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997:. Often times the term spoiler will be applied to candidates or situations which do not meet the full definition, typically in real-world scenarios where the introduction of a new candidate can cause voters to change their opinions, either through their campaign or merely by existing. If a voting system is not affected by spoilers under this definition, it satisfies the
2347:
1353:, because each candidate's total in a paired comparison does not involve any other candidates. Instead, methods can separately compare every pair of candidates and check who would win in a one-on-one election. This pairwise comparison means that spoilers can only occur in the rare situation known as a
2232:
IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. ... Approval voting thus appears to solve the problem of vote splitting simply and
1360:
For each pair of candidates, there is a count for how many voters prefer the first candidate (in the pair) to the second candidate, and how many voters have the opposite preference. The resulting table of pairwise counts eliminates the step-by-step redistribution of votes, which causes vote splitting
1213:
still suffer from vote-splitting in each round though they reduce the effect. As a result, they do not eliminate the spoiler effect. The elimination of weak spoilers in earlier rounds somewhat reduces their effects on the results compared to single-round plurality voting, but spoiled elections remain
1510:
Independence of clones is the most commonly-fulfilled spoiler-resistance criterion, and says that "cloning" a candidate—adding a new candidate identical to an existing one—should not affect the results. Two candidates are considered identical if they are ranked side-by-side on every ballot; in other
2739:
to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential
Election in Florida did not use ranked ballots, it is plausible (see Magee 2003) that Al Gore (A) would have won without Ralph Nader (B) in the election, and Gore would have beaten Nader
2190:
to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential
Election in Florida did not use ranked ballots, it is plausible (see Magee 2003) that Al Gore (A) would have won without Ralph Nader (B) in the election, and Gore would have beaten Nader
1480:
can be interpreted as a kind of spoiler-resistance. In general, Condorcet methods are highly resistant to spoiler effects. Intuitively, this is because the only way to dislodge a beats-all champion is by beating them, so spoilers can only exist when there is no beats-all champion (which is rare).
1259:. If primary elections or party nominations are not used to identify a single candidate from each party, the party that has more candidates is more likely to lose because of vote splitting among the candidates from the same party. In a two-party system, party primaries effectively turn
2403:
plurality-rule voting is seriously vulnerable to vote-splitting ... runoff voting ... as French history shows, it too is highly subject to vote-splitting. ... majority rule avoids such vote-splitting debacles because it allows voters to rank the candidates and candidates are compared
1285:
similar candidates causes their vote total to be split between them, placing these candidates at a disadvantage. This is most visible in elections where a minor candidate draws votes away from a major candidate with similar politics, thereby causing a strong opponent of both to win.
1108:
have argued that voting methods should be spoiler-independent. While the concept in-and-of-itself is not controversial, strict mathematical satisfaction can be in direct conflict with other properties that are also considered valuable. The mathematician and political economist
1392:
Several weaker forms of independence of irrelevant alternatives (IIA) have been proposed as a way to compare ranked voting methods. Usually these procedures try to insulate the process from weak spoilers, ensuring that only a handful of candidates can change the outcome.
988:
or refers to a situation where a losing candidate affects the results of an election simply by participating, assuming voter opinions don't change. If a major candidate is perceived to have lost an election because of a minor candidate, the minor candidate is called a
1664:, say that Rock wins the election with a certain method. Then, Scissors is a spoiler candidate for Paper: if Scissors were to drop out, Paper would win the only one-on-one race (Paper defeats Rock). The same reasoning applies regardless of the winner.
1878:
Strategic voting can sometimes create the appearance of a spoiler for any method (including rated methods). However, this does not greatly affect the general ordering described here, except by making cardinal and
Condorcet methods closer to
1373:, which elects the candidate with the highest total number of points. Because voters rate candidates independently, changing one candidate's score does not affect those of other candidates, which is what allows rated methods to evade
1487:
is another kind of spoiler-resistance for
Condorcet methods. This criterion says that a candidate should not affect the results of an election, unless they have a "reasonable claim" to the title of Condorcet winner (fall in the
1129:, which lets any party "clone their way to victory" by running a large number of candidates. This famously forced de Borda to concede that "my system is meant only for honest men," and eventually led to its abandonment by the
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There is a
Condorcet ranking according to distance from the center, but Condorcet winner M, the most central candidate, was squeezed between the two others, got the smallest primary support, and was eliminated.
1096:
A man is deciding whether to order apple or blueberry pie before settling on apple. The waitress informs him that cherry pie is also an option, to which the man replies "in that case, I'll have the blueberry."
1334:
1522:
This criterion is very weak, as adding a substantially similar (but not quite identical) candidate to a race can still substantially affect the results, causing vote splitting. For example, the
1426:
Despite being a very weak form of spoiler-resistance (requiring that only the last-place finisher is unable to affect the outcome), LIIA is satisfied by only a few voting methods. These include
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have the opposite problem: because running many similar candidates at once can make it difficult for any one of them to win the election, these systems tend to concentrate power in the hands of
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IRV is excellent for preventing classic spoilers-minor candidates who tip the election from one major candidate to another. It is not so good when the 'spoiler' has a real chance of winning
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in response to candidates can create pseudo-spoiler effects (which can be distinguished from true spoilers in that they are caused by voter behavior, rather than the voting system itself).
