1843:
913:
1538:
five voters to all other alternatives makes it a beats-all champion. However the Borda count awards 2 points for 1st choice, 1 point for second and 0 points for third. Thus, from three voters who prefer A, A receives 6 points (3 Ă 2), and 0 points from the other two voters, for a total of 6 points. B receives 3 points (3 Ă 1) from the three voters who prefer A to B to C, and 4 points (2 Ă 2) from the other two voters who prefer B to C to A. With 7 points, B is the Borda winner.
48:
1829:
888:
900:
1250:
1513:
methods is unclear. Under the traditional definition of the
Condorcet criterionâthat if most votes prefer A to B, then A should defeat B (unless this causes a contradiction)âthese methods fail Condorcet, because they give voters with stronger preferences a greater say on the outcome of the election.
1571:
In this case, B is preferred to A by 65 votes to 35, and B is preferred to C by 66 to 34, so B is preferred to both A and C. B must then win according to the
Condorcet criterion. Under IRV, B is ranked first by the fewest voters and is eliminated, and then C wins with the transferred votes from B.
1537:
The Borda count does not comply with the
Condorcet criterion in the following case. Consider an election consisting of five voters and three alternatives, in which three voters prefer A to B and B to C, while two of the voters prefer B to C and C to A. The fact that A is preferred by three of the
1552:
In instant-runoff voting (IRV) voters rank candidates from first to last. The last-place candidate (the one with the fewest first-place votes) is eliminated; the votes are then reassigned to the non-eliminated candidate the voter would have chosen had the candidate not been present.
1590:
Highest medians is a system in which the voter gives all candidates a rating out of a predetermined set (e.g. {"excellent", "good", "fair", "poor"}). The winner of the election would be the candidate with the best median rating. Consider an election with three candidates A, B, C.
1215:. There are three options for what to do with the money. The government can spend it, use it to cut taxes, or use it to pay off the debt. The government holds a vote where it asks citizens which of two options they would prefer, and tabulates the results as follows:
1658:
Score voting is a system in which the voter gives all candidates a score on a predetermined scale (e.g. from 0 to 5). The winner of the election is the candidate with the highest total score. Score voting fails the majority-Condorcet criterion. For example:
1605:
B is preferred to A by 65 votes to 35, and B is preferred to C by 66 to 34. Hence, B is the beats-all champion. But B only gets the median rating "fair", while C has the median rating "good"; as a result, C is chosen as the winner by highest medians.
2325:
Mohsin, F., Han, Q., Ruan, S., Chen, P. Y., Rossi, F., & Xia, L. (2023, May). Computational
Complexity of Verifying the Group No-show Paradox. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems (pp.
1741:
Here, C is declared winner, even though a majority of voters would prefer B; this is because the supporters of C are much more enthusiastic about their favorite candidate than the supporters of B. The same example also shows that
1289:
In this case, the option of paying off the debt is the beats-all winner, because repaying debt is more popular than the other two options. But, it is worth noting that such a winner will not always exist. In this case,
1533:
Borda count is a voting system in which voters rank the candidates in an order of preference. Points are given for the position of a candidate in a voter's rank order. The candidate with the most points wins.
1556:
Instant-runoff does not comply with the
Condorcet criterion, i.e. it does not elect candidates with majority support. For example, the following vote count of preferences with three candidates {A, B, C}:
1623:
is a ranked voting system where voters rank candidates from first to last, and the best candidate gets one point (while later preferences are ignored). Plurality fails the
Condorcet criterion because of
1091:
and prefer candidates who are more similar to themselves, a majority-rule winner always exists and is the candidate whose ideology is most representative of the electorate, a result known as the
2211:
The analysis reveals that the underlying political landscapes ... are inherently multidimensional and cannot be reduced to a single left-right dimension, or even to a two-dimensional space.
1099:, this can lead to voting paradoxes. Previous research has found cycles to be somewhat rare in real elections, with estimates of their prevalence ranging from 1-10% of races.
1629:
941:
2384:
2248:
For instance, if preferences are distributed spatially, there need only be two or more dimensions to the alternative space for cyclic preferences to be almost inevitable
1325:. Intuitively, this is because the only way to dislodge a Condorcet winner is by beating them, implying spoilers can exist only if there is no majority-rule winner.
