2564:
1239:
2221:
374:
1214:
77:
179:
1226:
36:
274:
2217:). However, the rate of decline varies according to the type of progression employed. Lower preferences are more influential in election outcomes where the chosen progression employs a sequence of weightings that descend relatively slowly with rank position. The more slowly weightings decline, the more consensual and less polarising positional voting becomes.
1845:= 1/2). Such weightings are inherently valid for use in positional voting systems provided that a legitimate common ratio is employed. Using a common ratio of zero, this form of positional voting has weightings of 1, 0, 0, 0, … and so produces ranking outcomes identical to that for first-past-the-post or
2378:
Although not categorised as positional voting electoral systems, some non-ranking methods can nevertheless be analysed mathematically as if they were by allocating points appropriately. Given the absence of strict monotonic ranking here, all favoured options are weighted identically with a high value
2184:
This method is more favourable to candidates with many first preferences than the conventional Borda count. It has been described as a system "somewhere between plurality and the Borda count, but as veering more towards plurality". Simulations show that 30% of Nauru elections would produce different
4147:
To a greater or lesser extent, all positional voting systems are vulnerable to teaming; with the sole exception of a plurality-equivalent one. As only first preferences have any value, employing clones to ‘bury’ opponents down in rank never affects election outcomes. However, precisely because only
3237:
in determining the winning outcome. With all voters either strongly for or against
Memphis, it is a very ‘polarized’ option so Memphis finishes first under plurality and last with anti-plurality. Given its central location, Nashville is the ‘consensus’ option here. It wins under the Borda count and
1334:
preference for each option on the ballot in strict descending rank order. However, a particular positional voting system may permit voters to truncate their preferences after expressing one or more of them and to leave the remaining options unranked and consequently worthless. Similarly, some other
1326:
by expressing their preferences in rank order. The rank position of each voter preference is allotted a specific fixed weighting. Typically, the higher the rank of the preference, the more points it is worth. Occasionally, it may share the same weighting as a lower-ranked preference but it is never
3645:
of clones is quite likely to significantly affect the outcome of an election and it is often the intention behind doing so. A clone is a nominally identical candidate to one already standing where voters are unable to distinguish between them unless informed as to which of the two is the clone. As
3628:
Given the withdrawal of candidate B, the winner is now C and no longer A. Regardless of the specific points awarded to the rank positions of the preferences, there are always some cases where the addition or deletion of an irrelevant alternative alters the outcome of an election. Hence, positional
2365:
for positional voting does not have to be the reciprocal of such an integer. Any value between zero and just less than one is valid. For a slower descent of weightings than that generated using the binary number system, a common ratio greater than one-half must be employed. The higher the value of
1290:
in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is
4148:
first preferences have any value, plurality is instead particularly susceptible to vote-splitting. To a lesser extent, many other positional voting systems are also affected by ‘spoiler’ candidates. While inherently vulnerable to teaming, the Borda count is however invulnerable to vote-splitting.
1352:
highest-ranked options are selected. Positional voting is not only a means of identifying a single winner but also a method for converting sets of individual preferences (ranked ballots) into one collective and fully rank-ordered set. It is possible and legitimate for options to be tied in this
1361:
Consider a positional voting election for choosing a single winner from three options A, B and C. No truncation or ties are permitted and a first, second and third preference is here worth 4, 2 and 1 point respectively. There are then six different ways in which each voter may rank order these
1684:
so that the last preference is worth zero. Although it is convenient for counting, the common difference need not be fixed at one since the overall ranking of the candidates is unaffected by its specific value. Hence, despite generating differing tallies, any value of
1307:). The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
1343:
The counting process is straightforward. All the preferences cast by voters are awarded the points associated with their rank position. Then, all the points for each option are tallied and the one with the most points is the winner. Where a few winners
1339:
only their top ten preferences are ranked by each country although many more than ten songs compete in the contest. Again, unranked preferences have no value. In positional voting, ranked ballots with tied options are normally considered as invalid.
3512:
Therefore, candidate A is the single winner and candidates B and C are the two losers. As an irrelevant alternative (loser), whether B enters the contest or not should make no difference to A winning provided the voting system is IIA compliant.
3368:
Prior to voter preferences being cast, voting systems that treat all voters as equals and all candidates as equals pass the first two criteria above. So, like any other ranking system, positional voting cannot pass both of the other two. It is
2524:
is not fixed but varies according to the individual ranked ballots being cast. As rank positions would then have different weightings on different ballots, approval voting is not a positional voting system; nor can it be analysed as such.
2009:
2200:
uses a first preference worth 12 points, while a second one is given 10 points. The next eight consecutive preferences are awarded 8, 7, 6, 5, 4, 3, 2 and 1 point. All remaining preferences receive zero points.
3012:
order. The slower the decline in weighting values with descending rank order, the greater is the sum of the four weightings; see end column. Plurality declines the fastest while anti-plurality is the slowest.
2390:
and the two weightings be one point for these favoured candidates and zero points for those not favoured. When analytically represented using positional voting, favoured candidates must be listed in the top
3385:
Consider a positional voting election with three candidates A, B and C where a first, second and third preference is worth 4, 2 and 1 point respectively. The 12 voters cast their ranked ballots as follows:
2323:
The weightings of the digit positions in the binary number system were chosen here to highlight an example of a geometric progression in positional voting. In fact, the consecutive weightings of any
3646:
tied rankings are not permitted, these two candidates must be ranked by voters in adjacent positions instead. Cloning may well promote or demote the collective ranking of any non-cloned candidate.
2291:
To aid comparison, the actual weightings have been normalised; namely that the first preference is set at one and the other weightings in the particular sequence are scaled by the same factor of
1833:
1708:
Common systems for evaluating preferences, other than Borda, are typically "top-heavy". In other words, the method focuses on how many voters consider a candidate one of their "favourites".
1314:: in the former, the score that each voter gives to each candidate is uniquely determined by the candidate's rank; in the latter, the each voter is free to give any score to any candidate.
3377:. This failure means that the addition or deletion of a non-winning (irrelevant) candidate may alter who wins the election despite the ranked preferences of all voters remaining the same.
1197:
3649:
Consider a positional voting election in which three candidates may compete. There are just 12 voters and a first, second and third preference is worth 4, 2 and 1 point respectively.
881:
288:
1656:
4120:
By ‘team’ B signalling to its own supporters - but not to A supporters - which of its two candidates it wants to win, B has achieved its objective of gaining victory for B
1896:
900:
2316:
in a harmonic progression does affect the rate of its decline. The higher its value, the faster the weightings descend. Whereas the lower the value of the common ratio
4159:
has published various works that mathematically analyse positional voting electoral systems. The fundamental method explored in his analysis is the Borda count.
2853:, the table below states the value of each of the four weightings for a range of different positional voting systems that could be employed for this election:
1857:
Alternatively, the denominators of the above fractional weightings could form an arithmetic progression instead; namely 1/1, 1/2, 1/3, 1/4 and so on down to
1267:
1104:
4331:
1726:(FPP), the most-preferred option receives 1 point while all other options receive 0 points each. This is the most top-heavy positional voting system.
3125:
For each potential positional voting system that could be used in this election, the consequent overall rank order of the options is shown below:
1530:
Therefore, having the highest tally, option A is the winner here. Note that the election result also generates a full ranking of all the options.
3516:
Rerunning the election without candidate B while maintaining the correct ranked preferences for A and C, the 12 ballots are now cast as follows:
4263:
Fraenkel, Jon; Grofman, Bernard (2014-04-03). "The Borda Count and its real-world alternatives: Comparing scoring rules in Nauru and
Slovenia".
