2622:
define criteria mathematically, such that any electoral system either passes or fails. This gives perfectly objective results, but their practical relevance is still arguable. Another approach is to define ideal criteria that no electoral system passes perfectly, and then see how often or how close to passing various methods are over a large sample of simulated elections. This gives results which are practically relevant, but the method of generating the sample of simulated elections can still be arguably biased. A final approach is to consider practical criteria, and then assign a neutral body to evaluate each method according to these criteria or evaluate the performance of countries with these electoral systems. The practical criteria include
1267:
1344:, which is the most common system used for presidential elections around the world, being used in 88 countries. It is also used in 20 countries for electing the legislature. If no candidate achieves a majority of votes in the first round of voting, a second round is held to determine the winner. In most cases the second round is limited to the top two candidates from the first round, although in some elections more than two candidates may choose to contest the second round; in these cases the second round is decided by plurality voting. Some countries use a modified form of the two-round system, such as
2709:
2735:
931:
1145:
1584:
1418:
1944:. The elections featured two voter rolls (the 'A' roll being largely European and the 'B' roll largely African); the seats of the House Assembly were divided into 50 constituency seats and 15 district seats. Although all voters could vote for both types of seats, 'A' roll votes were given greater weight for the constituency seats and 'B' roll votes greater weight for the district seats. Weighted systems are still used in corporate elections, with votes weighted to reflect stock ownership.
66:
2261:
The third electoral college elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. They in turn elected a final electoral body of 41 members, who ultimately elected the Doge. Despite its complexity, the method had certain desirable properties such as being hard to game and ensuring that the winner reflected the opinions of both majority and minority factions. This process, with slight modifications, was central to the politics of the
2720:
906:
2008:
1230:
3773:
1498:, elections are carried out using 'pure' proportional representation, with the votes tallied on a national level before assigning seats to parties. However, in most cases several multi-member constituencies are used rather than a single nationwide constituency, giving an element of geographical representation; but this can result in the distribution of seats not reflecting the national vote totals. As a result, some countries have
1328:. If no candidate receives a majority of the vote in the first round, the second preferences of the lowest-ranked candidate are then added to the totals. This is repeated until a candidate achieves over 50% of the number of valid votes. If not all voters use all their preference votes, then the count may continue until two candidates remain, at which point the winner is the one with the most votes. A modified form of IRV is the
2234:), a slip of wood coated with wax, for all business done in the assemblies of the people. For the purpose of carrying resolutions a simple majority of votes was deemed sufficient. As a general rule equal value was made to attach to each vote; but in the popular assemblies at Rome a system of voting by groups was in force until the middle of the 3rd century BCE by which the richer classes secured a decisive preponderance.
918:
2056:, with the youngest being 16 and the oldest 21. People may be disenfranchised for a range of reasons, such as being a serving prisoner, being declared bankrupt, having committed certain crimes or being a serving member of the armed forces. Similar limits are placed on candidacy (also known as passive suffrage), and in many cases the age limit for candidates is higher than the voting age. A total of 21 countries have
1700:, in which voters cast votes for both single-member constituencies and multi-member constituencies; the allocation of seats in the multi-member constituencies is adjusted to achieve an overall seat allocation proportional to parties' vote share by taking into account the number of seats won by parties in the single-member constituencies.
1396:, each candidate is given a number of points equal to their rank, and the candidate with the least points wins. This system is intended to elect broadly acceptable options or candidates, rather than those preferred by a majority. This system is used to elect the ethnic minority representatives seats in the Slovenian parliament.
1244:; this is the second most common electoral system for national legislatures, with 58 countries using it for this purpose, the vast majority of which are current or former British or American colonies or territories. It is also the second most common system used for presidential elections, being used in 19 countries.
2198:. However, in Athenian democracy, voting was seen as the least democratic among methods used for selecting public officials, and was little used, because elections were believed to inherently favor the wealthy and well-known over average citizens. Viewed as more democratic were assemblies open to all citizens, and
2126:
are used in many countries to ensure representation for ethnic minorities, women, young people or the disabled. These seats are separate from general seats, and may be elected separately (such as in
Morocco where a separate ballot is used to elect the 60 seats reserved for women and 30 seats reserved
1673:
In non-compensatory, parallel voting systems, which are used in 20 countries, members of a legislature are elected by two different methods; part of the membership is elected by a plurality or majority vote in single-member constituencies and the other part by proportional representation. The results
1332:
where voters do not rank all candidates, but have a limited number of preference votes. If no candidate has a majority in the first round, all candidates are excluded except the top two, with the highest remaining preference votes from the votes for the excluded candidates then added to the totals to
2621:
Electoral systems can be compared by different means. Attitudes towards systems are highly influenced by the systems' impact on groups that one supports or opposes, which can make the objective comparison of voting systems difficult. There are several ways to address this problem. One approach is to
2260:
of nine members elected 40 people by approval voting; those 40 were reduced to form a second electoral college of 12 members by drawing lots again. The second electoral college elected 25 people by approval voting, which were reduced to form a third electoral college of nine members by drawing lots.
1301:
A runoff system in which candidates must receive a majority of votes to be elected, either in a runoff election or final round of voting. This is sometimes referred to as a type of majority voting, although usually only a plurality is required in the last round, and sometimes even in the first round
1257:
is a choose-all-you-like voting system which aims to increase the number of candidates that win with majority support. Voters are free to pick as many candidates as they like and each choice has equal weight, independent of the number of candidates a voter supports. The candidate with the most votes
2135:
the Senate seats reserved for women, young people and the disabled are allocated to parties based on how many seats they won in the general vote. Some countries achieve minority representation by other means, including requirements for a certain proportion of candidates to be women, or by exempting
1555:
being the most common). Candidates that pass the quota are elected. If necessary to fill seats, votes are transferred from the least successful candidates. Surplus votes held by successful candidates may also be transferred. Eventually all seats are filled by candidates who have passed the quota or
2205:
Generally, the taking of votes was effected in the form of a poll. The practice of the
Athenians, which is shown by inscriptions to have been widely followed in the other states of Greece, was to hold a show of hands, except on questions affecting the status of individuals: these latter, which
1213:
In all cases, where only a single winner is to be elected, the electoral system is winner-take all. The same can be said for elections where only one person is elected per district, since the district elections are also winner-take-all, therefore the electoral system as a whole is also usually
2500:
in 1977. Political scientists of the 20th century published many studies on the effects that the electoral systems have on voters' choices and political parties, and on political stability. A few scholars also studied which effects caused a nation to switch to a particular electoral system.
1368:
is not limited to two rounds, but sees the last-placed candidate eliminated in each round of voting. Due to the potentially large number of rounds, this system is not used in any major popular elections, but is used to elect the
Speakers of parliament in several countries and members of the
1403:
for parliamentary elections and sees voters rank the candidates. First preference votes are counted as whole numbers, the second preferences by two, third preferences by three, and so on; this continues to the lowest possible ranking. The totals for each candidate determine the winners.
2332:. Some of the apportionment methods devised in the United States were in a sense rediscovered in Europe in the 19th century, as seat allocation methods for the newly proposed method of party-list proportional representation. The result is that many apportionment methods have two names;
1807:
In addition to the various electoral systems in use in the political sphere, there are numerous others, some of which are proposals and some of which have been adopted for usage in business (such as electing corporate board members) or for organisations but not for public elections.
2075:
or districting defines the area covered by each constituency. Where constituency boundaries are drawn has a strong influence on the likely outcome of elections in the constituency due to the geographic distribution of voters. Political parties may seek to gain an advantage during
1753:
they are a formal part of the electoral system and take place two months before the main elections; any party receiving less than 1.5% of the vote is not permitted to contest the main elections. In the United States, there are both partisan and non-partisan
2091:
Some countries have minimum turnout requirements for elections to be valid. In Serbia this rule caused multiple re-runs of presidential elections, with the 1997 election re-run once and the 2002 elections re-run three times due insufficient turnout in the
2540:
after encountering difficulties or dissatisfaction with IRV; studies have found voter satisfaction with IRV tends to fall dramatically the first time a race produces a result different from first-past-the-post. This may be a result of the high rate of
1012:, areas may be divided into constituencies with one or more representatives or the electorate may elect representatives as a single unit. Voters may vote directly for an individual candidate or for a list of candidates put forward by a
2173:
it was customary for the king to invite pronouncements of his people on matters in which it was prudent to secure its assent beforehand. In these assemblies the people recorded their opinion by clamouring (a method which survived in
1882:
is a system where the total number of votes is used to calculate the number of seats each party is due, followed by a calculation of the constituencies in which the seats should be awarded in order to achieve the total due to them.
2304:
devised both the Borda count and a pairwise method that satisfied the
Condorcet criterion in the 13th century. The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001.
1717:
has a modified two-round system, which sees a second round of voting featuring the top two parties or coalitions if there is no majority in the first round. The winner of the second round is guaranteed 35 seats in the 60-seat
1007:
Some electoral systems elect a single winner to a unique position, such as prime minister, president or governor, while others elect multiple winners, such as members of parliament or boards of directors. When electing a
2458:. However, a series of court decisions ruling Bucklin to be unconstitutional caused a , while instant-runoff voting was soon repealed in every city that had implemented it over a combination of high costs and
1348:
where a candidate in the presidential election is declared the winner if they receive 40% of the vote and are 10% ahead of their nearest rival, or
Argentina (45% plus 10% ahead), where the system is known as
2650:. This approach can look at aspects of electoral systems, which the other two approaches miss, but both the definitions of these criteria and the evaluations of the methods are still inevitably subjective.