2008:
2834:
2602:
632:
1123:
2730:
2582:
664:
526:
521:
2829:
2607:
1068:). However, precise terminology on the topic is inconsistent. Surprisingly, an election may not have a beats-all winner: it is possible to have a
934:
627:
2592:
2377:
309:
1810:
833:
2956:
2233:
The Theory of
Committees and Elections by Duncan Black and Committee Decisions with Complementary Valuation by Duncan Black and R.A. Newing
84:
2639:
2994:
927:
2370:
2241:
1788:
2974:
828:
2824:
2770:
2231:
818:
568:
539:
479:
2622:
2951:
1746:
does not always cause score to comply with the criterion (as the
Condorcet winner B is not in the top-two according to score).
1434:
1361:
guarantees an even stronger kind of majority rule. It says that if there is no majority-rule winner, the winner must be in the
550:
75:
1341:. One study surveying 306 publicly-available election datasets found no examples of participation failures for methods in the
2750:
613:
255:
240:
225:
2793:
2778:
2597:
871:
491:
414:
335:
2844:
2567:
2557:
2418:
1581:
1478:
1143:
303:
285:
126:
856:
2500:
1768:
1441:
1127:
1111:
1072:-style cycle, when multiple candidates defeat each other (Rock < Paper < Scissors < Rock). This is called
747:
730:
677:
461:
449:
419:
220:
178:
111:
1337:
in constructed examples. However, studies suggest this is empirically rare for modern majority-rule systems, like
555:
2859:
2814:
2760:
2672:
1856:
1369:
603:
596:
80:
2849:
2735:
2693:
2612:
2537:
2473:
2431:
657:
585:
574:
437:
424:
407:
384:
362:
325:
315:
2468:
2874:
2864:
2839:
2655:
2532:
1615:
1334:
1147:
783:
637:
320:
2915:
2854:
2717:
2660:
1404:
1310:
1065:
812:
692:
622:
429:
2819:
2740:
2505:
1547:
1464:
1119:
720:
560:
444:
250:
229:
161:
139:
2176:
1842:
912:
778:
2889:
2458:
1200:
1192:
1188:
1092:
1005:
851:
838:
806:
70:
1095:. However, if political candidates differ substantially in ways unrelated to left-right ideology or
2869:
2463:
1409:
1397:
1291:
1069:
757:
591:
244:
2910:
2520:
2158:
2150:
1967:
1899:
1866:
1848:
1279:
1267:
1244:
1088:
989:
917:
788:
399:
183:
2478:
866:
2879:
2788:
2745:
2665:
2587:
2510:
2495:
2453:
2300:
2281:
2237:
2112:
2088:
2070:
2039:
2002:
1959:
1917:
1806:
1784:
1776:
1485:
1414:
1346:
1173:
1077:
823:
793:
715:
652:
486:
213:
188:
171:
39:
2337:
2920:
2552:
2408:
2393:
2349:
2308:
2273:
2200:
2192:
2142:
2104:
2031:
1951:
1909:
1861:
1620:
1496:
1386:
1131:
1096:
1024:
971:
904:
861:
752:
740:
454:
330:
156:
150:
132:
121:
116:
104:
65:
27:
1887:
2968:
2884:
2725:
2703:
2515:
2436:
2426:
2404:
1834:
1014:
970:
of all voters would support them in a one-on-one race against any one of their opponents.
892:
725:
580:
545:
466:
377:
280:
203:
145:
23:
1365:, which includes all the candidates who can beat every other candidate, either directly
47:
2783:
2488:
2448:
1761:
1637:
1625:
1585:
1474:
1429:
1424:
1322:
1107:
1073:
762:
702:
687:
498:
367:
342:
193:
1828:
887:
2988:
2527:
2162:
1453:
1212:
1196:
1184:
982:
976:
771:
471:
259:
97:
60:
35:
2196:
2542:
2483:
2223:
2130:
1756:
1653:
1510:
1419:
1342:
1338:
1139:
1135:
1103:
511:
275:
268:
198:
2338:"Varieties of failure of monotonicity and participation under five voting methods"
1333:
One disadvantage of majority-rule methods is they can all theoretically fail the
1180:
was lost soon after his death, his ideas were overlooked for the next 500 years.
2925:
2688:
2627:
2547:
2443:
1798:
1743:
1641:
1528:
1491:
1469:
1169:
1162:
1081:
389:
347:
290:
235:
2227:
1955:
1869:- contains information on some multiwinner variants of the Condorcet criterion.
1301:
by counting the number of voters who rated each candidate higher than another.