3652:
In this first scenario, two candidates A and B are nominated but no clone enters the contest. The voters cast their ranked ballots as follows:
2357:
As it has the smallest radix, the rate of decline in preference weightings is slowest when using the binary number system. Although the radix
2552:
4133:
3956:
3016:
For each positional voting system, the tallies for each of the four city options are determined from the above two tables and stated below:
2405:
rank positions. This is essential as the weighting of each rank position is fixed and common to each and every ballot in positional voting.
2064:
uses a variant called the
Dowdall system: the voter awards the first-ranked candidate with 1 point, while the 2nd-ranked candidate receives
4781:
2327:
can be employed since they all constitute geometric progressions. For example, the binary, ternary, octal and decimal number systems use a
4549:
3955:
By adding a clone of itself, B has handed victory to candidate A. This counter-productive ‘spoiler’ effect or act of self-harm is called
2041:
between adjacent denominators is also one. Numerous other harmonic sequences can also be used in positional voting. For example, setting
1770:
958:
292:
3267:
3247:
4211:
Reilly, Benjamin (2002). "Social Choice in the South Seas: Electoral
Innovation and the Borda Count in the Pacific Island Countries".
2379:
and all the remaining options with a common lower value. The two validity criteria for a sequence of weightings are hence satisfied.
1580:
th) preference that is worth just 1 point. So, for example, the points are respectively 4, 3, 2 and 1 for a four-candidate election.
4946:
4677:
4529:
990:
852:
847:
17:
1542:
in the rank of each candidate. In other words, a worse-ranked candidate must receive fewer points than a better-ranked candidate.
4941:
4776:
4554:
3374:
3361:
3302:
1260:
953:
189:
247:
141:
4539:
4324:
3342:, no ranked voting system can satisfy all of the following four criteria when collectively ranking three or more alternatives:
635:
3962:
To promote itself into first place, B should instead instruct all its supporters to always prefer one of its candidates (say B
2301:
The relative decline of weightings in any arithmetic progression is constant as it is not a function of the common difference
219:
113:
1750:
must be less than one so that weightings decrease as preferences descend in rank. Where the value of the first preference is
1467:
After voting closes, the points awarded by the voters are then tallied and the options ranked according to the points total.
1292:
4903:
4128:(an irrelevant alternative) has pushed the second preferences for A into third place while preferences for ‘team’ B (B or B
1159:
410:
4586:
226:
120:
2354:
ratios are respectively 1/2, 1/3, 1/8 and 1/10 for these positional number systems when employed in positional voting.
2228:
This figure illustrates such declines over ten preferences for the following four positional voting electoral systems:
1865:
1253:
94:
49:
4317:
4195:
2545:
2093:
1154:
332:
314:
160:
63:
1607:
4771:
4717:
3638:
3339:
3308:
1144:
894:
865:
805:
233:
127:
4898:
4569:
2224:
Relative decline in preference weightings with descending rank order for four positional voting electoral systems
876:
401:
296:
4921:
4697:
939:
204:
98:
1003:
215:
109:
581:
566:
551:
4124:. With no clone, A and B tie with equal numbers of first and second preferences. The introduction of clone B
1538:
For positional voting, any distribution of points to the rank positions is valid, so long as the points are
4740:
4725:
4544:
4132:) are unchanged in the first and third scenarios. This wilful act to ‘bury’ A and promote itself is called
3753:
Suppose B, anticipating this tie, decided to enter a clone of itself. The nominated candidates are now A, B
2538:
2451:
2089:
817:
740:
661:
4534:
4791:
4514:
4504:
4365:
3331:
1182:
629:
611:
452:
4756:
4447:
1717:
1073:
1056:
1023:
787:
775:
745:
546:
504:
437:
4806:
4761:
4707:
4619:
3319:
2495:
929:
922:
406:
4225:
2408:
Unranked single-winner methods that can be analysed as positional voting electoral systems include:
4796:
4682:
4640:
4559:
4484:
4420:
4378:
3250:
to evaluate its strengths and weaknesses in comparison with other single-winner electoral methods.
1837:
For example, the sequence of consecutively halved weightings of 1, 1/2, 1/4, 1/8, … as used in the
983:
911:
763:
750:
733:
710:
688:
651:
641:
2099:
Using the above example, in Nauru the point distribution among the four candidates would be this:
2092:, an unrelated method.) A similar system of weighting lower-preference votes was used in the 1925
1192:
4821:
4811:
4786:
4602:
4479:
4415:
3282:
3277:
2578:
2197:
2085:
1336:
1109:
963:
646:
87:
2030:
1304:
1078:
283:
may contain an excessive amount of intricate detail that may interest only a particular audience
4862:
4801:
4664:
4220:
3287:
2597:
2361:(the number of unique digits used in the number system) has to be an integer, the common ratio
1697:
1138:
1018:
948:
755:
240:
134:
55:
4607:
2415:(FPTP): The most preferred option receives 1 point; all other options receive 0 points each. (
4766:
4687:
4452:
4144:
in a tit-for-tat retaliation then the original tie between A and ‘team’ B is re-established.
3272:
2425:
1739:
1046:
886:
770:
576:
555:
487:
465:
2049:
to 2 generates the reciprocals of all the odd numbers (1, 1/3, 1/5, 1/7, …) whereas letting
4836:
4405:
3642:
2603:
2591:
1746:
between adjacent weightings. In order to satisfy the two validity conditions, the value of
1177:
1164:
1132:
396:
200:
2732:
th preference, the following table defines the resultant tally calculation for each city:
2213:) of consecutive preferences from first to last decline monotonically with rank position (
8:
4816:
4410:
3351:
3314:
3262:
2574:
2428:: The least preferred option receives 0 points; all other options receive 1 point each. (
2395:
rank positions in any order on each ranked ballot and the other candidates in the bottom
1300:
1083:
917:
570:
2454:: The most preferred option receives 1 point; all other options receive 0 points each. (
2386:-candidate ranked ballot, let the permitted number of favoured candidates per ballot be
4857:
4467:
4425:
4280:
4238:
2585:
2502:
most preferred options receive 1 point each; all other options receive 0 points each. (
1873:
1335:
systems may limit the number of preferences that can be expressed. For example, in the
1243:
1114:
725:
509:
4826:
4735:
4692:
4612:
4457:
4442:
4400:
4284:
4191:
3370:
3356:
3325:
3292:
1539:
1291:
never worth more. A valid progression of points or weightings may be chosen at will (
1238:
1149:
1119:
1041:
978:
812:
514:
497:
365:
4867:
4499:
4355:
4340:
4272:
4242:
4230:
3346:
3257:
3246:
As a class of voting systems, positional voting can be evaluated against objective
2563:
2412:
2338:
is also the common ratio of the geometric progression going up in rank order while
2188:
The system was devised by Nauru's
Secretary for Justice (Desmond Dowdall) in 1971.
2004:{\displaystyle w_{n}={\frac {a^{2}}{a+(n-1)d}}={\frac {a}{1+{\frac {(n-1)d}{a}}}},}
1846:
1723:
1287:
1230:
1187:
1066:
780:
656:
482:
476:
458:
447:
442:
430:
391:
353:
2305:. In other words, the relative difference between adjacent weightings is fixed at
4915:
4831:
4672:
4650:
4462:
4383:
4373:
4351:
4276:
4156:
2517:
2220:
1331:
1218:
1051:
906:
871:
792:
703:
606:
529:
471:
349:
4234:
4730:
4435:
4395:
3750:
Given equal support, there is an evitable tie for first place between A and B.
2464:
1088:
1028:
1013:
824:
693:
668:
519:
4935:
4474:
1838:
1742:
may also be used in positional voting. Here, there is instead a common ratio
1323:
1284:
1097:
797:
585:
423:
386:
361:
1841:
system constitutes a geometric progression with a common ratio of one-half (
1295:) or it may form a mathematical sequence such as an arithmetic progression (
295:
any relevant information, and removing excessive detail that may be against
196:
4489:
4430:
1311:
837:
601:
594:
524:
373:
4872:
4635:
4574:
4494:
4390:
2520:, voters are free to favour as many or as few candidates as they wish so
1551:
1296:
715:
673:
616:
561:
1868:. These particular descending rank-order weightings are in fact used in
1693:
for a Borda count election will result in identical candidate rankings.