2407:
Perhaps influenced by the rapid development of multiple-winner electoral systems, theorists began to publish new findings about single-winner methods in the late 19th century. This began around 1870, when
1766:
Some elections feature an indirect electoral system, whereby there is either no popular vote, or the popular vote is only one stage of the election; in these systems the final vote is usually taken by an
1251:(also known as multiple non-transferable vote or plurality-at-large), voters have as many votes as there are seats and can vote for any candidate, regardless of party, a system used in eight countries.
1741:
are a feature of some electoral systems, either as a formal part of the electoral system or informally by choice of individual political parties as a method of selecting candidates, as is the case in
2600:
rule. A ballot initiative that would prohibit both approval voting and ranked-choice has been placed on the
Missouri ballot, as a result of a similar conflation and backlash to the results of the
1240:
is a system in which the candidate(s) with the highest number of votes wins, with no requirement to get a majority of votes. In cases where there is a single position to be filled, it is known as
1791:
that in turn elects the
President. This can result in a situation where a candidate who receives the most votes nationwide does not win the electoral college vote, as most recently happened in
1509:(the minimum percentage of the vote that a party must obtain to win seats), there are several different ways to allocate seats in proportional systems. There are two main types of systems:
1928:
systems were used in some countries. These allocated a greater weight to the votes of some voters than others, either indirectly by allocating more seats to certain groups (such as the
1221:, voters can only vote for the list of candidates of a single party, with the party receiving the most votes winning all seats. This is used in five countries as part of mixed systems.
889:
980:
is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business,
2462:
in the system. Since the turn away from
Bucklin, STV was adopted by more than 20 cities in the U.S. and many cities elsewhere, and by Ireland and Malta for their national elections.
2601:
2432:. He also proposed a proportional representation system based on multi-member districts, quotas as minimum requirements to take seats, and votes transferable by candidates through
1952:
In addition to the specific method of electing candidates, electoral systems are also characterised by their wider rules and regulations, which are usually set out in a country's
2545:
in IRV, or of the difficulties involved in explaining how the rule works. In Canada, despite a three-decade-long reform and education movement, three separate referenda on the
1247:
In cases where there are multiple positions to be filled, most commonly in cases of multi-member constituencies, there are several types of plurality electoral systems. Under
573:
1713:
to either ensure one party or coalition gains a majority in the legislature, or to give the party receiving the most votes a clear advantage in terms of the number of seats.
3956:
1706:
are also compensatory, however they usually use different mechanism than seat linkage (top-up) method of MMP and usually aren't able to achieve proportional representation.
4210:
4149:
3034:
2994:
2984:
592:
2214:, in which voters chose the citizen they most wanted to exile for ten years, were determined by secret ballot (one of the earliest recorded elections in Athens was a
2093:
2320:
had to be allocated among the states proportionally to their population, but did not specify how to do so. A variety of methods were proposed by statesmen such as
2256:) and five rounds of approval voting. By drawing lots, a body of 30 electors was chosen, which was further reduced to nine electors by drawing lots again. An
1302:
winners can avoid a second round without achieving a majority. In social choice theory, runoff systems are not called majority voting, as this term refers to
1685:, in use in eight countries, provide enough compensatory seats to ensure that parties have a number of seats approximately proportional to their vote share.
2607:
Ranked-choice voting has been implemented in two states and banned in 10 others (in addition to other states with constitutional prohibitions on the rule).
3703:
2228:). But the system became subject to intimidation and corruption. Hence a series of laws enacted between 139 and 107 BCE prescribed the use of the ballot (
1878:
is a proposed system with two candidates elected in each constituency, one with the most votes and one to ensure proportionality of the combined results.
1476:
is the most widely used electoral system for national legislatures, with the parliaments of over eighty countries elected by various forms of the system.
959:
796:
1000:, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by
4504:
1490:
systems voters are able to both vote for the party list and influence the order in which candidates will be assigned seats. In some countries, notably
3788:
2558:
2554:
2550:
2131:
the reserved seats for women are given to the female candidates who failed to win constituency seats but with the highest number of votes, whilst in
2391:. Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former
1482:
is the single most common electoral system and is used by 80 countries, and involves voters voting for a list of candidates proposed by a party. In
1692:, where parties win more seats in the constituency system than they would be entitled to based on their vote share. Variations of this include the
1313:
and the other using multiple elections, to successively narrow the field of candidates. Both are primarily used for single-member constituencies.
2574:
1597:
1533:. This usually leaves some seats unallocated, which are awarded to parties based on which parties have the largest number of "leftover" votes.
4954:
2517:
1388:
are ranked voting systems that assign a certain number of points to each candidate, weighted by position. The most popular such system is
4722:
4237:
2097:
1563:(SNTV) voters can vote for only one candidate, with the candidates receiving the most votes declared the winners; this system is used in
650:
4472:
3793:
3809:
3922:
1539:(STV) is another form of proportional representation. In STV, multi-member districts are used and each voter casts one vote, being a
4850:
4702:
2998:
2980:
2958:
2521:
1937:
1796:
1792:
1682:
1678:
1667:
1373:. In some formats there may be multiple rounds held without any candidates being eliminated until a candidate achieves a majority.
682:
544:
539:
4949:
4727:
1902:
1875:
952:
645:
4712:
4497:
3246:
3236:
3226:
3216:
2939:
2929:
2919:
2508:
beginning around the 1990s, when proposals were made to replace plurality voting in governmental elections with other methods.
2317:
2113:
1755:
1479:
1450: Mixed-member proportional (seat linkage) type compensatory, some additional compensation for overhang seats (New Zealand)
327:
3895:
3595:
3544:
5076:
3390:
1214:
non-proportional. Some systems where multiple winners are elected at once (in the same district) are also winner-take-all.
1124:
851:
102:
3660:
2288:, who proposed instead the method of pairwise comparison that he had devised. Implementations of this method are known as
4759:
4141:
3942:
2577:
on IRV saw the proposal rejected by a two-to-one margin over concerns about cost and complexity. The United
Kingdom used
2383:. Party-list proportional representation began to be used to elect European legislatures in the early 20th century, with
2169:, the institution of suffrage already existed in a rudimentary form at the outset of the historical period. In the early
3325:
or local/regional legislatures, partly elected in single-member districts by FPTP, and partly appointed by head of state
3518:
Voters can vote for as many candidates as they want. The votes are tallied, and the candidate with the most votes wins!
3448:
2667:
According to a 2006 survey of electoral system experts, their preferred electoral systems were in order of preference:
2127:
for young people in the House of
Representatives), or be allocated to parties based on the results of the election; in
2105:
2101:
2088:, constituencies with unusually small populations, were used by wealthy families to gain parliamentary representation.
945:
3719:
3037:(party-list PR and FPTP) ((partially compensatory semi-proportional implementation of of MMP) (party-list PR and FPTP)
4490:
4344:
4085:
Arend Lijphart (1992) "Democratization and Constitutional Choices in Czecho-Slovakia, Hungary and Poland, 1989â1991"
4065:
4019:
3999:
3950:
3576:"Republic of Slovenia. The Documentation and Library Department of the National Assembly of the Republic of Slovenia"
2657:
2513:
2439:
Ranked voting electoral systems eventually gathered enough support to be adopted for use in government elections. In
2372:
1788:
1358:
846:
2596:
passed with 70% support, despite opposition from politicians on the city council who confused it with the unrelated
1787:, the president is indirectly elected using a two-stage process; a popular vote in each state elects members to the
4944:
4890:
2653:
2481:
2480:
to analyze electoral systems led to discoveries about the effects of certain methods. Earlier developments such as
1088:
836:
586:
557:
497:
1783:, the vote is taken by an electoral college consisting of the national legislature and state legislatures. In the
5071:
4742:
3375:
2616:
1941:
1727:
1320:(IRV), whereby voters rank candidates in order of preference; this system is used for parliamentary elections in
568:
93:
2416:(IRV). Soon, mathematicians began to revisit Condorcet's ideas and invent new methods for Condorcet completion;
1726:
the party receiving the most votes was given an additional 50 seats, a system which was abolished following the
5144:
5094:
4870:
4145:
3700:
2420:
combined the newly described instant runoff voting with the Borda count to yield a new Condorcet method called
2194:
Voting has been used as a feature of democracy since the 6th century BCE, when democracy was introduced by the
1929:
1750:
1456: Mixed-member proportional (seat linkage) type compensatory, no additional compensation for overhang seats
631:
17:
3877:
695:
5139:
5129:
5114:
2562:
2388:
273:
258:
243:
4076:
Arend Lijphart (1985) "The Field of Electoral Systems Research: A Critical Survey" Electoral Studies, Vol. 4
4913:
4898:
4717:
3561:
3180:
2893:
2443:, IRV was first adopted in 1893 and STV in 1896 (Tasmania). IRV continues to be used along with STV today.
