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58-446: Its 103 members are elected in 57 districts by single non-transferable vote (SNTV) to four-year terms. The assembly is responsible for enacting and amending prefectural ordinances, voting on important administrative appointments made by the governor including the vice-governors and approving the budget – Aichi has been in recent years the only prefecture besides Tokyo with a "fiscal strength index" ( zaiseiryoku shisū ) above 1, i.e. it

116-473: A utility function , describing the amount of happiness an individual i derives from each possible state. A social choice rule is a mechanism which uses the data ( u i ) i ∈ I {\displaystyle (u_{i})_{i\in I}} to select some element(s) from X {\displaystyle X} which are 'best' for society. The question of what 'best' means

174-451: A majority-strength Condorcet winner , then selecting that winner is the unique resolvable , neutral , anonymous , and non-manipulable voting rule. Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have preferences , and it follows that they can be modeled using utility functions , by

232-503: A city's seats, a thing common in First past the post elections. The number of wasted votes in an SNTV election is generally lower than in First past the post elections as well. Under SNTV, parties often do not receive representation exactly proportional to their strength, because it is difficult to accurately judge their strength when deciding how many candidates to field ( strategic nomination ) and difficult to direct party supporters as

290-517: A hundred years later than Saint-Just's proposal. In 1880s Japan adopted SNTV for provincial politicians and in 1900 for national politicians. SNTV is used for elections in Puerto Rico , Kuwait , Indonesia , Japan , Taiwan , Thailand , Libya , Iraq , Hong Kong and Vanuatu . In Puerto Rico , SNTV is known as at-large representation ("representación por acumulación" in Spanish), SNTV

348-434: A measure of aggregate utility. Utilitarian ethics call for maximizing this aggregate. In contrast many twentieth century economists, following Lionel Robbins , questioned whether such measures of utility could be measured, or even considered meaningful. Following arguments similar to those espoused by behaviorists in psychology , Robbins argued concepts of utility were unscientific and unfalsifiable . Consider for instance

406-422: A single candidate. Party A has about 35% support among the electorate (with one particularly well-liked candidate), Party B around 25% (with two well-liked candidates) and the remaining voters primarily support independent candidates, but mostly lean towards party B if they have to choose between the two parties. All voters vote sincerely ; there is no tactical voting. Percent of votes under MNTV and Limited Voting

464-442: A social choice function creates situations where we have A better than B and B better than C, but C is also better than A. This contrasts with May's theorem , which shows that simple majority is the optimal voting mechanism when there are only two outcomes, and only ordinal preferences are allowed. Harsanyi 's utilitarian theorem shows that if individuals have preferences that are well-behaved under uncertainty (i.e. coherent ),

522-581: A system of vote allocation which had been adopted by all parties for the 2004 ROC legislative elections . Single Non-transferable Voting was first proposed in solid form by Saint-Just in 1793, in a proposal to the French National Convention . He proposed having the whole country as one multi-seat district; but the idea was not adopted in France at that time. Japan was the first country to adopt SNTV for election of government members

580-490: A two-thirds majority of votes). Nine districts elect three or more assembly members. Single non-transferable vote Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Single non-transferable vote or SNTV

638-421: A variant of dot voting where each voter has only one point to assign. Unlike block voting or limited voting , where voters can cast multiple votes, under SNTV each voter casts just one. This produces a kind of semi-proportional representation at the district level, meaning small parties, as well as large parties, have a chance to be represented. Under certain assumptions, such as perfect tactical voting SNTV

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696-409: A whole to spread their votes efficiently. If they field too many, supporters' votes might be split across too many candidates. The party votes might spread their vote numbers to the point where all of a party's candidates lose to a less thinly spread opposing party. If a party fields too few candidates, they might elect all their candidates but not win seats proportional to their level of support, and

754-513: Is strategyproof (i.e. does not depend on other voters' preferences) for elections with 3 or more outcomes. The Gibbard–Satterthwaite theorem proves a stronger result for ranked-choice voting systems , showing that no such voting rule can be sincere (i.e. free of reversed preferences). The field of mechanism design , a subset of social choice theory, deals with the identification of rules that preserve while incentivizing agents to honestly reveal their preferences. One particularly important result