1213:
4645:
4581:
2057:
be 1/2 produces those of all the even numbers (1/2, 1/4, 1/6, 1/8, …).
4882:
4877:
2570:
2084:
of a point, etc. (This system should not be confused with the use of
683:
678:
4309:
178:
76:
4702:
4300:
3970:). In this third scenario, the 12 ballots are now cast as follows:
3785:. In this second scenario, the 12 ballots are now cast as follows:
1735:
1594:) is defined below; where the weighting of the first preference is
1550:
The classic example of a positional voting electoral system is the
934:
2482:) receive 1 point each; all other options receive 0 points each. (
4564:
4303:
Mathematical
Structure of Voting Paradoxes: II. Positional Voting
4136:. Note that if A signals to its own supporters to always prefer B
2342:
is the complementary common ratio descending in rank. Therefore,
720:
2320:
for a geometric progression, the faster its weightings decline.
4852:
2579:
All voters want the capital to be as close to them as possible.
1887:) is defined below; where the value of the first preference is
1225:
2370:, the slower the decrease in weightings with descending rank.
1362:
options. The 100 voters cast their ranked ballots as follows:
2328:
2324:
2061:
3241:
2588:, the largest city, but far from the others (42% of voters)
2577:. The population is concentrated around four major cities.
2443:
And unranked methods for multiple-winner elections (with
4258:
4256:
4254:
4252:
1864:. This further mathematical sequence is an example of a
4249:
1899:
1773:
1610:
1330:
Usually, every voter is required to express a unique
3253:
Positional voting satisfies the following criteria:
3234:
3009:
3761:. As the voters are unable to distinguish between B
3008:These five positional voting systems are listed in
2287:
Eurovision Song
Contest (non-zero preferences only)
1828:{\displaystyle w_{n}=ar^{n-1},\qquad 0\leq r\leq 1}
101:. Unsourced material may be challenged and removed.
2373:
2204:
2003:
1827:
1650:
4933:
3298:But it fails to satisfy the following criteria:
2185:outcomes if counted using standard Borda rules.
1348:) are instead required following the count, the
4262:
1696:The consecutive Borda count weightings form an
1554:. Typically, for a single-winner election with
1310:Positional voting should be distinguished from
2594:, near the center of the state (26% of voters)
2573:is holding an election on the location of its
1872:-candidate positional voting elections to the
1673:The value of the first preference need not be
1583:Mathematically, the point value or weighting (
4325:
2610:The preferences of each region's voters are:
2546:
1876:. For such electoral systems, the weighting (
1518:(20 + 10) x 4 + (18 + 16) x 2 + (24 + 12) x 1
1504:(12 + 16) x 4 + (24 + 10) x 2 + (18 + 20) x 1
1490:(24 + 18) x 4 + (12 + 20) x 2 + (16 + 10) x 1
1261:
4782:Independence of Smith-dominated alternatives
205:introducing citations to additional sources
2074:a point, the 3rd-ranked candidate receives
64:Learn how and when to remove these messages
4332:
4318:
4204:
2553:
2539:
2334:of 2, 3, 8 and 10 respectively. The value
1268:
1254:
4301:Economic Theory, Vol. 15, Issue 1, 2000:
4224:
3242:Evaluation against voting system criteria
1852:
1590:) associated with a given rank position (
333:Learn how and when to remove this message
315:Learn how and when to remove this message
161:Learn how and when to remove this message
3233:This table highlights the importance of
2219:
1558:candidates, a first preference is worth
1322:In positional voting, voters complete a
195:Relevant discussion may be found on the
27:Class of ranked-choice electoral systems
4777:Independence of irrelevant alternatives
4555:Sequential proportional approval voting
4265:Australian Journal of Political Science
4181:
4179:
4177:
4175:
4173:
4171:
3362:Independence of Irrelevant Alternatives
3303:Independence of Irrelevant Alternatives
2528:
2037:is worth one and the common difference
14:
4934:
4213:International Political Science Review
4210:
3375:independent of irrelevant alternatives
2606:, far to the northeast (17% of voters)
2209:In positional voting, the weightings (
1883:) allocated to a given rank position (
1533:
1317:
4339:
4313:
4190:. Springer-Verlag. pp. 101–103.
4185:
4051:The revised election outcome is now:
3334:(except when equivalent to plurality)
4168:
3238:the two other non-polarized systems
1761:) awarded to a given rank position (
1353:resultant set; even in first place.
267:
172:
99:adding citations to reliable sources
70:
29:
4587:Indirect single transferable voting
3579:The rerun election outcome is now:
1711:
1545:
24:
3769:, they are just a likely to rank B
372:
25:
4958:
4294:
3886:The new election outcome is now:
3637:Positional voting also fails the
2094:Oklahoma primary electoral system
1576:points and so on until the last (
45:This article has multiple issues.
2562:
2088:in proportional systems such as
1237:
1224:
1212:
1160:McKelvey–Schofield chaos theorem
806:Semi-proportional representation
438:First preference plurality (FPP)
272:
188:relies largely or entirely on a
177:
75:
34:
4947:Single-winner electoral systems
3701:The election outcome is hence:
3449:The election outcome is hence:
2600:, somewhat east (15% of voters)
2374:Analysis of non-ranking systems
2205:Comparison of progression types
2033:) system, the first preference
1809:
86:needs additional citations for
53:or discuss these issues on the
4942:Preferential electoral systems
4698:Mixed ballot transferable vote
3632:
3380:
2471:most preferred options (where
1983:
1971:
1944:
1932:
1651:{\displaystyle w_{n}=a-(n-1)d}
1642:
1630:
1198:Harsanyi's utilitarian theorem
1155:Moulin's impossibility theorem
1120:Conflicting majorities paradox
13:
1:
4162:
3629:voting is not IIA compliant.
3340:Arrow’s impossibility theorem
2843:For a first preference worth
2191:
1598:and the common difference is
1024:Frustrated majorities paradox
4899:Comparison of voting systems
4741:Satisfaction approval voting
4726:Single non-transferable vote
4545:Proportional approval voting
4277:10.1080/10361146.2014.900530
2452:Single non-transferable vote
2312:. In contrast, the value of
2253:Binary number system (where
2090:proportional approval voting
1734:An alternative mathematical
1729:
1703:
1670:, the number of candidates.
1562:points, a second preference
1193:Condorcet dominance theorems
1133:Social and collective choice
297:Knowledge's inclusion policy
7:
4505:Graduated majority judgment
4235:10.1177/0192512102023004002
4108:(0 x 4) + (9 x 2) + (3 x 1)
4091:(6 x 4) + (3 x 2) + (3 x 1)
4074:(6 x 4) + (0 x 2) + (6 x 1)
3943:(3 x 4) + (6 x 2) + (3 x 1)
3926:(3 x 4) + (6 x 2) + (3 x 1)
3909:(6 x 4) + (0 x 2) + (6 x 1)
3500:(3 x 4) + (4 x 2) + (5 x 1)
3486:(4 x 4) + (5 x 2) + (3 x 1)
3472:(5 x 4) + (3 x 2) + (4 x 1)
2741:Vote tally per 1200 voters
1569:points, a third preference
859:By mechanism of combination
630:Proportional representation
10:
4963:
4757:Condorcet winner criterion
4448:First-past-the-post voting
3268:Summability (with order N)
1724:first-preference plurality
1718:First-preference plurality
1715:
1356:
1057:Multiple districts paradox
788:Fractional approval voting
776:Interactive representation
4912:
4904:Voting systems by country
4891:
4845:
4807:Mutual majority criterion
4762:Condorcet loser criterion
4749:
4716:
4708:Vote linkage mixed system
4663:
4628:
4620:Largest remainders method
4595:
4522:
4513:
4364:
4347:
4186:Saari, Donald G. (1995).