2123:
1906:
1898:
1879:
1560:
509:
432:
353:
4707:
2048:
Electoral rules place limits on suffrage and candidacy. Most countries's electorates are characterised by
4964:
4687:
4677:
4538:
4286:
3616:
3206:
3150:
2909:
2854:
1910:
1681:
the results of the proportional vote are adjusted to balance the seats won in the constituency vote. The
1473:
1130:
874:
321:
303:
144:
4211:"First Past the Post to be introduced for all local mayoral and police and crime commissioner elections"
3843:
2660:
prove that no single-winner system using ranked voting can meet all such criteria simultaneously, while
1918:
984:
and informal organisations. These rules govern all aspects of the voting process: when elections occur,
5119:
4929:
4620:
2827:
2582:
2542:
2537:
2459:
2313:
2281:
2085:
2060:, although in some there is an upper age limit on enforcement of the law. Many countries also have the
1742:
1389:
1241:
1029:
765:
748:
715:
479:
467:
437:
238:
196:
129:
2080:
by ensuring their voter base has a majority in as many constituencies as possible, a process known as
4979:
4934:
4880:
4792:
3817:
3160:
3030:
2864:
2249:
1719:
1703:
1248:
1129:
The most common categorizations of electoral systems are: single-winner vs. multi-winner systems and
1120:
621:
614:
98:
4173:"Comeâfromâbehind victories under rankedâchoice voting and runoff: The impact on voter satisfaction"
4969:
4855:
4813:
4732:
4657:
4593:
4551:
3256:
2968:
2642:
for new political movements. The quality of electoral systems can be measured on outcomes, such as
2546:
2356:
2309:
2072:
1859:
1693:
1536:
1514:
675:
603:
455:
442:
425:
402:
380:
343:
333:
1529:, then rounding normally. In the largest remainder system, parties' vote shares are divided by an
1266:
884:
4994:
4984:
4959:
4775:
4652:
4588:
4127:(1999) "Setting the Rules of the Game: The Choice of Electoral Systems in Advanced Democracies",
3350:
3101:
3067:
3054:
2623:
1886:
1831:
1510:
1237:
801:
655:
338:
770:
5124:
5035:
4974:
4837:
4100:
Citizens, Elections, Parties: Approaches to the Comparative Study of the Process of Development
3862:
3114:
2818:
2728:
2396:
1659:
1350:
1138:
1134:
1021:
981:
830:
710:
640:
447:
28:
4780:
2345:
1486:
systems voters do not have any influence over the candidates put forward by the party, but in
4939:
4860:
4625:
4469:
3143:
3044:
2847:
2771:
2578:
2525:
2451:
2413:
2273:
1997:
1710:
1697:
1543:
ballot marked for individual candidates, rather than voting for a party list. STV is used in
1370:
1317:
1294:
1037:
738:
578:
462:
268:
247:
179:
157:
3778:
One or more of the preceding sentences incorporates text from a publication now in the
1502:
to award to parties whose seat totals are lower than their proportion of the national vote.
1309:
There are two main forms of runoff systems, one conducted in a single round of voting using
5009:
4578:
3831:
2708:
2661:
2597:
2285:
2238:
1823:
1540:
1526:
1310:
1100:
1064:
869:
856:
824:
88:
1897:, where a candidate is scored from a set range of numbers. Other cardinal systems include
8:
5134:
4989:
4583:
4172:
3123:
2751:
2734:
2429:
2409:
2380:
1827:
1776:
1548:
1506:
1354:
1285:
1076:
1056:
1001:
775:
609:
262:
4261:
2116:
going to a fourth round of voting before enough parliamentarians were elected to make a
996:, how the ballots are counted, how votes translate into the election outcome, limits on
5149:
5030:
4640:
4598:
4443:
4400:
4369:
4361:
4342:
Lijphart, Arend (March 1997). "Unequal Participation: Democracy's Unresolved Dilemma".
4317:
3731:
3478:
3077:
2421:
2321:
2262:
2195:
2068:
2049:
1993:
1965:
1843:
1270:
Countries by electoral system used to (directly) elect their Head of State (President):
1017:
935:
806:
417:
201:
2524:
in the United States, various municipalities in the United States have begun to adopt
4999:
4908:
4865:
4785:
4630:
4615:
4573:
4447:
4435:
4373:
4192:
4061:
4015:
3995:
3946:
3591:
3385:
3322:
3312:
3302:
3200:
2794:
2775:
2639:
2493:
2337:
2293:
2257:
2061:
2057:
1914:
1855:
1839:
1835:
1768:
1381:
1365:
1104:
1072:
930:
841:
811:
733:
670:
504:
231:
206:
189:
57:
3502:
2241:
were held using plurality voting or some variant, but as an exception, the state of
1421:
Countries by proportional electoral system (lower house or unicameral legislature):
5040:
4672:
4528:
4427:
4396:
4353:
4184:
4058:
Electoral Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945â1990
3583:
3133:
3064:
2837:
2761:
2647:
2505:
2471:
2417:
2325:
2289:
2215:
2199:
2166:
1961:
1932:), or by weighting the results of the vote. The latter system was used in colonial
1819:
1738:
1568:
1341:
1325:
1303:
1276:
1144:
1108:
1080:
1068:
1041:
1033:
1025:
997:
922:
879:
758:
472:
348:
174:
168:
150:
139:
134:
122:
83:
45:
3755:
3743:
3688:
3676:
3640:
3541:
3529:
2252:
was a particularly convoluted process, consisting of five rounds of drawing lots (
5088:
5004:
4845:
4823:
4635:
4556:
4546:
4524:
4476:
3936:
3881:
3707:
3664:
3548:
3452:
3268:
3008:
2589:
2497:
2447:
2001:
1981:
1925:
1890:
1674:
of the constituency vote have no effect on the outcome of the proportional vote.
1663:
1587:
Countries using a mixed electoral system (lower house or unicameral legislature):
1530:
1517:. Highest average systems involve dividing the votes received by each party by a
1329:
1254:
1045:
1013:
910:
743:
598:
563:
484:
395:
298:
221:
163:
41:
4238:"St. Louis, Missouri, Proposition D, Approval Voting Initiative (November 2020)"
3657:
2104:
attempts to run the election. The turnout requirement was scrapped prior to the
4903:
4608:
4568:
4387:
Blais, Andre (1990). "Does proportional representation foster voter turnout?".
3575:
3400:
3196:
3170:
2884:
2874:
2570:
2455:
2392:
2368:
2329:
2162:
2081:
1989:
1969:
1851:
1815:
1746:
1650:
1218:
1096:
780:
720:
705:
516:
385:
360:
211:
4431:
3587:
2536:
Many cities which adopted instant-runoff voting have subsequently returned to
1889:
allow voters to evaluate candidates independently. The complexity ranges from
1583:
1556:
there are only as many remaining candidates as the number of remaining seats.
1417:
5108:
4647:
4439:
4287:"Missouri joins other red states in trying to stamp out ranked choice voting"
4196:
3784:
3779:
3341:
2713:
2643:
2635:
2627:
2566:
2485:
2425:
2077:
1977:
1973:
1871:
1811:
1784:
1689:
1499:
1153:
1148:
Map showing the main types electoral systems used to elect candidates to the
1092:
993:
789:
489:
277:
115:
78:
53:
4415:
3445:
2360:
4662:
4603:
4416:"Expert opinion on electoral systems: So which electoral system is "best"?"
4111:
Ronald Rogowski (1987) "Trade and the Variety of Democratic Institutions",
3580:
Parliamentary Libraries and Research Services in Central and Eastern Europe
2489:
2433:
2222:
the method which prevailed up to the 2nd century BCE was that of division (
2219:
2170:
1957:
1953:
1894:
1847:
1607:
529:
293:
286:
216:
2245:
in the 13th century adopted approval voting to elect their Great Council.
1984:. Other regulations include the selection of voting devices such as paper
65:
27:
For a mathematical representation and treatment of electoral systems, see
5045:
4808:
4747:
4667:
4563:
4124:
3395:
2903:
2785:
2739:
2724:
2631:
2509:
2477:
2301:
2277:
2265:
throughout its remarkable lifespan of over 500 years, from 1268 to 1797.
1867:
1862:. There are also several variants of single transferable vote, including
1688:
Other systems may be insufficiently compensatory, and this may result in
1552:
1495:
1483:
1393:
1385:
1149:
1084:
1052:
1009:
407:
365:
308:
253:
3979:
Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It)
3797:. Vol. 28 (11th ed.). Cambridge University Press. p. 216.
3482:
3466:
2719:
1893:
where voters simply state whether they approve of a candidate or not to
905:
4818:
4754:
4365:
4321:
4188:
3405:
3359:
2053:
1714:
1337:
presidential elections, with voters allowed to give three preferences.
4305:
2520:. After plurality voting was a factor in the contested results of the
1779:, the post of President is elected by the legislature. In others like
1353:. In some cases, a runoff may be held using a different system, as in
1071:, but the question has also engendered substantial contributions from
5055:
5050:
2949:
2593:
2440:
2253:
2211:
1772:
1487:
1334:
1321:
1060:
989:
375:
370:
4482:
4357:
2664:
proves the same for all single-winner deterministic voting methods.
2007:
1551:. To be certain of being elected, candidates must pass a quota (the
4875:
3898:
3884:
3874:
3380:
2376:
1933:
1229:
985:
626:
4032:
Seats and Votes: The Effects and Determinants of Electoral Systems
2375:
in 1857. STV elections were first held in Denmark in 1856, and in
1020:. There are many variations in electoral systems. The most common
4737:
4414:
Bowler, Shaun; Farrell, David M.; Pettit, Robin T. (2005-04-01).