2698:
2634:
2353:
2312:
2277:
1824:
1000:
2285:
2116:
2074:
2043:
1963:
1921:
1400:
satisfy the
Condorcet criterion. Other methods satisfying the criterion are:
2935:
2930:
2261:
2092:
1362:
1358:
988:
In situations where equal or tied ranks are allowed, a candidate who wins a
357:
352:
1986:
899:
2755:
1294:
search for the candidate who is closest to being an undefeated champion.
1166:
967:
955:
608:
2023:
1971:
1939:
1372:. Most, but not all, Condorcet systems satisfy the top-cycle criterion.
2617:
2205:
2154:
2058:
1633:
1298:
394:
1913:
2905:
2035:
2362:
2108:
2146:
1904:
1598:
34 voters rate candidate C "excellent", B "fair", and A "poor", and
1159:
2180:
974:
where a majority winner will always win are said to satisfy the
2366:
1601:
31 voters rate candidate B "excellent", C "good", and A "poor".
1595:
35 voters rate candidate A "excellent", B "fair", and C "poor",
2301:"Ramon Llull: from 'Ars electionis' to social choice theory"
1039:
46:
1886:
Brandl, Florian; Brandt, Felix; Seedig, Hans Georg (2016).
1048:
1030:
1187:
coincided with the rediscovery of these ideas during the
1146:, fail the majority winner criterion intentionally (see
1158:
Condorcet methods were first studied in detail by the
2133:(1948). "On the Rationale of Group Decision-making".
1045:
1033:
1027:
2181:"Political space representations with approval data"
1309:
The
Condorcet criterion is related to several other
1172:
in the 13th century, during his investigations into
1036:
2944:
2898:
2802:
2769:
2716:
2681:
2648:
2575:
2566:
2417:
2262:"On the empirical relevance of Condorcet's paradox"
1042:
2024:"Choix social positionnel et principe majoritaire"
1760:
1640:, but Bush won as a result of spoiler candidate
1509:The applicability of the Condorcet criterion to
2230:; McMillan, Alistair; Monroe, Burt L. (eds.).
2378:
2022:Lepelley, Dominique; Merlin, Vincent (1998).
1297:Majority-rule winners can be determined from
935:
8:
2835:Independence of Smith-dominated alternatives
1102:Systems that elect majority winners include
2336:Felsenthal, Dan; Tideman, Nicolaus (2013).
1076:, and is analogous to the counterintuitive
2572:
2385:
2371:
2363:
2007:: CS1 maint: location missing publisher (
1661:
1321:Condorcet methods are highly resistant to
942:
928:
18:
2236:. Springer Science & Business Media.
2204:
1940:"Majority decision and Condorcet winners"
1903:
1888:"Consistent Probabilistic Social Choice"
1217:
1193:Nicolas de Caritat, Marquis de Condorcet
2830:Independence of irrelevant alternatives
2608:Sequential proportional approval voting
1878:
999:âmore votes for than against, ignoring
985:to elections with multiple candidates.
981:, because they extend the principle of
34:
2000:
1763:The Theory of Committees and Elections
1211:Suppose the government comes across a
1991:(SSRN Scholarly Paper), Rochester, NY
1087:However, if voters are arranged on a
1013:
7:
2028:Annales d'Ăconomie et de Statistique
1988:Two Cheers for Instant Runoff Voting
1933:
1931:
1803:Collective Choice and Social Welfare
2640:Indirect single transferable voting
2299:Colomer, Josep M. (February 2013).
2179:; GraniÄ, Äura-Georg (2015-09-01).
2097:SIAM Journal on Applied Mathematics
2093:"Condorcet Social Choice Functions"
2063:SIAM Journal on Applied Mathematics
2059:"Condorcet Social Choice Functions"
1124:ranked-choice in the United States
14:
2260:Van Deemen, Adrian (2014-03-01).
1460:satisfy the Condorcet criterion.
2135:The Journal of Political Economy
1841:
1827:
1248:
1023:
911:
898:
886:
834:McKelveyâSchofield chaos theorem
480:Semi-proportional representation
112:First preference plurality (FPP)
2197:10.1016/j.electstud.2015.04.003
2751:Mixed ballot transferable vote
1632:, where most voters preferred
872:Harsanyi's utilitarian theorem
829:Moulin's impossibility theorem
794:Conflicting majorities paradox
1:
2226:; Newing, R.A. (2013-03-09).
