to actions/choices made by people (voters) in elections
- This is about human conduct/actions in a social/political context

Now let me examine each sense:

1. sense_key=behavior%1:04:00:: | definition=manner of acting or controlling yourself | synonyms=behaviour, conduct, doings
- This is a general sense about how someone acts or conducts themselves
- Could apply to voters and how they act

2. sense_key=behavior%1:26:00:: | definition=the action or reaction of something (as a machine or substance) under specified circumstances | synonyms=behaviour | examples=the behavior of small particles can be studied in experiments
- This is about physical things (machines, substances, particles)
- Not applicable to voters

3. sense_key=behavior%1:07:00:: | definition=(behavioral attributes) the way a person behaves toward other people | synonyms=demeanor, demeanour, behaviour, conduct, deportment
- This is specifically about interpersonal behavior - how someone treats/behaves toward other people
- Not quite right - voting behavior isn't really about how voters treat other people

4. sense_key=behavior%1:04:01:: | definition=(psychology) the aggregate of the responses or reactions or movements made by an organism in any situation | synonyms=behaviour
- This is a psychological sense about organisms' responses/reactions
- Could apply but seems more technical/scientific

The context is about voting behavior - how voters act/decide in the voting booth. This is about human conduct and decision-making patterns, not interpersonal behavior (sense 3) or physical/chemical behavior (sense 2).

Between senses 1 and 4:
- Sense 1 is a general sense about "manner of acting or controlling yourself" - this fits well with "voter behavior" as general conduct/action
- Sense 4 is specifically psychological/technical about "responses or reactions or movements made by an organism"

While sense 4 could work (voters are organisms responding to stimuli), the context is more about the general manner of how voters act, not a technical psychological sense. The passage discusses voting patterns and choices in a political science context, not a strict psychological experimental context.

Sense 1 "manner of acting or controlling yourself" with synonyms "conduct" seems most appropriate for "voter behavior" in a voting booth context. Voters are acting/conducting themselves by making certain voting decisions.

The best answer is sense 1.

provider: DeepInfra


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: display
Target surface form: display
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters <t>display</t> in the voting booth may have an exceedingly rational explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=display%2:39:00:: | definition=to show, make visible or apparent | synonyms=expose, exhibit | examples=The Metropolitan Museum is exhibiting Goya's works this month; Why don't you show your nice legs and wear shorter skirts?
2. sense_key=display%2:41:00:: | definition=attract attention by displaying some body part or posing; of animals

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the Target Lemma:** "display" (verb).
2.  **Analyze the Target Surface Form:** "display" (verb, present tense, plural agreement with "voters").
3.  **Analyze the Context:**
    *   The sentence is: "In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters <t>display</t> in the voting booth may have an exceedingly rational explanation."
    *   Subject: "voters" (specifically "seemingly irrational behavior voters display").
    *   Object/Complement: "in the voting booth".
    *   Meaning: Voters show or exhibit behavior. The behavior is made visible/manifest through their actions.
    *   The context discusses political science analysis: how voters act (ticket splitting, voting patterns based on taxes). They are "showing" this behavior.

4.  **Analyze Candidate Sense 1:**
    *   sense_key=display%2:39:00::
    *   definition="to show, make visible or apparent"
    *   synonyms=expose, exhibit
    *   examples="The Metropolitan Museum is exhibiting Goya's works this month; Why don't you show your nice legs and wear shorter skirts?"
    *   Analysis: This fits perfectly. The voters "exhibit" or "show" behavior. The definition "make visible or apparent" aligns with observing behavior in a voting booth. The synonyms (exhibit) fit well. The examples are about showing physical objects or attributes, but the schematic definition covers abstract behaviors as well.

5.  **Analyze Candidate Sense 2:**
    *   sense_key=display%2:41:00::
    *   definition="attract attention by displaying some body part or posing; of animals"
    *   synonyms=(none listed in prompt, but implied courtship behavior or threat displays).
    *   Analysis: This is wrong. It specifies "of animals" and "attract attention by displaying some body part". Voters are humans, and they are not performing a mating dance or puffing up feathers. They are voting.

6.  **Compare and Decide:**
    *   Sense 1 is the general verb meaning "to show/exhibit".
    *   Sense 2 is a specific ethological (animal behavior) term.
    *   The context is about human behavior (voters) being shown/manifested.
    *   Therefore, Sense 1 is the correct choice.

7.  **Format Output:** JSON object `{"sense_index": 1}`.


[System] You are an English linguist performing fine-grained Word Sense Disambiguation. WordNet glosses are schematic. Use the sentence context, the examples, and the synonyms to choose the best indexed sense. Do not hedge. Choose the single best indexed sense.