2997:(party-list PR and FPTP) (less proportional implementation of of
2384:
2364:
2207:
2141:
2109:
1985:
1863:
1572:
1345:
1004:, and can use multiple types of elections for different offices.
412:
3832:
Electing the Doge of Venice: Analysis of a 13th Century Protocol
5025:
2242:
2183:
2175:
2145:
2137:
2128:
2117:
1723:
1564:
1491:
917:
3923:
Municipal Voting System Reform: Overcoming the Legal Obstacles
2218:
that it was undesirable to win, namely an ostracism vote). At
3315:
or local/regional legislatures and appointed by head of state
2179:
2136:
minority parties from the electoral threshold, as is done in
2132:
1780:
1544:
1400:
4464:
4045:
Democracy or Anarchy? A Study of Proportional Representation
2581:
for most local elections up until 2022, before returning to
1208:
2588:
Other referenda have had different results; a 2020 vote on
2412:
proposed applying STV to single-winner elections, yielding
1224:
4470:
The International IDEA Handbook of Electoral System Design
2300:. However, recent research has shown that the philosopher
2044:
Historical: the country had compulsory voting in the past.
1087:. The field has produced several major results, including
1044:. Many countries combine two or more electoral systems in
2512:
adopted mixed-member proportional representation for the
2504:
The study of electoral systems influenced a new push for
2428:, proposed the straightforward Condorcet method known as
1107:
voting system, i.e. one where it is always obvious to a
2565:, which attempted to expand instant-runoff voting into
2178:
as late as the 4th century BCE), or by the clashing of
3807:
4171:
Cerrone, Joseph; McClintock, Cynthia (August 2023).
3921:
Tony Anderson SolgĂĽrd and Paul Landskroener (2002) "
3720:
Pro-Western Candidate Wins Serbian Presidential Poll
3271:/ Mixed-member majoritarian (party-list PR and FPTP)
3011:/ mixed member majoritarian (party-list PR and FPTP)
1233:
Countries using first-past-the-post for legislatures
34:
Method by which voters make a choice between options
4413:
3277: Parallel voting (party-list PR and BV or PBV)
3023: Parallel voting (party-list PR and BV or PBV)
2352:is identical to the Hare largest remainder method.
1921:where voters can cast positive and negative votes.
1161: Majoritarian representation (winner-take-all)
2610:
1316:Runoff can be achieved in a single election using
1185: Semi-proportional representation (non-mixed)
1059:study of voting rules falls under the branches of
4170:
3934:
2585:over concerns regarding the system's complexity.
1662:are used to elect the legislature. These include
5106:
4420:Journal of Elections, Public Opinion and Parties
3808:O'Connor, J.J.; Robertson, E. F. (August 2002).
2280:in 1770 as a method for electing members to the
1802:
4303:
3925:", Bench & Bar of Minnesota, Vol. 59, no. 9
3292: Varies by federal states, or constituency
2446:In the United States in the early-20th-century
3283: Parallel voting (party-list PR and SNTV)
1666:(also known as mixed-member majoritarian) and
1179: Mixed-member proportional representation
1173: Mixed-member majoritarian representation
4498:
4030:Rein Taagapera and Matthew S. Shugart (1989)
3677:Consiglio grande e generale: Electoral system
3017: Parallel voting (party-list PR and TRS)
2268:
1333:determine the winner. This system is used in
1114:
953:
4955:Independence of Smith-dominated alternatives
4012:The Political Consequences of Electoral Laws
3824:
2569:, was defeated by a 10-point margin. In the
1340:The other main form of runoff system is the
3935:Farrell, David M.; McAllister, Ian (2006).
3830:Miranda Mowbray and Dieter Gollmann (2007)
2932:(party-list PR, open list for some parties)
2229:
2223:
1643: Parallel voting (Party list + BV/PBV)
1156:) house of national legislatures in 2022:
4505:
4491:
3911:Principles of Parliamentary Representation
3573:
3328:No relevant electoral system information:
3082:No relevant electoral system information:
2699:
2496:to formally define and promote the use of
2037:Compulsory voting, not enforced (only men)
960:
946:
3766:
3764:
1749:by ensuring a single party candidate. In
1631: Parallel voting (Party list + FPTP)
1462: Personalized proportional (Germany)
1357:when no candidate wins a majority of the
1209:Single-winner and winner-take-all systems
4341:
3783:
2981:Mixed-member proportional representation
2959:Personalised proportional representation
2402:
2006:
1947:
1668:mixed-member proportional representation
1637: Parallel voting (Party list + TRS)
1610:type partially compensatory (supermixed)
1582:
1416:
1265:
1228:
1225:Plurality voting and first-past-the-post
1143:
4950:Independence of irrelevant alternatives
4728:Sequential proportional approval voting
3464:
2531:
2054:age at which people are allowed to vote
1903:sequential proportional approval voting
1876:Dual-member proportional representation
1412:
1407:
14:
5107:
4389:European Journal of Political Research
3761:
3653:
3651:
3649:
3441:
3439:
3437:
3435:
3433:
3431:
3429:
3427:
3247:party-list proportional representation
3237:Party-list proportional representation
3227:Party-list proportional representation
3217:Party-list proportional representation
2940:Party-list proportional representation
2930:Party-list proportional representation
2920:Party-list proportional representation
2465:
2379:in 1896 after its use was promoted by
2318:United States House of Representatives
2298:intransitivity of majority preferences
2030:Compulsory voting, enforced (only men)
1745:. Primary elections limit the risk of
1480:Party-list proportional representation
1444: Panachage party list (open list)
1103:(showing it is impossible to design a
4512:
4486:
4386:
4284:
4232:
4230:
3858:
3856:
3844:Llull's writings on electoral systems
3689:Hellenic Parliament: Electoral system
3582:, DE GRUYTER SAUR, pp. 194â207,
3467:"Approval Voting: Do Moderates Gain?"
3261:Mixed majoritarian and proportional:
2973:Mixed majoritarian and proportional:
2802: Not elected (mostly monarchies)
2602:2022 Alaska at-large special election
1761:
1376:
4152:from the original on 6 December 2023
3959:from the original on 6 December 2023
3875:Proportional Voting Around the World
3842:G. Hägele and F. Pukelsheim (2001) "
3617:"How do elections work in Slovenia?"
3446:Table of Electoral Systems Worldwide
3391:List of electoral systems by country
3239:(party-list PR, partially-open list)
1733:
1125:List of electoral systems by country
1028:-with-runoff family, which includes
4760:Indirect single transferable voting
3801:
3756:Narodna skupstina: Electoral system
3646:
3424:
2450:, some municipalities began to use
2424:. Charles Dodgson, better known as
2316:, which mandated that seats in the
2052:, but there are differences on the
1438: Party list (partly-open list)
24:
4401:10.1111/j.1475-6765.1990.tb00227.x
4227:
3853:
3641:Nauru Parliament: Electoral system
2484:had already shown the issues with
2387:the first to implement it for its
2189:
1392:. Another well-known variant, the
64:
25:
5161:
4458:
4345:American Political Science Review
4129:American Political Science Review
3530:Sri Lanka: Election for President
3509:. The Center for Election Science
2202:, as well as rotation of office.
2156:
1968:, in addition to the location of
1709:Some electoral systems feature a
1683:mixed-member proportional systems
1596: Mixed-member proportional (
1261:
1203: No election (e.g. Monarchy)
1167: Proportional representation
3771:
3574:Filipovska, Majda (1998-12-31),
2733:
2718:
2707:
2284:. His method was opposed by the
1960:. Participatory rules determine
1771:. In several countries, such as
1622: Two round majority jackpot
1578:
1111:which ballot they should cast).
929:
916:
904:
852:McKelveyâSchofield chaos theorem
498:Semi-proportional representation
130:First preference plurality (FPP)
4465:ACE Electoral Knowledge Network
4407:
4380:
4335:
4297:
4278:
4262:"Missouri 2024 ballot measures"
4254:
4203:
4164:
4134:
4118:
4105:
4092:
4087:Journal of Theoretical Politics
4079:
4070:
4050:
4037:
4024:
4004:
3984:
3971:
3938:The Australian Electoral System
3928:
3915:
3903:
3889:
3868:
3836:
3814:MacTutor History of Mathematics
3749:
3737:
3725:
3713:
3694:
3682:
3670:
3542:Ecuador: Election for President
3376:Comparison of electoral systems
2617:Comparison of electoral systems
2611:Comparison of electoral systems
2064:option on their ballot papers.