2636:
2629:
2622:
2615:
1677:. It is sometimes set to
1004:Paradoxes and pathologies
853:Mixed-member proportional
848:Mixed-member majoritarian
843:By results of combination
734:Approval-based committees
4797:Majority loser criterion
4683:Additional member system
4641:Hagenbach-Bischoff quota
4560:Single transferable vote
4485:Positional voting system
4421:Minimax Condorcet method
4379:Combined approval voting
4188:Basic Geometry of Voting
4151:
3328:(except the Borda count)
3322:(except the Borda count)
2728:is the weighting of the
1301:positional number system
1183:Condorcet's jury theorem
984:Double simultaneous vote
959:Rural–urban proportional
954:Dual-member proportional
916:
905:
872:Parallel (superposition)
764:Fractional social choice
751:Expanding approvals rule
580:
565:
550:
481:
470:
446:
18:Positional voting system
4822:Resolvability criterion
4812:Participation criterion
4787:Later-no-harm criterion
4603:Highest averages method
3219:Chattanooga / Nashville
2198:Eurovision Song Contest
1337:Eurovision Song Contest
1293:Eurovision Song Contest
1110:Tyranny of the majority
887:Fusion (majority bonus)
704:Quota-remainder methods
4863:First-preference votes
4802:Monotonicity criterion
4772:Independence of clones
4475:Simple majoritarianism
3639:independence of clones
3309:Independence of Clones
2225:
2005:
1853:Dowdall system (Nauru)
1829:
1698:arithmetic progression
1652:
1244:Mathematics portal
1150:Majority impossibility
1139:Impossibility theorems
935:Negative vote transfer
756:Method of equal shares
377:
4767:Consistency criterion
4688:Alternative vote plus
4453:Instant-runoff voting
3641:(IoC) criterion. The
3248:mathematical criteria
3165:Binary number system
3056:Binary number system
2927:Binary number system
2426:Anti-plurality voting
2346:is the reciprocal of
2325:digital number system
2223:
2060:The island nation of
2006:
1830:
1740:geometric progression
1653:
1303:) or a harmonic one (
1047:Best-is-worst paradox
1036:Pathological response
771:Direct representation
424:Single-winner methods
376:
4837:Seats-to-votes ratio
4608:Webster/Sainte-Laguë
4060:Points to be tallied
3895:Points to be tallied
3710:Points to be tallied
3643:strategic nomination
3588:Points to be tallied
3458:Points to be tallied
2529:Comparative examples
2270:Nauru method (where
1897:
1866:harmonic progression
1771:
1765:) is defined below.
1608:
1476:Points to be tallied
1327:worth fewer points.
1305:Nauru/Dowdall method
1299:), a geometric one (
1231:Economics portal
1178:Median voter theorem
397:Comparative politics
201:improve this article
95:improve this article
4817:Plurality criterion
4416:Kemeny–Young method
3966:) over the other (B
3352:Unrestricted domain
3263:Unrestricted domain
2232:Borda count (where
2086:sequential divisors
1534:Point distributions
1318:Voting and counting
1219:Politics portal
930:Vote linkage system
901:Seat linkage system
488:Ranked-choice (RCV)
216:"Positional voting"
110:"Positional voting"
4858:Election threshold
4792:Majority criterion
4468:Supplementary vote
2447:winners) include:
2226:
2001:
1825:
1648:
1115:Discursive dilemma
1074:Lesser evil voting
949:Supermixed systems
652:Largest remainders
510:Round-robin voting
378:
4929:
4928:
4827:Reversal symmetry
4736:Cumulative voting
4718:Semi-proportional
4693:Mixed single vote
4659:
4658:
4535:Mixed single vote
4443:Exhaustive ballot
4406:Copeland's method
4401:Condorcet methods
4341:Electoral systems
4305:, Donald G. SAARI
4118:
4117:
4049:
4048:
3985:Third preference
3982:Second preference
3976:Number of ballots
3953:
3952:
3884:
3883:
3800:Third preference
3797:Second preference
3791:Number of ballots
3748:
3747:
3738:(6 x 4) + (6 x 2)
3724:(6 x 4) + (6 x 2)
3699:
3698:
3667:Third preference
3664:Second preference
3658:Number of ballots
3626:
3625:
3616:(7 x 4) + (5 x 2)
3602:(5 x 4) + (7 x 2)
3577:
3576:
3531:Third preference
3528:Second preference
3522:Number of ballots
3510:
3509:
3447:
3446:
3401:Third preference
3398:Second preference
3392:Number of ballots
3357:Pareto efficiency
3326:Reversal symmetry
3293:Pareto efficiency
3231:
3230:
3123:
3122:
3006:
3005:
2841:
2840:
2738:Voters' home city
2719:
2718:
2641:
2634:
2627:
2620:
2581:The options are:
2182:
2181:
1996:
1993:
1951:
1754:, the weighting (
1540:weakly decreasing
1528:
1527:
1465:
1464:
1377:Third preference
1374:Second preference
1368:Number of ballots
1281:Positional voting
1278:
1277:
1165:Gibbard's theorem
1105:Dominance paradox
1042:Perverse response
746:Phragmen's method
612:Majority judgment
540:Positional voting
498:Condorcet methods
366:electoral systems
343:
342:
335:
325:
324:
317:
266:
265:
251:
171:
170:
163:
145:
68:
16:(Redirected from
4954:
4868:Liquid democracy
4520:
4519:
4500:Two-round system
4411:Dodgson's method
4334:
4327:
4320:
4311:
4310:
4289:
4288:
4260:
4247:
4246:
4228:
4208:
4202:
4201:
4183:
4054:
4053:
3979:First preference
3973:
3972:
3889:
3888:
3794:First preference
3788:
3787:
3704:
3703:
3661:First preference
3655:
3654:
3582:
3581:
3525:First preference
3519:
3518:
3452:
3451:
3395:First preference
3389:
3388:
3371:Pareto efficient
3347:Non-dictatorship
3315:Condorcet winner
3258:Non-dictatorship
3235:progression type
3128:
3127:
3019:
3018:
3010:progression type
2899:
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2413:Plurality voting
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1989:
1969:
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1908:
1890:
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1874:Nauru parliament
1871:
1863:
1847:plurality voting
1844:
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1749:
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1712:Plurality voting
1692:
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1601:
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1546:Borda (Unbiased)
1470:
1469:
1371:First preference
1365:
1364:
1351:
1347:
1288:electoral system
1270:
1263:
1256:
1242:
1241:
1229:
1228:
1217:
1216:
1172:Positive results
1067:Strategic voting
964:Majority jackpot
921:
910:
781:Liquid democracy
657:National remnant
647:Highest averages
584:
569:
554:
486:
477:Alternative vote
475:
459:Partisan primary
451:
392:Mechanism design
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38:
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30:
21:
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4951:
4932:
4931:
4930:
4925:
4908:
4887:
4841:
4832:Smith criterion
4745:
4712:
4673:Parallel voting
4655:
4651:Imperiali quota
4624:
4591:
4509:
4463:Contingent vote
4426:Nanson's method
4384:Unified primary
4374:Approval voting
4360:
4343:
4338:
4297:
4292:
4261:
4250:
4226:10.1.1.924.3992
4209:
4205:
4198:
4184:
4169:
4165:
4157:Donald G. Saari
4154:
4143:
4139:
4131:
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4019:
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3999:
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3814:
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3780:
3776:
3772:
3768:
3764:
3760:
3756:
3635:
3383:
3320:Condorcet loser
3244:
3216:Anti-plurality
3107:Anti-plurality
2987:Anti-plurality
2898:
2892:
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2882:
2878:
2872:
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2850:
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2808:
2804:
2800:
2788:
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2776:
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2760:
2756:
2752:
2729:
2726:
2722:
2638:
2631:
2624:
2617:
2560:
2559:
2531:
2521:
2518:approval voting
2503:
2499:
2483:
2472:
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2207:
2194:
2080:
2076:
2075:
2070:
2066:
2065:
2054:
2050:
2046:
2042:
2038:
2034:
2029:For the Nauru (
2020:
2014:
1970:
1968:
1961:
1956:
1925:
1919:
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1320:
1274:
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1203:
1202:
1169:
1145:Arrow's theorem
1135:
1125:
1124:
1093:
1063:
1052:No-show paradox
1033:
1019:Cloning paradox
1009:Spoiler effects
1006:
996:
995:
970:
857:
840:
830:
829:
802:
793:Maximal lottery
760:
741:Thiele's method
730:
700:
632:
622:
621:
607:Approval voting
595:Cardinal voting
591:
536:
530:Maximal lottery
494:
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339:
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287:Please help by
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4731:Limited voting
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4458:Coombs' method
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4436:Schulze method
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4408:
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4396:Bucklin voting
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4295:External links
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4271:(2): 186–205.