[User]
Target lemma: rational
Target surface form: rational
Context:
An additional piece of evidence from the Senate: Holding other factors constant, such as incumbency advantages and regional factors, the difference between popular votes for Republican presidential and senatorial candidates in states conducting a Senate election turns out to be a positive function of how onerous the federal government's tax burden is per state -LRB- a progressive tax rate hits higher - income states harder -RRB-. Put more simply, GOP candidates for president are looked on more kindly by voters than Republican candidates for the Senate when the prisoner's sentence is more severe. Moreover, ticket splitting appears to take the same peculiar pattern at the state government level as it does at the federal level. State government is more typically split along Republican-governor / Democratic-legislature lines than the reverse. A cross-state econometric investigation, furthermore, reveals that, holding other factors constant, the difference between a state's major - party vote going to the Republican gubernatorial candidate and the Republican share of the lower state house is a positive function of the state tax rate. In sum, at both the federal and state government levels at least part of the seemingly irrational behavior voters display in the voting booth may have an exceedingly <t>rational</t> explanation. Mr. Zupan teaches at the University of Southern California's business school.

Candidate senses:
1. sense_key=rational%3:00:00:: | definition=consistent with or based on or using reason | examples=rational behavior; a process of rational inference
2. sense_key=rational%5:00:00:mental:00 | definition=of or associated with or requiring the use of the mind | synonyms=intellectual, noetic | examples=intellectual problems; the triumph of the rational over the animal side of man
3. sense_key=rational%3:01:00:: | definition=capable of being expressed as a quotient of integers | examples=rational numbers
4. sense_key=rational%5:00:00:intellectual:00 | definition=having its source in or being guided by the intellect (as distinguished from experience or emotion) | examples=a rational analysis

Instructions:
1. Choose the single best indexed sense for the target word in context.
2. WordNet glosses are schematic; use the context, synonyms, and examples together.
3. Do not answer with a WordNet sense key.
4. Return only a JSON object exactly like {"sense_index": 3}.

reasoning_content:
1.  **Analyze the context:**
    *   The text discusses voting behavior (ticket splitting) in US elections (Senate, Presidential, Gubernatorial, State House).
    *   It presents a counter-intuitive finding: voters split tickets in specific ways correlated with tax rates.
    *   Initially, this behavior seems "irrational".
    *   However, the author argues that econometric investigation shows a pattern: voters punish one party more when taxes are high.
    *   The conclusion sentence says: "...at least part of the seemingly irrational behavior voters display... may have an exceedingly **rational** explanation."
    *   Here, "rational" contrasts with "irrational". "Irrational" in this context implies "makes no sense" or "random/chaotic". The "rational explanation" means there is an underlying logic, reason, or cause-and-effect relationship (voters acting based on tax burdens) that explains the behavior. It implies the voters are acting based on reason or logic, or at least that there is a logical underlying reason for their actions.

2.  **Analyze the candidate senses:**

    *   **Sense 1:** `rational%3:00:00::` | Definition: "consistent with or based on or using reason" | Examples: "rational behavior", "rational inference".
        *   *Fit:* This fits very well. The text contrasts irrational (unreasonable/nonsensical) behavior with a rational (reasonable/logical) explanation. The voters' behavior is shown to be consistent with reason (punishing the party in power for taxes).

    *   **Sense 2:** `rational%5:00:00:mental:00` | Definition: "of or associated with or requiring the use of the mind" | Synonyms: intellectual, noetic.
        *   *Fit:* While voting requires the mind, the context is specifically about logic vs. chaos/absurdity in decision-making, not just the faculty of thinking. "Intellectual explanation" or "noetic explanation" doesn't fit the phrase "rational explanation" as well as "logical/reasonable explanation".

    *   **Sense 3:** `rational%3:01:00::` | Definition: "capable of being expressed as a quotient of integers" | Examples: "rational numbers".
        *   *Fit:* Mathematical context. Not applicable here.

    *   **Sense 4:** `rational%5:00:00:intellectual:00` | Definition: "having its source in or being guided by the intellect (as distinguished from experience or emotion)".
        *   *Fit:* This is close to Sense 2. It contrasts intellect with emotion. While voting might involve emotion, the phrase "rational explanation" usually refers to logical coherence (Sense 1) rather than just the source being the intellect vs emotion. The contrast here is between behavior that seems random/nonsensical (irrational) and behavior that follows a logical pattern (rational). Sense 1 is the broad, standard definition for "logical" or "based on reason".

3.  **Compare Sense 1 and Sense 4:**
    *   Sense 1 focuses on "reason" as a method or basis for logic. "Rational behavior" matches the context of voting behavior perfectly. A "rational explanation" is one that uses reason/logic.
    *   Sense 4 focuses on the distinction between intellect and emotion. The text doesn't explicitly contrast emotion vs. intellect; it contrasts seeming chaos (irrational) vs. logical pattern (rational).
    *   The phrase "rational explanation" is a strong collocation for Sense 1. It means an explanation that makes sense, is logical, and follows cause-and-effect. The findings show a correlation between tax rates and voting patterns, proving there is a reason (Sense 1) for the behavior.

4.  **Select the best index:**
    *   The text discusses "rational behavior" and a "rational explanation".
    *   Sense 1's example "rational behavior" is a near exact match for the context topic.
    *   The definition "consistent with or based on or using reason" fits the "rational explanation" phrase perfectly.

    Therefore, Sense 1 is the correct choice.

5.  **Format Output:**
    *   JSON object: `{"sense_index": 1}`