2039:
2032:
2025:
2023:Compulsory voting, not enforced
2018:
2011:
1996:, and consequently the type of
1359:United States Electoral College
994:how ballots are marked and cast
4871:Mixed ballot transferable vote
4146:Department of Internal Affairs
3634:
3609:
3567:
3554:
3535:
3523:
3495:
3458:
3305:or local/regional legislatures
2312:came to prominence due to the
1930:Prussian three-class franchise
1468: Single transferable vote
1426: Party list (closed list)
1399:The Dowdall system is used in
890:Harsanyi's utilitarian theorem
847:Moulin's impossibility theorem
812:Conflicting majorities paradox
13:
1:
3865:American Mathematical Society
3417:
3205:Multi-member constituencies,
3183:(SNTV) or mixed FPTP and SNTV
3149:Multi-member constituencies,
2908:Multi-member constituencies,
2896:(SNTV) or mixed FPTP and SNTV
2853:Multi-member constituencies,
2658:GibbardâSatterthwaite theorem
2563:2020 Massachusetts Question 2
2482:Arrow's impossibility theorem
2108:in 2004. Similar problems in
1803:Systems used outside politics
1525:that represents an idealized
1089:Arrow's impossibility theorem
716:Frustrated majorities paradox
5072:Comparison of voting systems
4914:Satisfaction approval voting
4899:Single non-transferable vote
4718:Proportional approval voting
4310:The American Economic Review
4306:"Entry Barriers in Politics"
4043:Ferdinand A. Hermens (1941)
3722:Deutsche Welle, 28 June 2004
3249:(party-list PR, closed list)
3219:(party-list PR, closed list)
3181:Single non-transferable vote
3115:Single-member constituencies
2922:(party-list PR, closed list)
2894:Single non-transferable vote
2819:Single-member constituencies
2695:Single non-transferable vote
2516:, having been approved in a
2359:(STV) method was devised by
2237:Most elections in the early
2114:1995 parliamentary elections
1907:satisfaction approval voting
1899:proportional approval voting
1880:Biproportional apportionment
1561:single non-transferable vote
1432: Party list (open list)
885:Condorcet dominance theorems
825:Social and collective choice
7:
4678:Graduated majority judgment
4047:, University of Notre Dame.
3977:Poundstone, William (2008)
3863:Apportionment: Introduction
3621:www.electoral-reform.org.uk
3368:
3173:(PBV) or mixed FPTP and PBV
2952:(party-list PR, free list)
2877:(PBV) or mixed FPTP and PBV
2522:2000 presidential elections
2308:Later in the 18th century,
2016:Compulsory voting, enforced
1474:Proportional representation
1131:proportional representation
1024:methods all fall under the
551:By mechanism of combination
322:Proportional representation
10:
5166:
4930:Condorcet winner criterion
4621:First-past-the-post voting
4113:International Organization
3503:"What is Approval Voting?"
3229:(party-list PR, open list)
2987:) (party-list PR and FPTP)
2942:(party-list PR, open list)
2614:
2469:
2314:United States Constitution
2292:. He also wrote about the
2282:French Academy of Sciences
2269:Development of new systems
2248:The Venetians' method for
2151:
2086:rotten and pocket boroughs
1887:Cardinal electoral systems
1704:Vote linkage mixed systems
1390:first-preference plurality
1118:
1115:Types of electoral systems
1038:ranked-choice runoff (RCV)
1030:first-preference plurality
749:Multiple districts paradox
480:Fractional approval voting
468:Interactive representation
26:
5085:
5077:Voting systems by country
5064:
5018:
4980:Mutual majority criterion
4935:Condorcet loser criterion
4922:
4889:
4881:Vote linkage mixed system
4836:
4801:
4793:Largest remainders method
4768:
4695:
4686:
4537:
4520:
4432:10.1080/13689880500064544
3990:Duverger, Maurice (1954)
3967:– via Google Books.
3588:10.1515/9783110954098.194
3163:(BV) or mixed FPTP and BV
3035:Seat linkage mixed system
3031:Vote linkage mixed system
2995:seat linkage mixed system
2985:Seat linkage mixed system
2867:(BV) or mixed FPTP and BV
2692:Mixed member majoritarian
2671:Mixed member proportional
1720:Grand and General Council
1121:List of electoral systems
696:Paradoxes and pathologies
545:Mixed-member proportional
540:Mixed-member majoritarian
535:By results of combination
426:Approval-based committees
4970:Majority loser criterion
4856:Additional member system
4814:Hagenbach-Bischoff quota
4733:Single transferable vote
4658:Positional voting system
4594:Minimax Condorcet method
4552:Combined approval voting
4304:Tullock, Gordon (1965).
4060:Oxford University Press
4014:, Yale University Press
3981:, Hill and Young, p. 198
3412:
3321: Partly elected by
3311: Partly elected by
3257:Single transferable vote
2969:Single transferable vote
2961:(party-list PR and FPTP)
2683:Closed list proportional
2674:Single transferable vote
2547:single transferable vote
2357:single transferable vote
1972:and the availability of
1694:Additional Member System
1537:Single transferable vote
1191: Indirect elections
1042:plurality-with-primaries
982:non-profit organisations
875:Condorcet's jury theorem
676:Double simultaneous vote
651:Ruralâurban proportional
646:Dual-member proportional
608:
597:
564:Parallel (superposition)
456:Fractional social choice
443:Expanding approvals rule
272:
257:
242:
173:
162:
138:
4995:Resolvability criterion
4985:Participation criterion
4960:Later-no-harm criterion
4776:Highest averages method
4131:Vol. 93 (3), pp. 609â24
4034:, Yale University Press
3909:Charles Dodgson (1884)
3810:"The history of voting"
3794:EncyclopĂŚdia Britannica
3349: No information /
3189: Mixed BV and SNTV
3068:majority jackpot system
3055:Majority jackpot system
2700:Systems by elected body
2686:Single member plurality
2624:political fragmentation
1135:winner-take-all systems
802:Tyranny of the majority
579:Fusion (majority bonus)
396:Quota-remainder methods
5036:First-preference votes
4975:Monotonicity criterion
4945:Independence of clones
4648:Simple majoritarianism
4102:, Universitetsforlaget
4089:Vol. 4 (2), pp. 207â23
4056:Arend Lijphart (1994)
4010:Douglas W. Rae (1971)
3744:Sejm: Electoral system
3732:Elections held in 1995
3465:Fenster, Mark (1983).
2729:unicameral legislature
2677:Open list proportional
2514:1996 general elections
2488:systems. Research led
2389:1900 general elections
2296:, which he called the
2230:
2224:
2045:
1658:In several countries,
1655:
1616: Majority jackpot
1470:
1298:
1234:
1205:
986:who is allowed to vote
936:Mathematics portal
842:Majority impossibility
831:Impossibility theorems
627:Negative vote transfer
448:Method of equal shares
69:
29:social choice function
5145:Administrative theory
4940:Consistency criterion
4861:Alternative vote plus
4626:Instant-runoff voting
4177:Politics & Policy
3564:opentextbookstore.com
3471:Political Methodology
3144:Instant-runoff voting
3094: Varies by state
3045:Majority bonus system
2848:Instant-runoff voting
2772:Instant-runoff voting
2579:instant-runoff voting
2526:instant-runoff voting
2452:instant-runoff voting
2414:instant-runoff voting
2403:Single-winner revival
2336:is equivalent to the
2310:apportionment methods
2274:Jean-Charles de Borda
2010:
1998:vote counting systems
1948:Rules and regulations
1711:majority bonus system
1698:Alternative Vote Plus
1586:
1420:
1371:Swiss Federal Council
1318:instant-runoff voting
1295:Instant-runoff voting
1269:
1232:
1147:
1095:cannot eliminate the
1077:analytic philosophers
988:, who can stand as a
739:Best-is-worst paradox
728:Pathological response
463:Direct representation
116:Single-winner methods
68:
5140:Social choice theory
5130:Public choice theory
5115:Comparative politics
5010:Seats-to-votes ratio
4781:Webster/Sainte-LaguĂŤ
4098:Stein Rokkan (1970)
3109: No information
2814: No information
2598:ranked-choice voting
2532:Repeals and backlash
2286:Marquis de Condorcet
2239:history of democracy
2067:In systems that use
1962:candidate nomination
1919:D21 â JaneÄek method
1911:highest median rules
1679:mixed-member systems
1527:seats-to-votes ratio
1413:Proportional systems
1408:Multi-winner systems
1355:contingent elections
1073:political scientists
1002:election commissions
923:Economics portal
870:Median voter theorem
89:Comparative politics
4990:Plurality criterion
4589:KemenyâYoung method
4115:Vol. 41, pp. 203â24
3340: Appointed by
3295:Indirect election:
3124:First past the post
2828:First past the post
2808: In transition
2752:First past the post
2583:first-past-the-post
2538:first-past-the-post
2466:Recent developments
2410:William Robert Ware
2381:Andrew Inglis Clark
2367:in 1855 and in the
2346:Sainte-LaguĂŤ method
2000:, verification and
1994:open ballot systems
1777:Trinidad and Tobago
1600:) type compensatory
1549:Republic of Ireland
1507:electoral threshold
1505:In addition to the
1286:First-past-the-post
1242:first-past-the-post
1197: In transition
1081:computer scientists
911:Politics portal
622:Vote linkage system
593:Seat linkage system
180:Ranked-choice (RCV)
5031:Election threshold
4965:Majority criterion
4641:Supplementary vote
4475:2020-11-24 at the
4331:– via JSTOR.
4285:Rosenbaum, Jason.