1052:
of party-list representation. Here, a new party entering an election can cause seats to shift from one unrelated party to another, even if the new party wins no seats; this is known as the
1369:
Rated voting methods ask voters to assign each candidate a score on a scale (usually from 0 to 10), instead of listing them from first to last. The best-known of these methods is
2553:
Those votes that are cast for minor party candidates are perceived as taking away pivotal votes from major party candidates. ... This phenomenon is known as the 'spoiler effect'.
963:
2613:
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does
2065:
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does
1618:
The social choice has changed the ranking of and . The changes in the social choice ranking are dependent on irrelevant changes in the preference profile. In particular,
1229:, Condorcet methods are completely invulnerable to spoilers; in practice, somewhere between 90% and 99% of real-world elections have a Condorcet winner. Some systems like
1170:
In some situations, a spoiler can extract concessions from other candidates by threatening to remain in the race unless they are bought off, typically with a promise of a
2377:
1415:
For every electoral method, it is possible to construct an order-of-finish that ranks candidates in terms of strength. This can be done by first finding the winner,
2007:"How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections"
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a spoiler effect occurs when entry by a third-party candidate causes party A to defeat party B even though Party B would have won in a two-candidate race.
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are not subject to Arrow's theorem, and many such systems are spoilerproof, so long as the defining assumption about voter opinions remains valid.
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A single example is enough to show that every
Condorcet method must fail independence of irrelevant alternatives. Say that 3 candidates are in a
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28:
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Now, the voter who ranks instead ranks ; and the voter who ranks instead ranks . They change their preferences only over the pairs , and .
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are vulnerable to the spoiler effect. However, the frequency and severity of spoiler effects depends substantially on the voting method.
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means that several similar (but not identical) candidates competing in the same race will tend to hurt each others' chances of winning.
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A spoiler effect occurs when a single party or a candidate entering an election changes the outcome to favor a different candidate.
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1419:. This process is repeated to find which candidates rank 3rd, 4th, etc. As a result, LIIA can also be thought of as indicating
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As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
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1152:. The parties signal to the voters a single candidate that they should focus their support on. In many cases, this leads
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Ranked Choice Voting And the Center
Squeeze in the Alaska 2022 Special Election: How Might Other Voting Methods Compare?
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have even stronger spoilerproofing guarantees that are applicable to most situations without a
Condorcet winner.
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1255:. The purpose of primary elections is to eliminate vote splitting among candidates in the same party before the
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Voting systems that violate independence of irrelevant alternatives are susceptible to being manipulated by
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2423:"Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*"
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2083:"Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*"
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have different levels of vulnerability to spoilers. As a rule of thumb, spoilers are extremely common with
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If the option that finished in last place is deleted from all the votes, the winner should not change.
2731:. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner
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2182:. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner
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If the option that finished in first place is deleted from all the votes, the runner-up should win.
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1333:(despite the election results showing Montroll would have won a one-on-one election with Kiss). In
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effects completely, because every one-on-one matchup is evaluated independently. If there is a
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happen if there is no
Condorcet winner. Condorcet cycles are rare in large elections, and the
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This property, of stability for
Condorcet winners, is a major advantage of Condorcet methods.
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words, if there is no other candidate ranked in between them. The criterion is satisfied by
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34:"Independence of spoilers" redirects here. For the logical property in decision theory, see
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You likely have opinions about all those candidates. And yet, you only get a say about one.
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This example also shows why Condorcet elections are rarely (if ever) spoiled: spoilers can
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methods, though slightly less often than in plurality. As a result, instant-runoff voting
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1404:(LIIA) is a weaker kind of independence that requires both of the following conditions:
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1492:). Smith candidates are ones who can defeat every other candidate either directly or
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1125:. Some systems are particularly infamous for their ease of manipulation, such as the
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head-to-head. Thus, Gore should still have won with Nader included in the election."
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head-to-head. Thus, Gore should still have won with Nader included in the election."
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1423:, i.e. the alternative who would not win unless every other candidate dropped out.
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are only rarely affected by spoilers, which are limited to rare situations called
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do away with the spoiler problem entirely, although it ... makes it less likely
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do away with the spoiler problem entirely, although it ... makes it less likely
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elegantly. ... Range voting solves the problems of spoilers and vote splitting
2210:
Gaming the vote : why elections aren't fair (and what we can do about it)
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1973:
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While true spoilers are not possible under score voting, voters who behave
2538:
Why Don't Americans Vote? Causes and Consequences: Causes and Consequences
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Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It)
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Hiring and Firing Public Officials: Rethinking the Purpose of Elections
2006:
1982:
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1660:. In a one-on-one race, Rock loses to Paper, Paper to Scissors, etc.
2022:
2720:
2691:
2171:
1337:, Nick Begich was defeated in the first round by spoiler candidate
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is less so, with both typically exhibiting this phenomenon through
2709:
2160:
1675:
shows cycles are impossible whenever candidates are arrayed on a
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is the most common cause of spoiler effects in the commonly-used
2598:
Mathematics of Social Choice: Voting, Compensation, and Division
2050:
Mathematics of Social Choice: Voting, Compensation, and Division
2005:
McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002).