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2179:
2174:
2171:
2168:
2164:
2163:
2158:
2155:
2152:
2148:
2147:
2142:
2139:
2136:
2132:
2131:
2126:
2123:
2120:
2116:
2115:
2112:
2109:
2106:
2018:
2000:
1992:
1988:
1985:
1982:
1979:
1976:
1973:
1967:
1964:
1960:
1955:
1949:
1946:
1943:
1940:
1937:
1934:
1931:
1928:
1922:
1918:
1912:
1907:
1903:
1879:
1854:
1851:
1824:
1821:
1818:
1815:
1812:
1808:
1803:
1800:
1797:
1793:
1789:
1786:
1781:
1777:
1757:
1731:
1728:
1716:Main article:
1713:
1710:
1705:
1702:
1647:
1644:
1641:
1638:
1635:
1632:
1629:
1626:
1623:
1618:
1614:
1586:
1547:
1544:
1535:
1532:
1526:
1525:
1522:
1519:
1516:
1512:
1511:
1508:
1505:
1502:
1498:
1497:
1494:
1491:
1488:
1484:
1483:
1480:
1477:
1474:
1463:
1462:
1459:
1456:
1453:
1449:
1448:
1445:
1442:
1439:
1435:
1434:
1431:
1428:
1425:
1421:
1420:
1417:
1414:
1411:
1407:
1406:
1403:
1400:
1397:
1393:
1392:
1389:
1386:
1383:
1379:
1378:
1375:
1372:
1369:
1358:
1355:
1319:
1316:
1276:
1275:
1273:
1272:
1265:
1258:
1250:
1247:
1246:
1234:
1233:
1221:
1208:
1205:
1204:
1201:
1200:
1195:
1190:
1185:
1180:
1168:
1167:
1162:
1157:
1152:
1147:
1136:
1131:
1130:
1127:
1126:
1123:
1122:
1117:
1112:
1107:
1092:
1091:
1089:Turkey-raising
1086:
1081:
1076:
1062:
1061:
1060:
1059:
1049:
1044:
1032:
1031:
1029:Center squeeze
1026:
1021:
1016:
1014:Spoiler effect
1007:
1002:
1001:
998:
997:
994:
993:
988:
987:
986:
973:By ballot type
969:
968:
967:
966:
961:
956:
946:
945:
944:
943:
942:
937:
927:
926:
925:
914:
891:
890:
889:
884:
879:
874:
856:
855:
850:
841:
836:
835:
832:
831:
828:
827:
825:Limited voting
822:
821:
820:
801:
800:
795:
790:
785:
784:
783:
778:
759:
758:
753:
748:
743:
729:
728:
723:
718:
713:
699:
698:
697:
696:
694:Localized list
691:
686:
681:
676:
666:
665:
664:
662:Biproportional
659:
654:
649:
633:
628:
627:
624:
623:
620:
619:
614:
609:
604:
590:
589:
574:
559:
535:
534:
533:
532:
527:
522:
517:
507:
493:
492:
491:
490:
479:
466:Instant-runoff
463:
462:
461:
453:Jungle primary
440:
429:Single vote -
427:
422:
421:
418:
417:
415:
414:
404:
399:
394:
389:
383:
380:
379:
369:
368:
358:
357:
341:
340:
323:
322:
280:
278:
271:
264:
263:
199:. Please help
185:
183:
176:
169:
168:
83:
81:
74:
69:
43:
42:
40:
33:
26:
9:
6:
4:
3:
2:
4959:
4948:
4945:
4943:
4940:
4939:
4937:
4924:
4923:
4918:
4917:
4911:
4905:
4902:
4900:
4897:
4896:
4894:
4890:
4884:
4881:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4859:
4856:
4854:
4851:
4850:
4848:
4844:
4838:
4835:
4833:
4830:
4828:
4825:
4823:
4820:
4818:
4815:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4773:
4770:
4768:
4765:
4763:
4760:
4758:
4755:
4754:
4752:
4748:
4742:
4739:
4737:
4734:
4732:
4729:
4727:
4724:
4723:
4721:
4719:
4715:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4686:
4684:
4681:
4679:
4676:
4674:
4671:
4670:
4668:
4666:
4662:
4652:
4649:
4647:
4644:
4642:
4639:
4637:
4634:
4633:
4631:
4627:
4621:
4618:
4614:
4611:
4609:
4606:
4605:
4604:
4601:
4600:
4598:
4594:
4588:
4585:
4583:
4580:
4576:
4573:
4571:
4568:
4566:
4563:
4562:
4561:
4558:
4556:
4553:
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4531:
4528:
4527:
4525:
4521:
4518:
4516:
4512:
4506:
4503:
4501:
4498:
4496:
4493:
4491:
4488:
4486:
4483:
4481:
4478:
4476:
4473:
4469:
4466:
4464:
4461:
4459:
4456:
4455:
4454:
4451:
4449:
4446:
4444:
4441:
4437:
4434:
4432:
4429:
4427:
4424:
4422:
4419:
4417:
4414:
4412:
4409:
4407:
4404:
4403:
4402:
4399:
4397:
4394:
4392:
4389:
4385:
4382:
4380:
4377:
4376:
4375:
4372:
4371:
4369:
4367:
4366:Single-winner
4363:
4359:
4357:
4353:
4346:
4342:
4335:
4330:
4328:
4323:
4321:
4316:
4315:
4312:
4306:
4304:
4299:
4298:
4286:
4282:
4278:
4274:
4270:
4266:
4259:
4257:
4255:
4253:
4244:
4240:
4236:
4232:
4227:
4222:
4218:
4214:
4207:
4199:
4197:3-540-60064-7
4193:
4189:
4182:
4180:
4178:
4176:
4174:
4172:
4167:
4160:
4158:
4149:
4145:
4135:
4113:
4110:
4107:
4101:
4100:
4096:
4093:
4090:
4084:
4083:
4079:
4076:
4073:
4070:
4069:
4066:Overall rank
4065:
4062:
4059:
4056:
4055:
4052:
4044:
4038:
4032:
4029:
4028:
4021:
4015:
4012:
4009:
4008:
4001:
3995:
3992:
3989:
3988:
3984:
3981:
3978:
3975:
3974:
3971:
3960:
3958:
3949:Second equal
3948:
3945:
3942:
3936:
3935:
3932:Second equal
3931:
3928:
3925:
3919:
3918:
3914:
3911:
3908:
3905:
3904:
3901:Overall rank
3900:
3897:
3894:
3891:
3890:
3887:
3879:
3873:
3867:
3864:
3863:
3859:
3853:
3847:
3844:
3843:
3836:
3830:
3827:
3824:
3823:
3816:
3810:
3807:
3804:
3803:
3799:
3796:
3793:
3790:
3789:
3786:
3751:
3743:
3740:
3737:
3734:
3733:
3729:
3726:
3723:
3720:
3719:
3716:Overall rank
3715:
3712:
3709:
3706:
3705:
3702:
3694:
3691:
3688:
3685:
3684:
3680:
3677:
3674:
3671:
3670:
3666:
3663:
3660:
3657:
3656:
3653:
3650:
3647:
3644:
3640:
3630:
3621:
3618:
3615:
3612:
3611:
3607:
3604:
3601:
3598:
3597:
3594:Overall rank
3593:
3590:
3587:
3584:
3583:
3580:
3572:
3569:
3566:
3563:
3562:
3558:
3555:
3552:
3549:
3548:
3544:
3541:
3538:
3535:
3534:
3530:
3527:
3524:
3521:
3520:
3517:
3514:
3505:
3502:
3499:
3496:
3495:
3491:
3488:
3485:
3482:
3481:
3477:
3474:
3471:
3468:
3467:
3464:Overall rank
3463:
3460:
3457:
3454:
3453:
3450:
3442:
3439:
3436:
3433:
3432:
3428:
3425:
3422:
3419:
3418:
3414:
3411:
3408:
3405:
3404:
3400:
3397:
3394:
3391:
3390:
3387:
3378:
3376:
3372:
3363:
3360:
3358:
3355:
3353:
3350:
3348:
3345:
3344:
3343:
3341:
3338:According to
3333:
3330:
3327:
3324:
3321:
3318:
3316:
3313:
3310:
3307:
3304:
3301:
3300:
3299:
3294:
3291:
3289:
3286:
3284:
3283:Resolvability
3281:
3279:
3278:Participation
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3255:
3254:
3251:
3249:
3239:
3236:
3226:
3223:
3221:
3218:
3215:
3214:
3210:
3207:
3204:
3201:
3198:
3197:
3193:
3190:
3187:
3184:
3182:Nauru method
3181:
3180:
3176:
3173:
3170:
3167:
3164:
3163:
3159:
3156:
3153:
3150:
3147:
3146:
3143:Fourth place
3142:
3139:
3136:
3133:
3131:Voting system
3130:
3129:
3126:
3118:
3115:
3112:
3109:
3106:
3105:
3101:
3098:
3095:
3092:
3089:
3088:
3084:
3081:
3078:
3075:
3073:Nauru method
3072:
3071:
3067:
3064:
3061:
3058:
3055:
3054:
3050:
3047:
3044:
3041:
3038:
3037:
3033:
3030:
3027:
3024:
3022:Voting system
3021:
3020:
3017:
3014:
3011:
3001:
2998:
2995:
2992:
2989:
2986:
2985:
2981:
2978:
2975:
2972:
2969:
2966:
2965:
2961:
2958:
2955:
2952:
2949:
2947:Nauru method
2946:
2945:
2941:
2938:
2935:
2932:
2929:
2926:
2925:
2921:
2918:
2915:
2912:
2909:
2906:
2905:
2901:
2895:
2891:
2885:
2881:
2875:
2871:
2865:
2861:
2859:Voting system
2858:
2857:
2854:
2847:
2837:) x 1200/100
2820:
2817:
2816:
2813:) x 1200/100
2796:
2793:
2792:
2789:) x 1200/100
2772:
2769:
2768:
2765:) x 1200/100
2748:
2745:
2744:
2740:
2737:
2736:
2733:
2712:
2709:
2706:
2704:
2701:
2700:
2699:
2694:
2691:
2688:
2686:
2683:
2682:
2681:
2676:
2673:
2670:
2668:
2665:
2664:
2663:
2658:
2655:
2652:
2650:
2647:
2646:
2645:
2644:
2637:17% of voters
2630:15% of voters
2623:26% of voters
2616:42% of voters
2614:
2611:
2605:
2602:
2599:
2596:
2593:
2590:
2587:
2584:
2583:
2582:
2580:
2576:
2572:
2569:Suppose that
2567:
2565:
2556:
2551:
2549:
2544:
2542:
2537:
2536:
2533:
2526:
2519:
2510:
2506:
2497:
2494:
2490:
2486:
2480:
2476:
2466:
2463:
2458:
2453:
2450:
2449:
2448:
2436:
2432:
2427:
2424:
2419:
2414:
2411:
2410:
2409:
2406:
2403:
2399:
2380:
2371:
2355:
2330:
2326:
2321:
2310:
2299:
2296:
2286:
2281:
2274:
2269:
2264:
2257:
2252:
2247:
2240:
2236:
2231:
2230:
2229:
2222:
2218:
2202:
2199:
2189:
2186:
2178:
2175:
2172:
2169:
2166:
2165:
2162:
2159:
2156:
2153:
2150:
2149:
2146:
2143:
2140:
2137:
2134:
2133:
2130:
2127:
2124:
2121:
2118:
2117:
2113:
2110:
2107:
2104:
2103:
2100:
2097:
2095:
2091:
2087:
2063:
2058:
2032:
2027:
2024:
2017:
2011:
1998:
1990:
1986:
1980:
1977:
1974:
1965:
1962:
1958:
1953:
1947:
1941:
1938:
1935:
1929:
1926:
1920:
1916:
1910:
1905:
1901:
1892:
1875:
1867:
1862:
1850:
1848:
1840:
1839:binary number
1835:
1822:
1819:
1816:
1813:
1810:
1806:
1801:
1798:
1795:
1791:
1787:
1784:
1779:
1775:
1766:
1741:
1737:
1727:
1725:
1719:
1709:
1701:
1699:
1694:
1681:
1671:
1668:
1664:
1658:
1645:
1639:
1636:
1633:
1627:
1624:
1621:
1616:
1612:
1603:
1581:
1573:
1566:
1553:
1543:
1541:
1531:
1523:
1520:
1517:
1514:
1513:
1509:
1506:
1503:
1500:
1499:
1495:
1492:
1489:
1486:
1485:
1482:Overall rank
1481:
1478:
1475:
1472:
1471:
1468:
1460:
1457:
1454:
1451:
1450:
1446:
1443:
1440:
1437:
1436:
1432:
1429:
1426:
1423:
1422:
1418:
1415:
1412:
1409:
1408:
1404:
1401:
1398:
1395:
1394:
1390:
1387:
1384:
1381:
1380:
1376:
1373:
1370:
1367:
1366:
1363:
1354:
1341:
1338:
1333:
1328:
1325:
1324:ranked ballot
1315:
1313:
1308:
1306:
1302:
1298:
1294:
1289:
1286:
1285:ranked voting
1282:
1271:
1266:
1264:
1259:
1257:
1252:
1251:
1249:
1248:
1245:
1240:
1232:
1227:
1222:
1220:
1215:
1210:
1209:
1207:
1206:
1199:
1196:
1194:
1191:
1189:
1188:May's theorem
1186:
1184:
1181:
1179:
1176:
1175:
1174:
1173:
1166:
1163:
1161:
1158:
1156:
1153:
1151:
1148:
1146:
1143:
1142:
1141:
1140:
1134:
1129:
1128:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1102:
1101:
1100:
1099:
1098:majority rule
1096:Paradoxes of
1090:
1087:
1085:
1082:
1080:
1077:
1075:
1072:
1071:
1070:
1069:
1068:
1058:
1055:
1054:
1053:
1050:
1048:
1045:
1043:
1040:
1039:
1038:
1037:
1030:
1027:
1025:
1022:
1020:
1017:
1015:
1012:
1011:
1010:
1005:
1000:
999:
992:
989:
985:
982:
981:
980:
977:
976:
975:
974:
965:
962:
960:
957:
955:
952:
951:
950:
947:
941:
938:
936:
933:
932:
931:
928:
924:
919:
915:
913:
908:
904:
903:
902:
899:
898:
897:
896:
892:
888:
885:
883:
880:
878:
875:
873:
870:
869:
868:
867:
862:
861:
860:
854:
851:
849:
846:
845:
844:
839:
838:Mixed systems
834:
833:
826:
823:
819:
816:
815:
814:
811:
810:
809:
808:
807:
799:
798:Random ballot
796:
794:
791:
789:
786:
782:
779:
777:
774:
773:
772:
769:
768:
767:
766:
765:
757:
754:
752:
749:
747:
744:
742:
739:
738:
737:
736:
735:
727:
724:
722:
719:
717:
714:
712:
709:
708:
707:
706:
705:
695:
692:
690:
687:
685:
682:
680:
677:
675:
672:
671:
670:
667:
663:
660:
658:
655:
653:
650:
648:
645:
644:
643:
642:Apportionment
640:
639:
638:
637:
631:
626:
625:
618:
615:
613:
610:
608:
605:
603:
600:
599:
598:
597:
596:
587:
583:
578:
577:Antiplurality
575:
572:
568:
563:
560:
557:
553:
548:
545:
544:
543:
542:
541:
531:
528:
526:
523:
521:
518:
516:
513:
512:
511:
508:
506:
505:Condorcet-IRV
503:
502:
501:
500:
499:
489:
484:
480:
478:
473:
469:
468:
467:
464:
460:
457:
456:
454:
449:
444:
441:
439:
436:
435:
434:
432:
425:
420:
419:
412:
408:
405:
403:
400:
398:
395:
393:
390:
388:
387:Social choice
385:
384:
382:
381:
375:
371:
370:
367:
363:
362:Social choice
360:
359:
355:
351:
347:
346:
337:
334:
319:
316:
308:
298:
294:
290:
284:
281:This article
279:
270:
269:
260:
249:
246:
242:
239:
235:
232:
228:
225:
221:
218: –
217:
213:
212:Find sources:
206:
202:
198:
192:
191:
190:single source
186:This article
184:
180:
175:
174:
165:
162:
154:
143:
140:
136:
133:
129:
126:
122:
119:
115:
112: –
111:
107:
106:Find sources:
100:
96:
90:
89:
84:This article
82:
78:
73:
72:
67:
65:
58:
57:
52:
51:
46:
41:
32:
31:
19:
4920:
4914:
4530:Mixed-member
4515:Proportional
4490:Score voting
4431:Ranked pairs
4350:Part of the
4349:
4302:
4268:
4264:
4216:
4212:
4206:
4187:
4155:
4146:
4119:
4050:
3961:
3954:
3885:
3752:
3749:
3744:First equal
3730:First equal
3700:
3651:
3648:
3636:
3627:
3578:
3515:
3511:
3448:
3384:
3367:
3337:
3297:
3288:Monotonicity
3252:
3245:
3232:
3199:Borda count
3160:Chattanooga
3137:Second place
3124:
3090:Borda count
3015:
3007:
2967:Borda count
2893:
2883:
2873:
2863:
2845:
2842:
2794:Chattanooga
2720:
2707:Chattanooga
2702:
2684:
2671:Chattanooga
2666:
2656:Chattanooga
2648:
2609:
2568:
2561:
2532:
2515:
2508:
2504:
2488:
2484:
2478:
2474:
2456:
2442:
2434:
2430:
2417:
2407:
2401:
2397:
2381:
2377:
2356:
2322:
2308:
2300:
2294:
2290:
2279:
2272:
2262:
2255:
2245:
2238:
2234:
2227:
2208:
2195:
2187:
2183:
2176:
2160:
2144:
2128:
2098:
2059:
2028:
2022:
2015:
2012:
1893:
1860:
1856:
1836:
1767:
1733:
1721:
1707:
1695:
1679:
1672:
1666:
1662:
1659:
1604:
1582:
1571:
1564:
1549:
1537:
1529:
1466:
1360:
1342:
1329:
1321:
1312:score voting
1309:
1280:
1279:
1171:
1170:
1137:
1095:
1094:
1079:Exaggeration
1065:
1064:
1035:
1034:
1008:
972:
971:
940:Mixed ballot
895:Compensatory
893:
866:compensatory
863:
858:
842:
804:
803:
762:
761:
732:
731:
702:
701:
689:List-free PR
634:
602:Score voting
593:
592:
539:
538:
537:
525:Ranked pairs
496:
495:
428:
329:
311:
302:
289:spinning off
282:
254:
244:
237:
230:
223:
211:
187:
157:
148:
138:
131:
124:
117:
105:
93:Please help
88:verification
85:
61:
54:
48:
47:Please help
44:
4873:Spoilt vote
4636:Droop quota
4575:Schulze STV
4550:Rural–urban
4495:STAR voting
4391:Borda count
3633:IoC example
3381:IIA example
3373:but is not
3273:Consistency
3205:Chattanooga
3191:Chattanooga
3174:Chattanooga
3140:Third place
3134:First place
3031:Chattanooga
2685:Chattanooga
2633:Center-East
2598:Chattanooga
2496:Bloc voting
2053:be 1/2 and
1738:known as a
1552:Borda count
1297:Borda count
979:Single vote
882:Conditional
877:Coexistence
726:Quota Borda
716:Schulze STV
674:Closed list
617:STAR voting
562:Borda count
305:August 2024
4936:Categories
4892:Comparison
4646:Hare quota
4596:Allocation
4582:Spare vote
4570:Hare-Clark
4540:Party-list
4163:References
3211:Knoxville
3194:Knoxville
3177:Knoxville
3148:Plurality
3039:Plurality
3034:Knoxville
2907:Plurality
2818:Knoxville
2770:Nashville
2710:Nashville
2692:Nashville
2689:Knoxville
2674:Knoxville
2659:Knoxville
2653:Nashville
2192:Eurovision
2154:Catherine
2108:Candidate
1084:Truncation
813:Cumulative
636:Party-list
411:By country
402:Comparison
293:relocating
257:March 2021
227:newspapers
151:March 2021
121:newspapers
50:improve it
4883:Unseating
4878:Sortition
4480:Plurality
4356:Economics
4285:153325225
4221:CiteSeerX
4057:Candidate
3892:Candidate
3707:Candidate
3585:Candidate
3455:Candidate
3224:Knoxville
3202:Nashville
3185:Nashville
3168:Nashville
3157:Knoxville
3154:Nashville
3028:Nashville
2703:Knoxville
2667:Nashville
2604:Knoxville
2592:Nashville
2571:Tennessee
2045:to 1 and
1978:−
1939:−
1820:≤
1814:≤
1799:−
1730:Geometric
1704:Top-heavy
1637:−
1628:−
991:Dual-vote
684:Panachage
679:Open list
669:List type
547:Plurality
443:Two-round
431:plurality
354:Economics
197:talk page
56:talk page
4750:Criteria
4703:Scorporo
4352:politics
3332:Majority
3227:Memphis
2746:Memphis
2713:Memphis
2695:Memphis
2677:Memphis
2640:Far-East
2619:Far-West
2350:and the
2111:Formula
2105:Ranking
1736:sequence
711:Hare STV
350:Politics
348:A joint
4922:Project
4613:D'Hondt
4565:CPO-STV
4523:Systems
4243:3213336
4134:teaming
4080:Second
3608:Second