4189:10.1111/polp.12544
3896:The History of IRV
3880:2008-12-16 at the
3710:CIA World Factbook
3706:2008-01-09 at the
3663:2017-06-11 at the
3547:2016-12-24 at the
3451:2017-05-23 at the
3334: No elections
3301: Election by
3171:Party block voting
3088: No elections
3078:Indirect elections
3047:(non-compensatory)
2875:Party block voting
2793: Election by
2784: Election by
2334:Jefferson's method
2322:Alexander Hamilton
2263:Republic of Venice
2196:Athenian democracy
2050:universal suffrage
2046:
1966:voter registration
1762:Indirect elections
1656:
1471:
1382:Positional systems
1377:Positional systems
1299:
1235:
1219:party block voting
1206:
807:Discursive dilemma
766:Lesser evil voting
641:Supermixed systems
344:Largest remainders
202:Round-robin voting
70:
5120:Electoral systems
5102:
5101:
5000:Reversal symmetry
4909:Cumulative voting
4891:Semi-proportional
4866:Mixed single vote
4832:
4831:
4708:Mixed single vote
4616:Exhaustive ballot
4579:Copeland's method
4574:Condorcet methods
4514:Electoral systems
4142:"STV Information"
3992:Political Parties
3658:Glossary of Terms
3597:978-3-598-21813-2
3386:Electronic voting
3366:
3365:
3323:electoral college
3313:electoral college
3303:electoral college
3201:cumulative voting
2795:electoral college
2776:contingent voting
2662:Gibbard's theorem
2640:barriers to entry
2350:Hamilton's method
2294:Condorcet paradox
2290:Condorcet methods
2258:electoral college
2250:electing the Doge
2210:and proposals of
2062:none of the above
2058:compulsory voting
1915:majority judgment
1860:positional voting
1836:Maximal lotteries
1820:Condorcet methods
1789:electoral college
1769:electoral college
1756:primary elections
1739:Primary elections
1734:Primary elections
1515:largest remainder
1366:exhaustive ballot
1304:Condorcet-methods
1101:Gibbard's theorem
998:campaign spending
970:
969:
857:Gibbard's theorem
797:Dominance paradox
734:Perverse response
438:Phragmen's method
304:Majority judgment
232:Positional voting
190:Condorcet methods
58:electoral systems
16:(Redirected from
5157:
5041:Liquid democracy
4693:
4692:
4673:Two-round system
4584:Dodgson's method
4507:
4500:
4493:
4484:
4483:
4452:
4451:
4411:
4405:
4404:
4384:
4378:
4377:
4339:
4333:
4332:
4330:
4328:
4316:(1/2): 458â466.
4301:
4295:
4294:
4282:
4276:
4275:
4273:
4272:
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4252:
4251:
4249:
4248:
4234:
4225:
4224:
4222:
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4207:
4201:
4200:
4168:
4162:
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4157:
4138:
4132:
4122:
4116:
4109:
4103:
4096:
4090:
4083:
4077:
4074:
4068:
4054:
4048:
4041:
4035:
4028:
4022:
4008:
4002:
3988:
3982:
3975:
3969:
3968:
3966:
3964:
3932:
3926:
3919:
3913:
3907:
3901:
3893:
3887:
3872:
3866:
3860:
3851:
3850:Vol. 3, pp. 3â38
3840:
3834:
3828:
3822:
3821:
3820:on Apr 11, 2021.
3816:. Archived from
3805:
3799:
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3777:
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3627:
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3607:
3606:
3605:
3604:
3571:
3565:
3560:Lippman, David.
3558:
3552:
3539:
3533:
3527:
3521:
3520:
3515:
3514:
3507:Election Science
3499:
3493:
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3333:
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3276:
3266:
3254:
3245: Partially
3244:
3234:
3224:
3214:
3194:
3188:
3178:
3168:
3158:
3141:
3134:Two-round system
3131:
3121:
3108:
3099:
3093:
3087:
3075:
3062:
3052:
3042:
3028:
3022:
3016:
3006:
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2947:
2937:
2927:
2917:
2901:
2891:
2882:
2872:
2862:
2845:
2838:Two-round system
2835:
2825:
2813:
2807:
2801:
2792:
2783:
2769:
2762:Two-round system
2759:
2749:
2737:
2722:
2711:
2704:
2703:
2680:Alternative vote
2648:political apathy
2634:, complexity of
2549:have failed (in
2506:electoral reform
2472:Electoral reform
2430:Dodgson's method
2418:Edward J. Nanson
2342:Webster's method
2326:Thomas Jefferson
2233:
2227:
2200:selection by lot
2043:
2042:
2036:
2035:
2029:
2028:
2022:
2021:
2015:
2014:
1677:In compensatory
1648:
1642:
1636:
1630:
1625:Non-compensatory
1621:
1615:
1605:
1595:
1569:Pitcairn Islands
1467:
1461:
1455:
1449:
1443:
1437:
1431:
1425:
1342:two-round system
1326:Papua New Guinea
1292:
1283:
1277:Two-round system
1274:
1238:Plurality voting
1202:
1196:
1190:
1184:
1178:
1172:
1166:
1160:
1069:mechanism design
962:
955:
948:
934:
933:
921:
920:
909:
908:
864:Positive results
759:Strategic voting
656:Majority jackpot
613:
602:
473:Liquid democracy
349:National remnant
339:Highest averages
276:
261:
246:
178:
169:Alternative vote
167:
151:Partisan primary
143:
84:Mechanism design
37:
36:
21:
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5160:
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5158:
5156:
5155:
5154:
5105:
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5103:
5098:
5081:
5060:
5014:
5005:Smith criterion
4918:
4885:
4846:Parallel voting
4828:
4824:Imperiali quota
4797:
4764:
4682:
4636:Contingent vote
4599:Nanson's method
4557:Unified primary
4547:Approval voting
4533:
4516:
4511:
4477:Wayback Machine
4461:
4456:
4455:
4412:
4408:
4385:
4381:
4358:10.2307/2952255
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3908:
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3894:
3890:
3882:Wayback Machine
3873:
3869:
3861:
3854:
3848:Studia Lulliana
3841:
3837:
3829:
3825:
3806:
3802:
3789:Vote and Voting
3787:, ed. (1911). "
3772:
3770:
3769:
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3708:Wayback Machine
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3665:Wayback Machine
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3549:Wayback Machine
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3528:
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3496:
3487:
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3463:
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3453:Wayback Machine
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3272:
3269:Parallel voting
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3018:
3014:
3012:
3009:Parallel voting
3004:
3002:
2990:
2988:
2976:
2971:
2964:
2962:
2954:
2945:
2943:
2935:
2933:
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2923:
2915:
2906:
2902: Modified
2899:
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2757:
2755:
2747:
2738:
2723:
2712:
2702:
2654:Arrow's theorem
2619:
2613:
2590:approval voting
2575:2011 referendum
2534:
2518:1993 referendum
2498:approval voting
2474:
2468:
2448:progressive era
2422:Nanson's method
2405:
2271:
2192:
2190:Early democracy
2159:
2154:
2084:. Historically
2040:
2038:
2033:
2031:
2026:
2024:
2019:
2017:
2012:
1982:absentee voting
1950:
1926:weighted voting
1913:(including the
1891:approval voting
1805:
1764:
1736:
1664:parallel voting
1654:
1646:
1644:
1640:
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1634:
1632:
1628:
1623:
1619:
1617:
1613:
1611:
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1601:
1593:
1588:
1581:
1531:electoral quota
1511:highest average
1469:
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1453:
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1447:
1445:
1441:
1439:
1435:
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1429:
1427:
1423:
1415:
1410:
1379:
1330:contingent vote
1297:
1290:
1288:
1281:
1279:
1272:
1264:
1255:Approval voting
1227:
1211:
1204:
1200:
1198:
1194:
1192:
1188:
1186:
1182:
1180:
1176:
1174:
1170:
1168:
1164:
1162:
1158:
1127:
1119:Main articles:
1117:
1109:strategic voter
1105:straightforward
1014:political party
966:
928:
927:
915:
903:
895:
894:
861:
837:Arrow's theorem
827:
817:
816:
785:
755:
744:No-show paradox
725:
711:Cloning paradox
701:Spoiler effects
698:
688:
687:
662:
549:
532:
522:
521:
494:
485:Maximal lottery
452:
433:Thiele's method
422:
392:
324:
314:
313:
299:Approval voting
287:Cardinal voting
283:
228:
222:Maximal lottery
186:
118:
108:
35:
32:
23:
22:
15:
12:
11:
5:
5163:
5153:
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4992:
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4942:
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4916:
4911:
4906:
4904:Limited voting
4901:
4895:
4893:
4887:
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4858:
4853:
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4675:
4670:
4665:
4660:
4655:
4650:
4645:
4644:
4643:
4638:
4633:
4631:Coombs' method
4623:
4618:
4613:
4612:
4611:
4609:Schulze method
4606:
4601:
4596:
4591:
4586:
4581:
4571:
4569:Bucklin voting
4566:
4561:
4560:
4559:
4554:
4543:
4541:
4535:
4534:
4521:
4518:
4517:
4510:
4509:
4502:
4495:
4487:
4481:
4480:
4467:
4460:
4459:External links
4457:
4454:
4453:
4406:
4395:(2): 167â181.
4379:
4334:
4296:
4277:
4253:
4226:
4202:
4183:(4): 569â587.
4163:
4133:
4117:
4104:
4091:
4078:
4069:
4049:
4036:
4023:
4003:
3983:
3970:
3951:
3927:
3914:
3902:
3888:
3867:
3852:
3835:
3823:
3800:
3785:Chisholm, Hugh
3760:
3748:
3736:
3724:
3712:
3693:
3681:
3669:
3645:
3633:
3608:
3596:
3566:
3553:
3534:
3522:
3494:
3477:(4): 355â376.