1329:
Andy Montroll in the second round, leading to the election of
1251:. In the United States vote splitting most commonly occurs in
1519:(including cardinal systems), and most tournament solutions.
2203:
2201:
2199:
2197:
1476:
Besides its interpretation in terms of majoritarianism, the
68:
29:
Elimination from postseason contention § Spoiler effect
1626:, even though no voter changed their preference over .
993:
candidate and the major candidate is said to have been
2346:
McLean, Iain; Urken, Arnold B.; Hewitt, Fiona (1995).
2279:"Independence of irrelevant alternatives before Arrow"
1417:
then repeatedly deleting them and finding a new winner
2212:. Farrar, Straus and Giroux. pp. 168, 197, 234.
1899:
Heckelman, Jac C.; Miller, Nicholas R. (2015-12-18).
2750:
Young, Peyton (1995-02-01). "Optimal Voting Rules".
2467:"On the empirical relevance of Condorcet's paradox"
2122:"On the empirical relevance of Condorcet's paradox"
1113:studied the the spoiler effect as early as 1780s.
1958:"Reflections on Arrow's theorem and voting rules"
1496:(e.g. if A can defeat B, who in turn defeats C).
2708:Holliday, Wesley H.; Pacuit, Eric (2023-02-11),
2535:King, Bridgett A.; Hale, Kathleen (2016-07-11).
2159:Holliday, Wesley H.; Pacuit, Eric (2023-02-11),
1550:3 voters rank . 1 voter ranks . 1 voter ranks .
1281:systems. In these systems, the presence of many
1239:methods can be fully immune to spoiler effects.
1163:, where the top-two candidates are nominated by
1402:Local independence from irrelevant alternatives
1302:at a substantially higher rate than for modern
1084:, should not depend on an unrealized outcome,
1040:Spoiler effects also occur in some methods of
1397:Local independence of irrelevant alternatives
1100:Amongst a long list of sometimes-conflicting
1076:, that says the choice between two outcomes,
957:
8:
1836:Independence of Smith-dominated alternatives
1468:Independence of Smith-dominated alternatives
2703:
2701:
2371:
2369:
1846:List of elections involving vote splitting
964:
950:
40:
2719:
2690:
2376:Sen, Amartya; Maskin, Eric (2017-06-08).
2322:. Springer Science & Business Media.
2170:
1981:
1421:independence from the weakest alternative
1319:Burlington, Vermont's second IRV election
1349:Spoiler effects rarely occur when using
1891:
1871:
1841:Independence of irrelevant alternatives
1517:independence of irrelevant alternatives
1070:independence of irrelevant alternatives
1000:independence of irrelevant alternatives
56:
36:Independence of irrelevant alternatives
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2458:
2456:
2416:
2414:
2412:
2341:
2339:
2319:The Theory of Committees and Elections
2245:
2243:
2241:
1705:with 7 voters ranking 3 alternatives (
1214:common, moreso than in other systems.
1017:is highly sensitive to spoilers while
2530:
2528:
2011:American Journal of Political Science
1247:Vote splitting most easily occurs in
7:
1951:
1949:
1902:Handbook of Social Choice and Voting
1802:are reversed by the introduction of
2505:"Top 5 Ways Plurality Voting Fails"
2421:Gehrlein, William V. (2002-03-01).
2378:"A Better Way to Choose Presidents"
2081:Gehrlein, William V. (2002-03-01).
27:For the same effect in sports, see
2681:Clelland, Jeanne N. (2023-02-28),
2629:Poundstone, William (2009-02-17).
1956:Miller, Nicholas R. (2019-04-01).
1312:still tends towards two-party rule
1205:Plurality-runoff methods like the
25:
2595:Borgers, Christoph (2010-01-01).
2465:Van Deemen, Adrian (2014-03-01).
2120:Van Deemen, Adrian (2014-03-01).
2047:Borgers, Christoph (2010-01-01).
1547:, 5 voters rank 5 alternatives .
2752:Journal of Economic Perspectives
2659:Stensholt, Eivind (2015-10-07).
2571:. Oxford University Press, USA.
2352:. University of Michigan Press.
1506:Independence of clones criterion
1335:Alaska's first-ever IRV election
933:
920:
908:
856:McKelvey–Schofield chaos theorem
502:Semi-proportional representation
134:First preference plurality (FPP)
2509:The Center for Election Science
2256:The Center for Election Science
1934:The Center for Election Science
1816:Comparison of electoral systems
1806:, an "irrelevant" alternative.
1767:In an election, initially only
1462:Condorcet independence criteria
1172:high-ranking political position
2661:"What Happened in Burlington?"
2565:Buchler, Justin (2011-04-20).
1072:is a fundamental principle of
894:Harsanyi's utilitarian theorem
851:Moulin's impossibility theorem
816:Conflicting majorities paradox
1:
2635:. Farrar, Straus and Giroux.
2208:Poundstone, William. (2013).