3492:Second
3208:Memphis
3188:Memphis
3171:Memphis
3151:Memphis
3025:Memphis
2649:Memphis
2586:Memphis
2575:capital
2473:1 <
2382:For an
2122:Andrew
2114:Points
2079:⁄
2069:⁄
2031:Dowdall
1524:Second
1357:Example
1332:ordinal
721:CPO-STV
571:Baldwin
520:Schulze
515:Minimax
433:methods
241:scholar
135:scholar
4916:Portal
4853:Ballot
4629:Quotas
4358:series
4283:
4241:
4223:
4194:
4140:over B
4114:Third
4097:First
3915:First
3781:over B
3773:over B
3622:First
3506:Third
3478:First
2962:2.083
2942:1.875
2721:Where
2626:Center
2498:: The
2467:: The
2170:David
2138:Brian
2013:where
1722:Under
1660:where
1510:Third
1496:First
1473:Option
586:Coombs
356:series
243:
236:
229:
222:
214:
137:
130:
123:
116:
108:
4846:Other
4665:Mixed
4281:S2CID
4239:S2CID
4152:Notes
4063:Total
3898:Total
3765:and B
3757:and B
3713:Total
3591:Total
3461:Total
3364:(IIA)
3311:(IoC)
3305:(IIA)
2833:+ 17w
2829:+ 15w
2825:+ 26w
2809:+ 17w
2805:+ 15w
2801:+ 26w
2785:+ 17w
2781:+ 15w
2777:+ 26w
2761:+ 17w
2757:+ 15w
2753:+ 26w
2477:<
2329:radix
2265:= 1/2
2062:Nauru
1479:Total
1283:is a
923:'MMP'
912:'AMS'
248:JSTOR
234:books
142:JSTOR
128:books
4354:and
4192:ISBN
3119:696
3116:1200
3113:1200
3102:621
3085:524
3068:435
3051:204
2982:2.5
2902:Sum
2821:(42w
2797:(42w
2773:(42w
2749:(42w
2277:and
2260:and
2243:and
2241:= 10
2196:The
2177:0.25
2173:1/4
2167:4th
2161:0.33
2157:1/3
2151:3rd
2145:0.50
2141:1/2
2135:2nd
2129:1.00
2125:1/1
2119:1st
864:Non-
818:SNTV
407:List
364:and
352:and
220:news
114:news
4678:MMP
4273:doi
4231:doi
3110:504
3099:819
3096:882
3093:678
3082:606
3079:692
3076:678
3065:564
3062:660
3059:591
3048:180
3045:312
3042:504
2979:1/4
2976:1/2
2973:3/4
2959:1/4
2956:1/3
2953:1/2
2939:1/8
2936:1/4
2933:1/2
2851:= 1
2516:In
2459:= 1
2437:– 1
2420:= 1
2282:= 1
2275:= 1
2258:= 1
2248:= 1
1700:.
1689:or
1682:– 1
1574:– 2
1567:– 1
1521:224
1507:218
1493:258
1452:10
1438:20
1424:16
1410:12
1396:18
1382:24
582:el.
567:el.
556:IRV
552:el.
291:or
203:by
97:by
4938::
4919:—
4279:.
4269:49
4267:.
4251:^
4237:.
4229:.
4217:23
4215:.
4170:^
4111:21
4094:33
4077:30
4071:A
4045:A
4030:6
4010:3
3990:3
3959:.
3946:27
3929:27
3912:30
3906:A
3880:A
3865:3
3860:A
3845:3
3825:3
3805:3
3741:36
3735:B
3727:36
3721:A
3695:-
3686:6
3681:-
3672:6
3619:38
3613:C
3605:34
3599:A
3573:-
3564:3
3559:-
3550:4
3545:-
3536:5
3503:25
3497:C
3489:29
3483:B
3475:30
3469:A
3443:B
3434:3
3429:A
3420:4
3415:C
3406:5
3002:3
2922:1
2507:=
2487:=
2433:=
2307:1/
2298:.
2293:1/
2237:=
2096:.
2026:.
2021:=
1891:.
1859:1/
1849:.
1665:=
1602:.
1515:C
1501:B
1487:A
1461:A
1447:B
1433:A
1419:C
1405:B
1391:C
918:NZ
907:UK
483:US
472:UK
455:)
448:US
59:.
4333:e
4326:t
4319:v
4287:.
4275::
4245:.
4233::
4200:.
4142:1
4138:2
4130:1
4126:2
4122:1
4104:2
4102:B
4087:1
4085:B
4041:2
4039:B
4035:1
4033:B
4024:1
4022:B
4018:2
4016:B
4013:A
4004:2
4002:B
3998:1
3996:B
3993:A
3968:2
3964:1
3939:2
3937:B
3922:1
3920:B
3876:1
3874:B
3870:2
3868:B
3856:2
3854:B
3850:1
3848:B
3839:1
3837:B
3833:2
3831:B
3828:A
3819:2
3817:B
3813:1
3811:B
3808:A
3783:1
3779:2
3775:2
3771:1
3767:2
3763:1
3759:2
3755:1
3692:A
3689:B
3678:B
3675:A
3570:A
3567:C
3556:A
3553:C
3542:C
3539:A
3440:A
3437:C
3426:C
3423:B
3412:B
3409:A
2999:0
2996:1
2993:1
2990:1
2970:1
2950:1
2930:1
2919:0
2916:0
2913:0
2910:1
2897:4
2894:w
2887:3
2884:w
2877:2
2874:w
2867:1
2864:w
2849:1
2846:w
2835:1
2831:2
2827:3
2823:4
2811:2
2807:1
2803:2
2799:3
2787:3
2783:3
2779:1
2775:2
2763:4
2759:4
2755:4
2751:1
2730:n
2725:n
2723:w
2554:e
2547:t
2540:v
2522:F
2512:)
2509:W
2505:F
2500:W
2492:)
2489:X
2485:F
2479:W
2475:X
2469:X
2461:)
2457:F
2445:W
2439:)
2435:N
2431:F
2422:)
2418:F
2402:F
2400:-
2398:N
2393:F
2388:F
2384:N
2368:r
2363:r
2359:R
2352:r
2348:R
2344:r
2340:r
2336:R
2332:R
2318:r
2314:d
2309:N
2303:d
2295:a
2284:)
2280:d
2273:a
2267:)
2263:r
2256:a
2250:)
2246:d
2239:N
2235:a
2215:n
2211:w
2081:3
2077:1
2071:2
2067:1
2055:d
2051:a
2047:d
2043:a
2039:d
2035:a
2023:a
2019:1
2016:w
1999:,
1991:a
1987:d
1984:)
1981:1
1975:n
1972:(
1966:+
1963:1
1959:a
1954:=
1948:d
1945:)
1942:1
1936:n
1933:(
1930:+
1927:a
1921:2
1917:a
1911:=
1906:n
1902:w
1889:a
1885:n
1880:n
1878:w
1870:N
1861:N
1843:r
1823:1
1817:r
1811:0
1807:,
1802:1
1796:n
1792:r
1788:a
1785:=
1780:n
1776:w
1763:n
1758:n
1756:w
1752:a
1748:r
1744:r
1691:d
1687:a
1680:N
1675:N
1667:N
1663:a
1646:d
1643:)
1640:1
1634:n
1631:(
1625:a
1622:=
1617:n
1613:w
1600:d
1596:a
1592:n
1587:n
1585:w
1578:N
1572:N
1565:N
1560:N
1556:N
1458:B
1455:C
1444:A
1441:C
1430:C
1427:B
1416:A
1413:B
1402:C
1399:A
1388:B
1385:A
1350:W
1346:W
1344:(
1269:e
1262:t
1255:v
920::
909::
588:)
579:(
573:)
564:(
558:)
549:(
485::
474::
450::
445:(
413:)
409:(
336:)
330:(
318:)
312:(
307:)
303:(
299:.
285:.
259:)
255:(
245:·
238:·
231:·
224:·
207:.
193:.
164:)
158:(
153:)
149:(
139:·
132:·
125:·
118:·
91:.
66:)
62:(
20:)
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