3457:
3422:
3421:
3419:
3416:
3414:
3411:
3409:
3408:
3403:
3401:Spoiler effect
3398:
3393:
3388:
3383:
3378:
3372:
3370:
3367:
3364:
3363:
3354:
3345:
3336:
3330:
3317:
3307:
3297:
3288:
3279:
3273:
3263:
3251:
3241:
3231:
3221:
3211:
3197:Limited voting
3191:
3185:
3175:
3165:
3155:
3138:
3128:
3118:
3112:
3105:
3096:
3090:
3084:
3072:
3070:(compensatory)
3059:
3057:(compensatory)
3049:
3039:
3025:
3019:
3013:
3003:
2993: Limited
2989:
2975:
2963:
2953:
2944:
2934:
2924:
2914:
2898:
2888:
2885:Limited voting
2879:
2869:
2859:
2842:
2832:
2822:
2816:
2810:
2804:
2798:
2789:
2780:
2766:
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2743:
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2731:
2716:
2701:
2698:
2697:
2696:
2693:
2690:
2687:
2684:
2681:
2678:
2675:
2672:
2646:, and reduced
2615:Main article:
2612:
2609:
2571:United Kingdom
2533:
2530:
2494:Peter Fishburn
2470:Main article:
2467:
2464:
2456:Bucklin voting
2404:
2401:
2369:United Kingdom
2338:D'Hondt method
2330:Daniel Webster
2270:
2267:
2216:plurality vote
2191:
2188:
2163:ancient Greece
2158:
2157:Pre-democratic
2155:
2153:
2150:
2124:Reserved seats
2082:gerrymandering
2069:constituencies
1990:machine voting
1970:polling places
1949:
1946:
1942:1965 elections
1924:Historically,
1856:Coombs' method
1818:, the various
1816:Bucklin voting
1812:Ranked systems
1804:
1801:
1763:
1760:
1747:vote splitting
1735:
1732:
1728:2019 elections
1690:overhang seats
1651:Majority bonus
1645:
1639:
1633:
1627:
1618:
1612:
1602:
1592:
1580:
1577:
1500:leveling seats
1464:
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1434:
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1422:
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1411:
1409:
1406:
1378:
1375:
1289:
1280:
1271:
1263:
1262:Runoff systems
1260:
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1223:
1210:
1207:
1199:
1193:
1187:
1181:
1175:
1169:
1163:
1157:
1116:
1113:
1097:spoiler effect
1091:(showing that
1085:mathematicians
968:
967:
965:
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950:
942:
939:
938:
926:
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913:
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814:
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804:
799:
784:
783:
781:Turkey-raising
778:
773:
768:
754:
753:
752:
751:
741:
736:
724:
723:
721:Center squeeze
718:
713:
708:
706:Spoiler effect
699:
694:
693:
690:
689:
686:
685:
680:
679:
678:
665:By ballot type
661:
660:
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638:
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634:
629:
619:
618:
617:
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571:
566:
548:
547:
542:
533:
528:
527:
524:
523:
520:
519:
517:Limited voting
514:
513:
512:
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487:
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477:
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451:
450:
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440:
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405:
391:
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386:Localized list
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354:Biproportional
351:
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209:
199:
185:
184:
183:
182:
171:
158:Instant-runoff
155:
154:
153:
145:Jungle primary
132:
121:Single vote -
119:
114:
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109:
107:
106:
96:
91:
86:
81:
75:
72:
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61:
60:
50:
49:
33:
18:Voting systems
9:
6:
4:
3:
2:
5162:
5151:
5148:
5146:
5143:
5141:
5138:
5136:
5133:
5131:
5128:
5126:
5125:Voting theory
5123:
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5110:
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4943:
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4938:
4936:
4933:
4931:
4928:
4927:
4925:
4921:
4915:
4912:
4910:
4907:
4905:
4902:
4900:
4897:
4896:
4894:
4892:
4888:
4882:
4879:
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4859:
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4779:
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4771:
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4758:
4756:
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4709:
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4565:
4562:
4558:
4555:
4553:
4550:
4549:
4548:
4545:
4544:
4542:
4540:
4539:Single-winner
4536:
4532:
4530:
4526:
4519:
4515:
4508:
4503:
4501:
4496:
4494:
4489:
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4300:
4292:
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4267:
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4239:
4233:
4231:
4216:
4212:
4206:
4198:
4194:
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4182:
4178:
4174:
4167:
4151:
4147:
4143:
4137:
4130:
4126:
4121:
4114:
4108:
4101:
4095:
4088:
4082:
4073:
4067:
4066:0-19-828054-8
4063:
4059:
4053:
4046:
4040:
4033:
4027:
4021:
4020:0-300-01517-8
4017:
4013:
4007:
4001:
4000:0-416-68320-7
3997:
3993:
3987:
3980:
3974:
3958:
3954:
3952:9780868408583
3948:
3944:
3940:
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3931:
3924:
3918:
3912:
3906:
3900:
3897:
3892:
3886:
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3876:
3871:
3864:
3859:
3857:
3849:
3845:
3839:
3833:
3827:
3819:
3815:
3811:
3804:
3796:
3795:
3790:
3786:
3781:
3780:public domain
3767:
3765:
3757:
3752:
3745:
3740:
3733:
3728:
3721:
3716:
3709:
3705:
3702:
3697:
3690:
3685:
3678:
3673:
3666:
3662:
3659:
3654:
3652:
3650:
3642:
3637:
3622:
3618:
3612:
3599:
3593:
3589:
3585:
3581:
3577:
3570:
3563:
3562:Voting Theory
3557:
3550:
3546:
3543:
3538:
3531:
3526:
3519:
3508:
3504:
3498:
3484:
3480:
3476:
3472:
3468:
3461:
3454:
3450:
3447:
3442:
3440:
3438:
3436:
3434:
3432:
3430:
3428:
3423:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3373:
3361:
3352:
3351:In transition
3343:
3342:head of state
3329:
3324:
3314:
3304:
3296:
3287:
3270:
3262:
3258:
3248:
3238:
3228:
3218:
3210:
3208:
3202:
3198:
3182:
3172:
3162:
3154:
3152:
3145:
3135:
3125:
3116:
3113:
3103:
3102:In transition
3083:
3079:
3069:
3066:
3056:
3046:
3036:
3032:
3010:
3000:
2996:
2986:
2982:
2974:
2970:
2960:
2951:
2941:
2931:
2921:
2913:
2911:
2905:
2895:
2886:
2876:
2866:
2858:
2856:
2849:
2839:
2829:
2820:
2817:
2796:
2787:
2777:
2773:
2763:
2753:
2745:
2744:
2741:
2736:
2732:
2730:
2726:
2721:
2717:
2715:
2714:Head of state
2710:
2706:
2705:
2694:
2691:
2688:
2685:
2682:
2679:
2676:
2673:
2670:
2669:
2668:
2665:
2663:
2659:
2655:
2651:
2649:
2645:
2644:voter turnout
2641:
2637:
2636:vote counting
2633:
2629:
2628:voter turnout
2625:
2618:
2608:
2605:
2603:
2599:
2595:
2591:
2586:
2584:
2580:
2576:
2572:
2568:
2567:Massachusetts
2564:
2560:
2556:
2552:
2548:
2544:
2539:
2529:
2527:
2523:
2519:
2515:
2511:
2507:
2502:
2499:
2495:
2491:
2487:
2486:ranked voting
2483:
2479:
2473:
2463:
2461:
2457:
2453:
2449:
2444:
2442:
2437:
2435:
2431:
2427:
2426:Lewis Carroll
2423:
2419:
2415:
2411:
2400:
2398:
2394:
2390:
2386:
2382:
2378:
2374:
2370:
2366:
2362:
2358:
2353:
2351:
2347:
2343:
2339:
2335:
2331:
2327:
2323:
2319:
2315:
2311:
2306:
2303:
2299:
2295:
2291:
2287:
2283:
2279:
2276:proposed the
2275:
2266:
2264:
2259:
2255:
2251:
2246:
2244:
2240:
2235:
2232:
2226:
2221:
2217:
2213:
2209:
2206:included all
2203:
2201:
2197:
2187:
2185:
2181:
2177:
2172:
2168:
2164:
2149:
2147:
2143:
2139:
2134:
2130:
2125:
2121:
2119:
2115:
2111:
2107:
2103:
2099:
2095:
2089:
2087:
2083:
2079:
2078:redistricting