812-533: Is a branch of welfare economics that analyzes methods of combining individual opinions, beliefs, or preferences to reach a collective decision or create measures of social well-being . It contrasts with political science in that it is a normative field that studies how societies should make decisions, whereas political science is descriptive (observing how societies do make decisions). Social choice incorporates insights from economics , mathematics , philosophy , political science , and game theory to find

870-536: Is a common question in social choice theory. The following rules are most common: A social choice function, sometimes called a voting system in the context of politics, is a rule that takes an individual's complete and transitive preferences over a set of outcomes and returns a single chosen outcome (or a set of tied outcomes). We can think of this subset as the winners of an election, and compare different social choice functions based on which axioms or mathematical properties they fulfill. Arrow's impossibility theorem

928-725: Is able to cover its calculated expenses with its own revenues. The last elections were held in the unified local elections in April 2011 : the Liberal Democratic Party remained strongest party with 49 seats but fell short of a majority without independents, former Democrat and Nagoya City mayor Takashi Kawamura 's Genzei Nippon ("Tax cuts Japan") and former Liberal Democrat and Aichi governor Hideaki Ōmura 's Nippon-ichi Aichi no Kai ("Aichi First in Japan Association") together won 18 seats. The Democratic Party

986-429: Is an electoral system used to elect multiple winners. It is a semi-proportional variant of first-past-the-post voting , applied to multi-member districts where each voter casts just one vote. It can also be seen as a variant of STV but with no vote transfers. SNTV generally makes it unlikely that a single party will take all seats in a city, as generally happens with winner-take-all systems . SNTV can be considered

1044-598: Is beyond positive science ; that is, one cannot measure changes in the utility of someone else, nor is it required by positive theory. Apologists for the interpersonal comparison of utility have argued that Robbins claimed too much. John Harsanyi agreed that perfect comparisons of mental states are not practically possible, but people can still make some comparisons thanks to their similar backgrounds, cultural experiences, and psychologies. Amartya Sen argues that even if interpersonal comparisons of utility are imperfect, we can still say that (despite being positive for Nero )

1102-755: Is common even after STV vote transfers to elect the same as would be elected under SNTV. But not having transfers, SNTV sees more votes wasted than under STV due to votes being placed on un-electable candidate or due to surpluses received by successful candidate over and above the quota used in STV elections that are not able to be transferred under SNTV. SNTV produces representation that is most proportional ( proportional representation ) when political parties have accurate information about their relative levels of electoral support, and nominate candidates in accordance with their respective levels of electoral support or when all parties suffer from poor information of that sort. Knowing

1160-510: Is elected does not mean that another specific candidate will not be. They both can be elected. Because running on issues may lead to a situation in which a candidate becomes too popular and therefore draws votes away from other allied candidates, SNTV may encourage legislators to join factions that consist of patron-client relationships in which a powerful legislator can apportion votes to his or her supporters. In addition, parties will do best if their supporters evenly distribute their votes among

1218-433: Is equivalent to proportional representation by the D'Hondt method . SNTV retains many of the problems of first-past-the-post voting (first-preference plurality voting), and as a result is sometimes viewed skeptically by social choice theorists . However, its extreme simplicity and easy vote-counting makes the system particularly popular for small elections to offices such as city councils , particularly when compared to

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1276-497: Is more chance in SNTV than a more orderly system of PR, such as list PR or STV.) If either party had risked trying to win all three seats, causing more vote splitting among supporters of Parties Y and Z, then A of Party X might have won a seat and either party Y or Z would then have taken one fewer seat. For example, 10,000 voters vote to elect three members. Cumulative voting is not used so each voter may not cast more than one vote for

1334-661: Is often recognized as inaugurating the modern era of social choice theory. Later work has also considered approaches to legal compensation , fair division , variable populations , partial strategy-proofing of social-choice mechanisms , natural resources , capabilities and functionings approaches , and measures of welfare . Arrow's impossibility theorem is a key result showing that social choice functions based only on ordinal comparisons , rather than cardinal utility , will behave incoherently (unless they are dictatorial ). Such systems violate independence of irrelevant alternatives , i.e. they suffer from spoiler effects