1345:Tournament (Condorcet) voting
1007:Arrow's impossibility theorem
720:Frustrated majorities paradox
2295:10.1016/0165-4896(95)00784-J
2283:Mathematical Social Sciences
1136:Vote-splitting systems like
889:Condorcet dominance theorems
829:Social and collective choice
2277:McLean, Iain (1995-10-01).
1905:. Edward Elgar Publishing.
1515:, all systems that satisfy
1513:ranked-choice runoff voting
1294:Spoilers also occur in the
1196:paired counting (Condorcet)
1117:Manipulation by politicians
1092:illustrates this principle:
1042:proportional representation
555:By mechanism of combination
326:Proportional representation
2808:
2735:by adding a new candidate
2186:by adding a new candidate
1794:The relative positions of
1686:
1662:Without loss of generality
1633:
1503:
1472:Condorcet winner criterion
1465:
1131:French Academy of Sciences
753:Multiple districts paradox
484:Fractional approval voting
472:Interactive representation
33:
26:
2483:10.1007/s11127-013-0133-3
2349:Classics of Social Choice
2138:10.1007/s11127-013-0133-3
1974:10.1007/s11127-018-0524-6
1156:systems to behave like a
1050:largest remainders method
1011:rank-based voting systems
700:Paradoxes and pathologies
549:Mixed-member proportional
544:Mixed-member majoritarian
539:By results of combination
430:Approval-based committees
2385:New York Review of Books
1192:plurality-runoff methods
1046:single transferable vote
879:Condorcet's jury theorem
680:Double simultaneous vote
655:Rural–urban proportional
650:Dual-member proportional
612:
601:
568:Parallel (superposition)
460:Fractional social choice
447:Expanding approvals rule
276:
261:
246:
177:
166:
142:
2439:10.1023/A:1015551010381
2316:Black, Duncan (1987) .
2099:10.1023/A:1015551010381
1703:plurality voting system
1689:Plurality voting system
1526:pathology that affects
1106:social choice theorists
806:Tyranny of the majority
583:Fusion (majority bonus)
400:Quota-remainder methods
1831:Independence of clones
1783:s 3, but the entry of
1693:Plurality voting is a
1500:Independence of clones
1198:, and impossible with
1098:
1009:demonstrates that all
940:Mathematics portal
846:Majority impossibility
835:Impossibility theorems
631:Negative vote transfer
452:Method of equal shares
73:
1856:Single-issue politics
1779:wins with 4 votes to
1591:The new Borda count:
1440:instant-runoff voting
1300:instant-runoff voting
1211:instant-runoff voting
1142:instant-runoff voting
1104:, activists and some
1094:
1027:Majority-rule methods
743:Best-is-worst paradox
732:Pathological response
467:Direct representation
120:Single-winner methods
72:
2251:"The Spoiler Effect"
1930:"The Spoiler Effect"
1861:Strategic nomination
1787:into the race makes
1699:ranked-choice voting
1673:median voter theorem
1622:now wins instead of
1351:tournament solutions
1123:strategic nomination
1111:Marquis de Condorcet
1035:Rated voting systems
978:social choice theory
927:Economics portal
874:Median voter theorem
93:Comparative politics
2427:Theory and Decision
2087:Theory and Decision
1826:Electoral threshold
1677:left-right spectrum
1478:Condorcet criterion
1178:By electoral system
1090:Sidney Morgenbesser
1088:. A famous joke by
1025:or vote splitting.
915:Politics portal
626:Vote linkage system
597:Seat linkage system
184:Ranked-choice (RCV)
2764:10.1257/jep.9.1.51
1534:Examples by system
1485:Smith-independence
1361:in other methods.
1150:political machines
1054:new states paradox
811:Discursive dilemma
770:Lesser evil voting
645:Supermixed systems
348:Largest remainders
206:Round-robin voting
74:
2665:Discussion Papers
1636:Condorcet paradox
1630:Condorcet methods
1456:majority judgment
1304:pairwise-counting
1253:primary elections
1219:tournament voting
1184:electoral systems
974:
973:
861:Gibbard's theorem
801:Dominance paradox
738:Perverse response
442:Phragmen's method
308:Majority judgment
236:Positional voting
194:Condorcet methods
62:electoral systems
18:Spoiler candidate
16:(Redirected from
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2562:
2556:
2555:
2532:
2523:
2522:
2517:
2516:
2501:
2495:
2494:
2462:
2451:
2450:
2418:
2407:
2406:
2400:
2399:
2382:
2373:
2364:
2363:
2343:
2334:
2333:
2313:
2307:
2306:
2274:
2268:
2267:
2265:
2264:
2247:
2236:
2235:
2205:
2192:
2181:
2180:
2179:
2174:
2156:
2150:
2149:
2117:
2111:
2110:
2078:
2072:
2071:
2044:
2038:
2037:
2002:
1996:
1995:
1985:
1953:
1944:
1943:
1941:
1940:
1926:
1920:
1919:
1896:
1880:
1876:
1821:Electoral fusion
1791:the new winner.