2074:
2073:apportionment
2070:
2065:
2063:
2059:
2055:
2051:
2009:
2005:
2003:
1999:
1995:
1991:
1987:
1983:
1979:
1978:postal voting
1975:
1974:online voting
1971:
1967:
1963:
1959:
1958:electoral law
1955:
1945:
1943:
1939:
1935:
1931:
1927:
1922:
1920:
1916:
1912:
1908:
1904:
1900:
1896:
1892:
1888:
1884:
1881:
1877:
1873:
1872:Wright system
1869:
1865:
1861:
1857:
1853:
1849:
1845:
1841:
1837:
1833:
1829:
1825:
1821:
1817:
1813:
1809:
1800:
1798:
1794:
1790:
1786:
1785:United States
1782:
1778:
1774:
1770:
1759:
1757:
1752:
1748:
1744:
1740:
1731:
1729:
1725:
1721:
1716:
1712:
1707:
1705:
1701:
1699:
1695:
1691:
1686:
1684:
1680:
1675:
1671:
1669:
1665:
1661:
1660:mixed systems
1652:
1626:
1609:
1599:
1591:
1585:
1579:Mixed systems
1576:
1574:
1570:
1566:
1562:
1557:
1554:
1550:
1546:
1542:
1538:
1534:
1532:
1528:
1524:
1520:
1516:
1512:
1508:
1503:
1501:
1497:
1493:
1489:
1485:
1481:
1477:
1475:
1419:
1405:
1402:
1397:
1395:
1391:
1387:
1383:
1374:
1372:
1367:
1362:
1360:
1356:
1352:
1347:
1343:
1338:
1336:
1331:
1327:
1323:
1319:
1314:
1312:
1311:ranked voting
1307:
1305:
1296:
1287:
1278:
1268:
1259:
1256:
1252:
1250:
1245:
1243:
1239:
1231:
1222:
1220:
1215:
1155:
1151:
1146:
1142:
1140:
1139:mixed systems
1136:
1132:
1126:
1122:
1112:
1110:
1106:
1102:
1098:
1094:
1093:ranked voting
1090:
1086:
1082:
1078:
1074:
1070:
1066:
1065:social choice
1062:
1058:
1054:
1049:
1047:
1046:superposition
1043:
1039:
1035:
1031:
1027:
1023:
1022:single-winner
1019:
1015:
1011:
1005:
1003:
999:
995:
991:
987:
983:
979:
978:voting system
975:
963:
958:
956:
951:
949:
944:
943:
941:
940:
937:
932:
924:
919:
914:
912:
907:
902:
901:
899:
898:
891:
888:
886:
883:
881:
880:May's theorem
878:
876:
873:
871:
868:
867:
866:
865:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
834:
833:
832:
826:
821:
820:
813:
810:
808:
805:
803:
800:
798:
795:
794:
793:
792:
791:
790:majority rule
788:Paradoxes of
782:
779:
777:
774:
772:
769:
767:
764:
763:
762:
761:
760:
750:
747:
746:
745:
742:
740:
737:
735:
732:
731:
730:
729:
722:
719:
717:
714:
712:
709:
707:
704:
703:
702:
697:
692:
691:
684:
681:
677:
674:
673:
672:
669:
668:
667:
666:
657:
654:
652:
649:
647:
644:
643:
642:
639:
633:
630:
628:
625:
624:
623:
620:
616:
611:
607:
605:
600:
596:
595:
594:
591:
590:
589:
588:
584:
580:
577:
575:
572:
570:
567:
565:
562:
561:
560:
559:
554:
553:
552:
546:
543:
541:
538:
537:
536:
531:
530:Mixed systems
526:
525:
518:
515:
511:
508:
507:
506:
503:
502:
501:
500:
499:
491:
490:Random ballot
488:
486:
483:
481:
478:
474:
471:
469:
466:
465:
464:
461:
460:
459:
458:
457:
449:
446:
444:
441:
439:
436:
434:
431:
430:
429:
428:
427:
419:
416:
414:
411:
409:
406:
404:
401:
400:
399:
398:
397:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
363:
362:
359:
355:
352:
350:
347:
345:
342:
340:
337:
336:
335:
334:Apportionment
332:
331:
330:
329:
323:
318:
317:
310:
307:
305:
302:
300:
297:
295:
292:
291:
290:
289:
288:
279:
275:
270:
269:Antiplurality
267:
264:
260:
255:
252:
249:
245:
240:
237:
236:
235:
234:
233:
223:
220:
218:
215:
213:
210:
208:
205:
204:
203:
200:
198:
197:Condorcet-IRV
195:
194:
193:
192:
191:
181:
176:
172:
170:
165:
161:
160:
159:
156:
152:
149:
148:
146:
141:
136:
133:
131:
128:
127:
126:
124:
117:
112:
111:
104:
100:
97:
95:
92:
90:
87:
85:
82:
80:
79:Social choice
77:
76:
74:
73:
67:
63:
62:
59:
55:
54:Social choice
52:
51:
47:
43:
39:
38:
30:
19:
5093:
5087:
4703:Mixed-member
4688:Proportional
4663:Score voting
4604:Ranked pairs
4523:Part of the
4522:
4513:
4423:
4419:
4409:
4392:
4388:
4382:
4349:
4343:
4337:
4325:. Retrieved
4313:
4309:
4299:
4290:
4280:
4269:. Retrieved
4265:
4256:
4245:. Retrieved
4241:
4218:. Retrieved
4214:
4205:
4180:
4176:
4166:
4154:. Retrieved
4136:
4128:
4120:
4112:
4107:
4099:
4094:
4086:
4081:
4072:
4057:
4052:
4044:
4039:
4031:
4026:
4011:
4006:
3991:
3986:
3978:
3973:
3961:. Retrieved
3937:
3930:
3917:
3910:
3905:
3891:
3870:
3847:
3838:
3826:
3818:the original
3813:
3803:
3792:
3751:
3739:
3727:
3715:
3696:
3684:
3672:
3636:
3624:. Retrieved
3620:
3611:
3601:, retrieved
3579:
3569:
3556:
3537:
3525:
3517:
3511:. Retrieved
3506:
3497:
3486:. Retrieved
3474:
3470:
3460:
3327:
3294:
3285:
3260:
3207:proportional
3204:
3161:Block voting
3151:majoritarian
3148:
3081:
2972:
2910:proportional
2907:
2865:Block voting
2855:majoritarian
2852:
2774:, including
2666:
2652:
2632:wasted votes
2620:
2606:
2587:
2535:
2503:
2490:Steven Brams
2475:
2445:
2438:
2434:proxy voting
2406:
2354:
2349:
2341:
2333:
2307:
2297:
2272:
2247:
2236:
2204:
2193:
2160:
2122:
2090:
2066:
2047:
1954:constitution
1951:
1923:
1895:range voting
1885:
1848:Ranked pairs
1832:Kemeny-Young
1810:
1806:
1765:
1737:
1708:
1702:
1687:
1676:
1672:
1657:
1624:
1608:Vote linkage
1598:seat linkage
1590:Compensatory
1589:
1558:
1535:
1523:vote average
1522:
1518:
1504:
1478:
1472:
1398:
1380:
1363:
1339:
1315:
1308:
1300:
1253:
1249:block voting
1246:
1236:
1216:
1212:
1128:
1053:mathematical
1050:
1006:
977:
973:
971:
863:
862:
829:
787:
786:
771:Exaggeration
757:
756:
727:
726:
700:
664:
663:
632:Mixed ballot
587:Compensatory
585:
558:compensatory
555:
550:
534:
496:
495:
454:
453:
424:
423:
394:
393:
381:List-free PR
326:
294:Score voting
285:
284:
230:
229:
217:Ranked pairs
188:
187:
120:
5046:Spoilt vote
4809:Droop quota
4748:Schulze STV
4723:Ruralâurban
4668:STAR voting
4564:Borda count
4426:(1): 3â19.
4352:(1): 1â14.
4327:25 February
4266:Ballotpedia
4242:Ballotpedia
4125:Carles Boix
3963:25 February
3626:25 February
3396:Matrix vote
3033:or limited
2904:Borda count
2786:legislature
2740:Upper house
2725:Lower house
2543:pathologies
2510:New Zealand
2478:game theory
2476:The use of
2460:pathologies
2373:Thomas Hare
2302:Ramon Llull
2278:Borda count
2112:led to the
2106:fourth vote
1917:), and the
1868:Schulze STV
1553:Droop quota
1496:Netherlands
1484:closed list
1394:Borda count
1386:Borda Count
1010:legislature
671:Single vote
574:Conditional
569:Coexistence
418:Quota Borda
408:Schulze STV
366:Closed list
309:STAR voting
254:Borda count
5135:Psephology
5109:Categories
5065:Comparison
4819:Hare quota
4769:Allocation
4755:Spare vote
4743:Hare-Clark
4713:Party-list
4271:2024-09-03
4247:2024-09-03
4220:2024-09-03
4156:6 December
3943:UNSW Press
3603:2023-11-13
3513:2024-05-24
3488:2024-05-24
3418:References
3406:Psephology
3360:Unicameral
2399:colonies.
2361:Carl AndrĂŚ
2171:monarchies
1824:Copeland's
1715:San Marino
1335:Sri Lankan
1154:unicameral
776:Truncation
505:Cumulative
328:Party-list
103:By country
94:Comparison
5150:Elections
5056:Unseating
5051:Sortition
4653:Plurality
4529:Economics
4448:144919388
4440:1745-7289
4374:143172061
4197:1555-5623
3065:Two-round
2950:Panachage
2594:St. Louis
2441:Australia
2254:sortition
2225:discessio
2212:ostracism
1828:Dodgson's
1773:Mauritius
1751:Argentina
1488:open list
1384:like the
1351:ballotage
1322:Australia
1152:or sole (
1061:economics
1057:normative
1034:two-round
1026:plurality
990:candidate
974:electoral
683:Dual-vote
376:Panachage
371:Open list
361:List type
239:Plurality
135:Two-round
123:plurality
46:Economics
4923:Criteria
4876:Scorporo
4525:politics
4473:Archived
4150:Archived
3994:, Wiley
3957:Archived
3899:FairVote
3885:FairVote
3878:Archived
3704:Archived
3701:Suffrage
3661:Archived
3545:Archived
3483:25791202
3449:Archived
3381:Election
3369:See also
2656:and the
2377:Tasmania
2348:, while
2340:, as is
2208:lawsuits
2002:auditing
1936:for the
1934:Rhodesia
1870:and the
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