1089:left-right political spectrum
698:Frustrated majorities paradox
16:Property of electoral systems
2952:Comparison of voting systems
2794:Satisfaction approval voting
2779:Single non-transferable vote
2598:Proportional approval voting
1435:Tideman's alternative method
1317:Stability (no-weak-spoilers)
1078:intransitive dice phenomenon
964:majority-preferred candidate
867:Condorcet dominance theorems
807:Social and collective choice
2558:Graduated majority judgment
2057:Fishburn, Peter C. (1977).
1582:Highest median voting rules
533:By mechanism of combination
304:Proportional representation
3011:
2810:Condorcet winner criterion
2501:First-past-the-post voting
1956:10.1007/s00355-020-01244-4
1769:Cambridge University Press
1651:
1628:. An example would be the
1613:
1579:
1545:
1526:
1442:Category:Condorcet methods
1384:
1128:first preference plurality
1112:Tideman alternative method
1074:Condorcet's voting paradox
958:, a candidate is called a
731:Multiple districts paradox
462:Fractional approval voting
450:Interactive representation
2995:Electoral system criteria
2965:
2957:Voting systems by country
2860:Mutual majority criterion
2815:Condorcet loser criterion
2761:Vote linkage mixed system
2673:Largest remainders method
2400:
2354:10.1007/s11238-012-9306-7
2313:10.1007/s00355-011-0598-2
2305:Social Choice and Welfare
2278:10.1007/s11127-013-0133-3
1944:Social Choice and Welfare
1857:Condorcet loser criterion
1477:(and the closely related
1283:
1275:
1260:
1232:
1176:. Because his manuscript
678:Paradoxes and pathologies
527:Mixed-member proportional
522:Mixed-member majoritarian
517:By results of combination
408:Approval-based committees
2850:Majority loser criterion
2736:Additional member system
2694:Hagenbach-Bischoff quota
2613:Single transferable vote
2538:Positional voting system
2474:Minimax Condorcet method
2432:Combined approval voting
1630:2000 election in Florida
1213:windfall source of funds
1183:The first revolution in
857:Condorcet's jury theorem
658:Double simultaneous vote
633:Ruralâurban proportional
628:Dual-member proportional
590:
579:
546:Parallel (superposition)
438:Fractional social choice
425:Expanding approvals rule
254:
239:
224:
155:
144:
120:
2875:Resolvability criterion
2865:Participation criterion
2840:Later-no-harm criterion
2656:Highest averages method
1985:Lewyn, Michael (2012),
1616:Plurality voting system
1335:participation criterion
1148:tyranny of the majority
1066:round-robin tournaments
784:Tyranny of the majority
561:Fusion (majority bonus)
378:Quota-remainder methods
2916:First-preference votes
2855:Monotonicity criterion
2825:Independence of clones
2528:Simple majoritarianism
1626:vote-splitting effects
1311:voting system criteria
918:Mathematics portal
824:Majority impossibility
813:Impossibility theorems
609:Negative vote transfer
430:Method of equal shares
51:
2820:Consistency criterion
2741:Alternative vote plus
2506:Instant-runoff voting
1938:Sen, Amartya (2020).
1783:. Oxford: Blackwell.
1548:Instant-runoff voting
1542:Instant-runoff voting
1465:Instant-runoff voting
1201:political philosopher
1120:instant-runoff voting
1070:rock, paper, scissors
721:Best-is-worst paradox
710:Pathological response
445:Direct representation
98:Single-winner methods
50:
2890:Seats-to-votes ratio
2661:Webster/Sainte-Laguë
1398:tournament solutions
1305:Desirable properties
1292:tournament solutions
1189:Age of Enlightenment
1093:median voter theorem
905:Economics portal
852:Median voter theorem
71:Comparative politics
2870:Plurality criterion
2469:KemenyâYoung method
2342:Theory and Decision
2177:AlĂłs-Ferrer, Carlos
1567:B > C > A: 31
1564:C > B > A: 34
1561:A > B > C: 35
1359:top-cycle criterion
1223:... vs. Spend more
893:Politics portal
604:Vote linkage system
575:Seat linkage system
162:Ranked-choice (RCV)
2911:Election threshold
2845:Majority criterion
2521:Supplementary vote
2089:Fishburn, Peter C.