1392-497: Is the revelation principle , which is almost a reversal of Gibbard's theorem: for any given social choice function, there exists a mechanism that obtains the same results but incentivizes participants to be completely honest. Because mechanism design places stronger assumptions on the behavior of voters or , it is sometimes possible to design mechanisms for social choice that accomplish "impossible" tasks. For example, by allowing agents to compensate each other for losses with transfers,

1450-424: Is the percent of voters who voted for the candidate, not the percent of votes cast. SNTV facilitates minority representation, that is, it produces mixed representation of large and small parties where no party takes all the seats. In fact, SNTV would elect the same people as are elected in STV contests where the vote transfers do not move an initially-lower-placing candidate over an initially-higher-placing one. It

1508-517: Is used to elect the 11 at-large members in each of the House of Representatives and the Senate. Under at-large representation , political parties vary the ballot order of their candidates across electoral divisions, in order to ensure each candidate has a roughly equal chance of success. Since most voters choose the candidates placed at the top of their party lists on their ballots, at-large candidates from

1566-410: Is what often comes to mind when one thinks about impossibility theorems in voting. There are several famous theorems concerning social choice functions. The Gibbard–Satterthwaite theorem implies that the only rule satisfying non-imposition (every alternative can be chosen) and strategyproofness when there are more than two candidates is the dictatorship mechanism . That is, a voter may be able to cast

1624-471: The Great Fire of Rome had a negative overall value. Harsanyi and Sen thus argue that at least partial comparability of utility is possible, and social choice theory should proceed under that assumption. Despite the similar names, "public choice" and "social choice" are two distinct fields that are only weakly related. Public choice deals with the modeling of political systems as they actually exist in

1682-656: The VNM theorem . But much of the research in the field assumes that those utility functions are internal to humans, lack a meaningful unit of measure and cannot be compared across different individuals. Whether this type of interpersonal utility comparison is possible or not significantly alters the available mathematical structures for social welfare functions and social choice theory. In one perspective, following Jeremy Bentham , utilitarians have argued that preferences and utility functions of individuals are interpersonally comparable and may therefore be added together to arrive at

1740-544: The Vickrey–Clarke–Groves (VCG) mechanism can achieve the "impossible" according to Gibbard's theorem: the mechanism ensures honest behavior from participants, while still achieving a Pareto efficient outcome. As a result, the VCG mechanism can be considered a "better" way to make decisions than voting (though only so long as monetary transfers are possible). If the domain of preferences is restricted to those that include

1798-401: The law of diminishing marginal utility , according to which utility of an added quantity of a good decreases with the amount of the good that is already in possession of the individual. It has been used to defend transfers of wealth from the "rich" to the "poor" on the premise that the former do not derive as much utility as the latter from an extra unit of income. Robbins argued that this notion

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1856-419: The best ways to combine individual preferences into a coherent whole, called a social welfare function . Because of its strong connections to political philosophy and voting , social choice is sometimes also called voting theory . Real-world examples include enacting laws under a constitution or voting , where individual preferences over candidates are collected to elect a person that best represents

1914-401: The frequency of such paradoxes depends heavily on the number of options and other factors. Let X {\displaystyle X} be a set of possible 'states of the world' or 'alternatives'. Society wishes to choose a single state from X {\displaystyle X} . For example, in a single-winner election , X {\displaystyle X} may represent

1972-506: The frequency of various voting paradoxes, such as the Condorcet paradox . A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox for a total likelihood of 9.4%. While examples of the paradox seem to occur often in small settings like parliaments, very few examples have been found in larger groups (electorates), although some have been identified. However,

2030-452: The group's preferences. The field is closely related to mechanism design , which can be thought of as modelling social choice with self-interested and potentially dishonest citizens; it thus involves the application of game theory . Social choice differs from decision theory in that the latter is concerned with how individuals , rather than societies , can make rational decisions. The earliest work on social choice theory comes from

2088-445: The information offered in campaigns (polls, reporting, fundraising totals, endorsements, etc.), to rationally decide who the most viable candidates are and then vote for them. SNTV can result in complicated intra-party dynamics because in a SNTV system, a candidate runs against candidates from their own party as well as against candidates from the other party. SNTV elections are not zero-sum contests. Just because one particular candidate