1296:two-round system
1279:two-round runoff
1265:two-round system
1261:plurality voting
1257:general election
1249:plurality voting
1243:Plurality voting
1227:Condorcet winner
1207:two-round system
1188:plurality voting
1161:two-round system
1154:plurality voting
966:
959:
952:
938:
937:
925:
924:
913:
912:
868:Positive results
763:Strategic voting
660:Majority jackpot
617:
606:
477:Liquid democracy
353:National remnant
343:Highest averages
280:
265:
250:
182:
173:Alternative vote
171:
155:Partisan primary
147:
88:Mechanism design
41:
21:
2807:
2806:
2802:
2801:
2800:
2798:
2797:
2796:
2782:
2781:
2780:
2779:
2749:
2748:
2744:
2726:
2724:
2707:
2706:
2699:
2680:
2679:
2675:
2658:
2657:
2653:
2643:
2628:
2627:
2623:
2609:
2594:
2593:
2589:
2579:
2564:
2563:
2559:
2549:
2534:
2533:
2526:
2514:
2512:
2503:
2502:
2498:
2464:
2463:
2454:
2420:
2419:
2410:
2397:
2395:
2380:
2375:
2374:
2367:
2360:
2345:
2344:
2337:
2330:
2315:
2314:
2310:
2276:
2275:
2271:
2262:
2260:
2249:
2248:
2239:
2220:
2207:
2206:
2195:
2177:
2175:
2158:
2157:
2153:
2119:
2118:
2114:
2080:
2079:
2075:
2061:
2046:
2045:
2041:
2023:10.2307/3088418
2004:
2003:
1999:
1955:
1954:
1947:
1938:
1936:
1928:
1927:
1923:
1913:
1898:
1897:
1893:
1888:
1883:
1877:
1873:
1869:
1812:
1751:2 voters rank (
1736:2 voters rank (
1721:3 voters rank (
1691:
1685:
1642:Condorcet cycle
1638:
1632:
1541:
1536:
1508:
1502:
1474:
1466:Main articles:
1464:
1448:approval voting
1399:
1390:
1375:Arrow's theorem
1367:
1355:Condorcet cycle
1347:
1292:
1245:
1237:Cardinal voting
1180:
1165:party primaries
1119:
1102:voting criteria
1066:decision theory
1062:
970:
932:
931:
919:
907:
899:
898:
865:
841:Arrow's theorem
831:
821:
820:
789:
759:
748:No-show paradox
729:
715:Cloning paradox
705:Spoiler effects
702:
692:
691:
666:
553:
536:
526:
525:
498:
489:Maximal lottery
456:
437:Thiele's method
426:
396:
328:
318:
317:
303:Approval voting
291:Cardinal voting
287:
232:
226:Maximal lottery
190:
122:
112:
39:
32:
23:
22:
15:
12:
11:
5:
2805:
2803:
2795:
2794:
2784:
2783:
2778:
2777:
2742:
2697:
2673:
2651:
2641:
2621:
2607:
2587:
2577:
2557:
2547:
2524:
2496:
2477:(3): 311–330.
2452:
2433:(2): 171–199.
2408:
2365:
2359:978-0472104505
2358:
2335:
2328:
2308:
2289:(2): 107–126.
2269:
2237:
2218:
2193:
2151:
2132:(3): 311–330.
2112:
2093:(2): 171–199.
2073:
2059:
2039:
2017:(1): 134–147.
1997:
1968:(1): 113–124.
1945:
1921:
1911:
1890:
1889:
1887:
1884:
1882:
1881:
1870:
1868:
1865:
1864:
1863:
1858:
1853:
1848:
1843:
1838:
1833:
1828:
1823:
1818:
1811:
1808:
1765:
1764:
1749:
1734:
1687:Main article:
1684:
1681:
1634:Main article:
1631:
1628:
1540:
1537:
1535:
1532:
1524:center squeeze
1504:Main article:
1501:
1498:
1463:
1460:
1413:
1412:
1409:
1398:
1395:
1389:
1386:
1366:
1363:
1346:
1343:
1291:
1290:Runoff systems
1288:
1275:plurality vote
1271:Vote splitting
1244:
1241:
1223:vote splitting
1179:
1176:
1118:
1115:
1061:
1058:
1044:, such as the
1023:center-squeeze
1019:instant-runoff
986:spoiler effect
972:
971:
969:
968:
961:
954:
946:
943:
942:
930:
929:
917:
904:
901:
900:
897:
896:
891:
886:
881:
876:
864:
863:
858:
853:
848:
843:
832:
827:
826:
823:
822:
819:
818:
813:
808:
803:
788:
787:
785:Turkey-raising
782:
777:
772:
758:
757:
756:
755:
745:
740:
728:
727:
725:Center squeeze
722:
717:
712:
710:Spoiler effect
703:
698:
697:
694:
693:
690:
689:
684:
683:
682:
669:By ballot type
665:
664:
663:
662:
657:
652:
642:
641:
640:
639:
638:
633:
623:
622:
621:
610:
587:
586:
585:
580:
575:
570:
552:
551:
546:
537:
532:
531:
528:
527:
524:
523:
521:Limited voting
518:
517:
516:
497:
496:
491:
486:
481:
480:
479:
474:
455:
454:
449:
444:
439:
425:
424:
419:
414:
409:
395:
394:
393:
392:
390:Localized list
387:
382:
377:
372:
362:
361:
360:
358:Biproportional
355:
350:
345:
329:
324:
323:
320:
319:
316:
315:
310:
305:
300:
286:
285:
270:
255:
231:
230:
229:
228:
223:
218:
213:
203:
189:
188:
187:
186:
175:
162:Instant-runoff
159:
158:
157:
149:Jungle primary
136:
125:Single vote -
123:
118:
117:
114:
113:
111:
110:
100:
95:
90:
85:
79:
76:
75:
65:
64:
54:
53:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2804:
2793:
2792:Voting theory
2790:
2789:
2787:
2773:
2769:
2765:
2761:
2757:
2753:
2746:
2743:
2738:
2734:
2722:
2717:
2713:
2712:
2711:Stable Voting
2704:
2702:
2698:
2693:
2688:
2684:
2677:
2674:
2670:
2666:
2662:
2655:
2652:
2648:
2644:
2642:9781429957649
2638:
2634:
2633:
2625:
2622:
2618:
2616:
2610:
2608:9780898716955
2604:
2600:
2599:
2591:
2588:
2584:
2580:
2578:9780199759965
2574:
2570:
2569:
2561:
2558:
2554:
2550:
2548:9781440841163
2544:
2540:
2539:
2531:
2529:
2525:
2521:
2510:
2506:
2500:
2497:
2492:
2488:
2484:
2480:
2476:
2472:
2471:Public Choice
2468:
2461:
2459:
2457:
2453:
2448:
2444:
2440:
2436:
2432:
2428:
2424:
2417:
2415:
2413:
2409:
2405:
2394:
2390:
2386:
2379:
2372:
2370:
2366:
2361:
2355:
2351:
2350:
2342:
2340:
2336:
2331:
2329:9780898381894
2325:
2321:
2320:
2312:
2309:
2304:
2300:
2296:
2292:
2288:
2284:
2280:
2273:
2270:
2258:
2257:
2252:
2246:
2244:
2242:
2238:
2234:
2229:
2225:
2221:
2219:9781429957649
2215:
2211:
2204:
2202:
2200:
2198:
2194:
2189:
2185:
2173:
2168:
2164:
2163:
2162:Stable Voting
2155:
2152:
2147:
2143:
2139:
2135:
2131:
2127:
2126:Public Choice
2123:
2116:
2113:
2108:
2104:
2100:
2096:
2092:
2088:
2084:
2077:
2074:
2070:
2068:
2062:
2060:9780898716955
2056:
2052:
2051:
2043:
2040:
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2008:
2001:
1998:
1993:
1989:
1984:
1979:
1975:
1971:
1967:
1963:
1962:Public Choice
1959:
1952:
1950:
1946:
1935:
1931:
1925:
1922:
1918:
1914:
1912:9781783470730
1908:
1904:
1903:
1895:
1892:
1885:
1875:
1872:
1866:
1862:
1859:
1857:
1854:
1852:
1849:
1847:
1844:
1842:
1839:
1837:
1834:
1832:
1829:
1827:
1824:
1822:
1819:
1817:
1814:
1813:
1809:
1807:
1805:
1801:
1797:
1792:
1790:
1786:
1782:
1778:
1774:
1770:
1762:
1758:
1754:
1750:
1747:
1743:
1739:
1735:
1732:
1728:
1724:
1720:
1719:
1718:
1716:
1712:
1708:
1704:
1700:
1696:
1690:
1682:
1680:
1678:
1674:
1670:
1665:
1663:
1659:
1658:
1654:
1649:
1648:
1644:. Label them
1643:
1637:
1629:
1627:
1625:
1621:
1616:
1614:
1610:
1606:
1602:
1598:
1594:
1589:
1586:
1584:
1580:
1576:
1572:
1568:
1564:
1560:
1556:
1553:Borda count (
1551:
1548:
1546:
1538:
1533:
1531:
1529:
1525:
1520:
1518:
1514:
1507:
1499:
1497:
1495:
1491:
1486:
1482:
1479:
1473:
1469:
1461:
1459:
1457:
1453:
1449:
1445:
1444:Rated methods
1441:
1437:
1433:
1429:
1424:
1422:
1418:
1410:
1407:
1406:
1405:
1403:
1396:
1394:
1387:
1385:
1383:
1382:strategically
1378:
1376:
1372:
1364:
1362:
1358:
1356:
1352:
1344:
1342:
1340:
1336:
1332:
1328:
1324:
1320:
1315:
1313:
1309:
1305:
1301:
1297:
1289:
1287:
1284:
1283:ideologically
1280:
1276:
1272:
1268:
1266:
1262:
1258:
1254:
1250:
1242:
1240:
1238:
1234:
1232:
1228:
1224:
1220:
1215:
1212:
1208:
1203:
1201:
1197:
1193:
1189:
1185:
1177:
1175:
1173:
1168:
1166:
1162:
1159:
1155:
1151:
1147:
1143:
1139:
1134:
1132:
1128:
1124:
1116:
1114:
1112:
1107:
1103:
1097:
1093:
1091:
1087:
1083:
1079:
1075:
1071:
1067:
1059:
1057:
1055:
1051:
1047:
1043:
1038:
1036:
1032:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1002:
1001:
996:
992:
987:
983:
979:
967:
962:
960:
955:
953:
948:
947:
945:
944:
941:
936:
928:
923:
918:
916:
911:
906:
905:
903:
902:
895:
892:
890:
887:
885:
884:May's theorem
882:
880:
877:
875:
872:
871:
870:
869:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
838:
837:
836:
830:
825:
824:
817:
814:
812:
809:
807:
804:
802:
799:
798:
797:
796:
795:
794:majority rule
792:Paradoxes of
786:
783:
781:
778:
776:
773:
771:
768:
767:
766:
765:
764:
754:
751:
750:
749:
746:
744:
741:
739:
736:
735:
734:
733:
726:
723:
721:
718:
716:
713:
711:
708:
707:
706:
701:
696:
695:
688:
685:
681:
678:
677:
676:
673:
672:
671:
670:
661:
658:
656:
653:
651:
648:
647:
646:
643:
637:
634:
632:
629:
628:
627:
624:
620:
615:
611:
609:
604:
600:
599:
598:
595:
594:
593:
592:
588:
584:
581:
579:
576:
574:
571:
569:
566:
565:
564:
563:
558:
557:
556:
550:
547:
545:
542:
541:
540:
535:
534:Mixed systems
530:
529:
522:
519:
515:
512:
511:
510:
507:
506:
505:
504:
503:
495:
494:Random ballot
492:
490:
487:
485:
482:
478:
475:
473:
470:
469:
468:
465:
464:
463:
462:
461:
453:
450:
448:
445:
443:
440:
438:
435:
434:
433:
432:
431:
423:
420:
418:
415:
413:
410:
408:
405:
404:
403:
402:
401:
391:
388:
386:
383:
381:
378:
376:
373:
371:
368:
367:
366:
363:
359:
356:
354:
351:
349:
346:
344:
341:
340:
339:
338:Apportionment
336:
335:
334:
333:
327:
322:
321:
314:
311:
309:
306:
304:
301:
299:
296:
295:
294:
293:
292:
283:
279:
274:
273:Antiplurality
271:
268:
264:
259:
256:
253:
249:
244:
241:
240:
239:
238:
237:
227:
224:
222:
219:
217:
214:
212:
209:
208:
207:
204:
202:
201:Condorcet-IRV
199:
198:
197:
196:
195:
185:
180:
176:
174:
169:
165:
164:
163:
160:
156:
153:
152:
150:
145:
140:
137:
135:
132:
131:
130:
128:
121:
116:
115:
108:
104:
101:
99:
96:
94:
91:
89:
86:
84:
83:Social choice
81:
80:
78:
77:
71:
67:
66:
63:
59:
58:Social choice
55:
51:
47:
43:
42:
37:
30:
19:
2758:(1): 51–64.
2755:
2751:
2745:
2736:
2732:
2725:, retrieved
2710:
2682:
2676:
2668:
2664:
2654:
2646:
2631:
2624:
2614:
2612:
2597:
2590:
2582:
2567:
2560:
2552:
2541:. ABC-CLIO.
2537:
2519:
2513:. Retrieved
2511:. 2015-03-30
2508:
2499:
2474:
2470:
2430:
2426:
2402:
2396:. Retrieved
2384:
2348:
2318:
2311:
2286:
2282:
2272:
2261:. Retrieved
2259:. 2015-05-20
2254:
2231:
2209:
2187:
2183:
2176:, retrieved
2161:
2154:
2129:
2125:
2115:
2090:
2086:
2076:
2066:
2064:
2049:
2042:
2034:
2014:
2010:
2000:
1965:
1961:
1937:. Retrieved
1933:
1924:
1916:
1901:
1894:
1874:
1851:Protest vote
1803:
1799:
1795:
1793:
1788:
1784:
1780:
1776:
1772:
1768:
1766:
1760:
1756:
1752:
1745:
1741:
1737:
1730:
1726:
1722:
1714:
1710:
1706:
1692:
1668:
1666:
1656:
1652:
1645:
1639:
1623:
1619:
1617:
1612:
1608:
1604:
1600:
1596:
1592:
1590:
1587:
1582:
1578:
1574:
1570:
1566:
1562:
1558:
1554:
1552:
1549:
1542:
1521:
1509:
1483:
1475:
1452:range voting
1432:ranked pairs
1428:Kemeny-Young
1425:
1420:
1414:
1401:
1400:
1391:
1388:Weaker forms
1379:
1371:score voting
1368:
1365:Rated voting
1359:
1348:
1325:knocked out
1316:
1308:rated voting
1293:
1269:
1246:
1235:
1231:ranked pairs
1216:
1204:
1200:rated voting
1194:, rare with
1190:, common in
1181:
1169:
1157:
1135:
1120:
1099:
1095:
1085:
1081:
1077:
1069:
1063:
1039:
1005:
998:
994:
990:
985:
975:
867:
866:
833:
791:
790:
775:Exaggeration
761:
760:
731:
730:
709:
704:
668:
667:
636:Mixed ballot
591:Compensatory
589:
562:compensatory
559:
554:
538:
500:
499:
458:
457:
428:
427:
398:
397:
385:List-free PR
330:
298:Score voting
289:
288:
234:
233:
221:Ranked pairs
192:
191:
124:
1983:11603/20937
1545:Borda count
1539:Borda count
1458:also pass.