2146-399: The largest numbers of votes would win office. SNTV, like single transferable vote , can be used with non-partisan ballots, in election contests where there are no parties. Three seats are to be filled among five candidates: A, B, C, D and E fielded by 3 parties X, Y and Z. E, D and C are the winning candidates. Thus, Party Z gets two seats and Party Y gets one seat. No one party took all

2204-806: The legislatures of Japan , South Korea and the Republic of China ( Taiwan ), but its use has been discontinued for the most part. It is still used in Japan for some seats in the House of Councillors (Sangi-in), prefectural assemblies and municipal assemblies. Social choice theorist Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Social choice theory

2262-401: The more-intricate single transferable vote (STV) system, and has resulted in the method becoming commonly used for ordering open party lists . In any election, each voter casts one vote for one candidate in a multi-candidate race for multiple offices. Posts are filled by the candidates with the most votes ( plurality voting ). Thus, in a three-seat constituency, the three candidates receiving

2320-403: The much smaller Puerto Rican Independence Party runs a single-candidate slate for the at-large members in the Senate and the House of Representatives. The SNTV-elected members are a small part of the chambers compared to the members elected in the sixteen Senate districts, elected by block voting, and the forty House districts, elected by first-past-the-post voting . SNTV was once used to elect

2378-466: The only coherent and Pareto efficient social choice function is the utilitarian rule . This lends some support to the viewpoint expressed of John Stuart Mill , who identified democracy with the ideal of maximizing the common good (or utility ) of society as a whole, under an equal consideration of interests . Gibbard's theorem provides limitations on the ability of any voting rule to elicit honest preferences from voters, showing that no voting rule

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2436-409: The party was not as popular as they thought. If every party does that, all suffer the same inefficiency and the final result is proportional. If one party is more prudent, it may do better than the others. Because votes cannot be transferred, there is more chance of vote wastage than under STV. But in elections that use SNTV, representation is usually mixed. It is rare for one party to make a sweep of

2494-657: The party's candidates. Historically, in Taiwan , the Kuomintang did this by sending members a letter telling them which candidate to vote for. With the Democratic Progressive Party , vote sharing is done informally, as members of a family or small group will coordinate their votes. The New Party had a surprisingly effective system by asking party supporters to vote for the candidate whose identification number corresponded to their birthdate. This led to

2552-715: The portion of the votes a party can take allows it to avoid vote waste due to lessening the chance of vote splitting and inefficient placement of party support. Under 'perfect' tactical voting and strategic nomination, SNTV would be equivalent to the D'Hondt (Jefferson) method of proportional representation. But under SNTV even inefficient distribution of votes allows more balanced representation than would be elected under either single-member plurality or block voting . Given n {\displaystyle n} candidates to be elected, Candidate A can guarantee success by receiving one more than 1 n + 1 {\displaystyle {\frac {1}{n+1}}} of

2610-889: The real world, and is primarily limited to positive economics (predicting how politicians and other stakeholders will act). It is therefore often thought of as the application of microeconomic models to political science , in order to predict the behavior of political actors . By contrast, social choice has a much more normative bent, and deals with the abstract study of decision procedures and their properties. The Journal of Economic Literature classification codes place Social Choice under Microeconomics at JEL D71 (with Clubs, Committees, and Associations) whereas Public Choice falls under JEL D72 (Economic Models of Political Processes: Rent-Seeking , Elections, Legislatures, and Voting Behavior). Since Arrow, social choice theory has been characterized by being predominantly mathematical and theoretical , but some research has aimed at estimating

2668-561: The same party usually obtain approximately equal vote totals. When the party's candidates are equally supported, the most-popular party is often able to take six seats of the 11. The two major Puerto Rican political parties, the Popular Democratic Party and the New Progressive Party , usually each run six candidates for the 11 at-large members in each of the House of Representatives and the Senate, while

2726-550: The seats as might have been the result under first past the post or plurality block voting . But counting the votes by party gives these vote tallies: Party Y has more votes than Party Z, but receives fewer seats because of an inefficient spread of votes across the candidates. If Party Y's two candidates had had more equal vote tallies, it would have won two seats and Party Z only one. Or if Party Z's candidates had received less equal vote tallies, Party Y would have won two seats even if its candidates were not equally popular. (There

2784-513: The set of candidates; in a resource allocation setting, X {\displaystyle X} may represent all possible allocations. Let I {\displaystyle I} be a finite set, representing a collection of individuals. For each i ∈ I {\displaystyle i\in I} , let u i : X ⟶ R {\displaystyle u_{i}:X\longrightarrow \mathbb {R} } be

2842-505: The side of too many candidates, hoping to gain as many seats as possible, perhaps even winning more than its proportion of the electorate if they can edge out candidates from larger parties with just a few votes. As well, a small party running just one candidate would not suffer from vote spitting, while a larger party running four or more may suffer from that. SNTV electoral systems, like STV and proportional electoral systems generally, typically produce more proportional electoral outcomes as

2900-442: The single non-transferable vote becomes equivalent to first-past-the-post voting and a plurality of votes suffices to win 100% of seats. 20 districts are two-member districts where usually – depending on nomination strategy and local strength of third parties – an even seat split between the major two parties is likely (in the absence of third parties and assuming realistic nomination strategies, winning both seats would require at least

2958-589: The size of the electoral districts (number of seats in each constituency) increases. The potential for tactical voting in a single non-transferable vote system is large. Casting only one vote, a rational voter wanting to maximize the number of seats captured by his party should vote for a candidate of the party that has a chance of winning, but one that will not win by too great a margin and thus take votes away from party colleagues. This creates opportunities for tactical nominations, with parties nominating candidates similar to their opponents' candidates in order to split

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3016-437: The system can behave erratically in response to changes in the quality or popularity of one of the options. Condorcet's example demonstrates that democracy cannot be thought of as being the same as simple majority rule or majoritarianism; otherwise, it will be self-contradictory when three or more options are available. Majority rule can create cycles that violate the transitive property : Attempting to use majority rule as

3074-635: The vote tallies of others, not with a theoretical threshold or quota. In the 2020 Vanuatuan general election , using SNTV, as few as 5 percent of the vote was enough to be elected in a seven-seat district, where about 13 percent is Droop quota. Vote splitting due to poor information on voters' behaviour may deny a popular party its due share of representation. (Single Transferable Voting does not suffer from this handicap as votes are transferable and many are transferred and used that are wasted under SNTV.) Parties organizing slates of multiple candidates may nominate many candidates and then learn on election night that

3132-488: The vote. Like all multiple-winner selections, parties find it advantageous to run a range of candidates in SNTV elections. SNTV has been measured through the lens of such concepts as decision-theoretic analysis . Professor Gary W. Cox , an expert on SNTV, has studied this system's use in Japan. Cox has an explanation of real-world data finding the, "two systems [plurality and semi-proportional] are alike in their strategic voting equilibria." His research found that voters use

3190-511: The votes (the Droop quota ), because n {\displaystyle n} +1 other candidates cannot each receive more than Candidate A (too many would not pass Droop quota) But as SNTV is a plurality system and votes are wasted (not used to elect anyone), it is possible to win with less than Droop quota (but never possible to lose if you have at least Droop). To determine the successful candidates, candidates' vote tallies are compared with

3248-513: The winning candidates would have more support than necessary and thus wasting votes. The risks of poor strategic nomination are not equal for parties of various strengths. A large party would have much more to lose from the split vote effect than to gain from avoiding the wasted vote effect, and so would likely decide to err on the side of fielding fewer candidates (but probably not less than their existing number of seats). A small party with little representation would be more risk-tolerant and err on

3306-588: The writings of the Marquis de Condorcet , who formulated several key results including his jury theorem and his example showing the impossibility of majority rule . His work was prefigured by Ramon Llull 's 1299 manuscript Ars Electionis ( The Art of Elections ), which discussed many of the same concepts, but was lost in the Late Middle Ages and only rediscovered in the early 21st century. Kenneth Arrow 's book Social Choice and Individual Values

3364-535: Was reduced to 26 seats – down from 38 in 2007 – in one of its few (relative) strongholds in local politics. Kōmeitō won six seats, four seats went to independents. The Japanese Communist Party has not been represented in the assembly since 2003. As of March 2014, the assembly is composed as follows: As in all prefectures, most electoral districts correspond to wards of "major cities designated by government ordinance" (Nagoya City), ordinary cities and former counties . 28 districts are single-member districts where

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