1339:Sarah Palin
1323:Kurt Wright
1221:eliminates
1127:Borda count
1074:rationality
1031:cyclic ties
1003:criterion.
675:Single vote
578:Conditional
573:Coexistence
422:Quota Borda
412:Schulze STV
370:Closed list
313:STAR voting
258:Borda count
2727:2024-03-11
2721:2108.00542
2692:2303.00108
2515:2017-10-07
2398:2019-07-20
2263:2017-01-29
2178:2024-03-11
2172:2108.00542
1939:2024-03-03
1886:References
1695:degenerate
1494:indirectly
1434:, but not
1321:, spoiler
1182:Different
1138:choose-one
1060:Motivation
780:Truncation
509:Cumulative
332:Party-list
107:By country
98:Comparison
2772:0895-3309
2491:1573-7101
2447:1573-7187
2393:0028-7504
2303:0165-4896
2228:872601019
2146:1573-7101
2107:1573-7187
2031:0092-5853
1992:1573-7101
1683:Plurality
1490:Smith set
1015:Plurality
687:Dual-vote
380:Panachage
375:Open list
365:List type
243:Plurality
139:Two-round
127:plurality
50:Economics
2786:Category
2601:. SIAM.
2404:pairwise
2053:. SIAM.
1810:See also
1697:form of
1657:Scissors
1446:such as
1331:Bob Kiss
1327:Democrat
1158:de facto
1048:and the
982:politics
407:Hare STV
46:Politics
44:A joint
1436:Schulze
1263:into a
1217:Modern
1146:parties
995:spoiled
991:spoiler
417:CPO-STV
267:Baldwin
216:Schulze
211:Minimax
129:methods
2770:
2667:: 13.
2639:
2605:
2575:
2545:
2489:
2445:
2391:
2356:
2326:
2301:
2226:
2216:
2144:
2105:
2057:
2029:
1990:
1909:
1655:, and
1615:wins.
1585:wins.
1454:, and
984:, the
282:Coombs
52:series
2716:arXiv
2687:arXiv
2381:(PDF)
2167:arXiv
1879:even.
1867:Notes
1775:run:
1653:Paper
1603:=12,
1599:=13,
1595:=14,
1573:=11,
1569:=12,
1565:=13,
1561:=1):
1543:In a
619:'MMP'
608:'AMS'
2768:ISSN
2637:ISBN
2603:ISBN
2573:ISBN
2543:ISBN
2487:ISSN
2443:ISSN
2389:ISSN
2354:ISBN
2324:ISBN
2299:ISSN
2224:OCLC
2214:ISBN
2142:ISSN
2103:ISSN
2055:ISBN
2027:ISSN
1988:ISSN
1907:ISBN
1798:and
1771:and
1759:>
1755:>
1744:>
1740:>
1729:>
1725:>
1669:only
1647:Rock
1611:=5.
1607:=6,
1581:=6.
1577:=8,
1557:=0,
1470:and
1430:and
1298:and
1277:and
1209:and
1148:and
1140:and
1056:.
980:and
560:Non-
514:SNTV
103:List
60:and
48:and
2760:doi
2615:not
2479:doi
2475:158
2435:doi
2291:doi
2134:doi
2130:158
2095:doi
2067:not
2019:doi
1978:hdl
1970:doi
1966:179
1717:).
1528:RCV
1438:or
1317:In
1306:or
1080:or
1064:In
976:In
278:el.
263:el.
252:IRV
248:el.
2788::
2766:.
2754:.
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2297:.
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2285:.
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2253:.
2240:^
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2222:.
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2140:.
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2124:.
2101:.
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2089:.
2085:.
2063:.
2033:.
2025:.
2015:46
2013:.
2009:.
1986:.
1976:.
1964:.
1960:.
1948:^
1932:.
1915:.
1781:A'
1713:,
1709:,
1679:.
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1442:.
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1341:.
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1267:.
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1167:.
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1068:,
1033:.
614:NZ
603:UK
179:US
168:UK
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144:US
2774:.
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2756:9
2737:B
2733:A
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2493:.
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2362:.
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2305:.
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2188:B
2184:A
2169::
2148:.
2136::
2109:.
2097::
2021::
1994:.
1980::
1972::
1942:.
1804:C
1800:B
1796:A
1789:A
1785:C
1777:B
1773:B
1769:A
1763:)
1761:A
1757:B
1753:C
1748:)
1746:C
1742:A
1738:B
1733:)
1731:C
1727:B
1723:A
1715:C
1711:B
1707:A
1624:C
1620:B
1613:B
1609:D
1605:E
1601:A
1597:C
1593:B
1583:C
1579:E
1575:D
1571:B
1567:A
1563:C
1559:b
1555:a
1086:C
1082:B
1078:A
965:e
958:t
951:v
616::
605::
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260:(
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170::
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31:.
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