1867:Multiwinner voting
1849:Mathematics portal
1799:Sen, Amartya Kumar
1777:Farquharson, Robin
1226:... vs. Cut taxes
1114:. Methods that do
1097:overall competence
1015:[kÉÌdÉÊsÉ]
789:Discursive dilemma
748:Lesser evil voting
623:Supermixed systems
326:Largest remainders
184:Round-robin voting
52:
2982:
2981:
2880:Reversal symmetry
2789:Cumulative voting
2771:Semi-proportional
2746:Mixed single vote
2712:
2711:
2588:Mixed single vote
2496:Exhaustive ballot
2459:Copeland's method
2454:Condorcet methods
2394:Electoral systems
2185:Electoral Studies
1914:10.3982/ECTA13337
1812:978-0-8162-7765-0
1739:
1738:
1497:Choose-one voting
1486:positional voting
1430:Total Vote Runoff
1353:Stronger criteria
1287:
1286:
1174:church governance
1064:(by analogy with
1062:tournament winner
952:
951:
839:Gibbard's theorem
779:Dominance paradox
716:Perverse response
420:Phragmen's method
286:Majority judgment
214:Positional voting
172:Condorcet methods
40:electoral systems
3002:
2921:Liquid democracy
2573:
2553:Two-round system
2464:Dodgson's method
2387:
2380:
2373:
2364:
2358:
2357:
2333:
2327:
2323:
2317:
2316:
2296:
2290:
2289:
2257:
2251:
2250:
2220:
2214:
2213:
2208:
2173:
2167:
2166:
2127:
2121:
2120:
2085:
2079:
2078:
2054:
2048:
2047:
2036:10.2307/20076136
2019:
2013:
2012:
2006:
1998:
1997:
1996:
1982:
1976:
1975:
1950:(2/3): 211â217.
1935:
1926:
1925:
1907:
1898:(5): 1839â1880.
1883:
1862:Condorcet method
1851:
1846:
1845:
1837:
1832:
1831:
1816:
1794:
1781:Theory of Voting
1772:
1766:
1662:
1621:Plurality voting
1610:Plurality voting
1387:Condorcet method
1255:
1252:
1251:
1218:
1132:two-round system
1108:Schulze's method
1055:
1054:
1051:
1050:
1047:
1044:
1041:
1038:
1035:
1032:
1029:
1022:
1017:
1012:
944:
937:
930:
916:
915:
903:
902:
891:
890:
846:Positive results
741:Strategic voting
638:Majority jackpot
595:
584:
455:Liquid democracy
331:National remnant
321:Highest averages
258:
243:
228:
160:
151:Alternative vote
149:
133:Partisan primary
125:
66:Mechanism design
19:
3010:
3009:
3005:
3004:
3003:
3001:
3000:
2999:
2985:
2984:
2983:
2978:
2961:
2940:
2894:
2885:Smith criterion
2798:
2765:
2726:Parallel voting
2708:
2704:Imperiali quota
2677:
2644:
2562:
2516:Contingent vote
2479:Nanson's method
2437:Unified primary
2427:Approval voting
2413:
2396:
2391:
2361:
2335:
2334:
2330:
2324:
2320:
2298:
2297:
2293:
2259:
2258:
2254:
2244:
2228:McLean, Iain S.
2222:
2221:
2217:
2175:
2174:
2170:
2129:
2128:
2124:
2109:10.1137/0133030
2087:
2086:
2082:
2056:
2055:
2051:
2021:
2020:
2016:
1999:
1994:
1992:
1984:
1983:
1979:
1937:
1936:
1929:
1885:
1884:
1880:
1876:
1847:
1840:
1835:Politics portal
1833:
1826:
1823:
1813:
1797:
1791:
1775:
1755:
1752:
1750:Further reading
1744:adding a runoff
1670:
1667:
1656:
1650:
1618:
1612:
1588:
1580:Main articles:
1578:
1550:
1544:
1531:
1525:
1520:
1507:
1450:
1394:
1389:
1383:
1378:
1355:
1331:
1323:spoiler effects
1319:
1307:
1253:
1249:
1209:
1156:
1026:
1020:
1019:
1010:
960:majority winner
948:
910:
909:
897:
885:
877:
876:
843:
819:Arrow's theorem
809:
799:
798:
767:
737:
726:No-show paradox
707:
693:Cloning paradox
683:Spoiler effects
680:
670:
669:
644:
531:
514:
504:
503:
476:
467:Maximal lottery
434:
415:Thiele's method
404:
374:
306:
296:
295:
281:Approval voting
269:Cardinal voting
265:
210:
204:Maximal lottery
168:
100:
90:
17:
12:
11:
5:
3008:
3006:
2998:
2997:
2987:
2986:
2980:
2979:
2966:
2963:
2962:
2960:
2959:
2954:
2948:
2946:
2942:
2941:
2939:
2938:
2933:
2928:
2923:
2918:
2913:
2908:
2902:
2900:
2896:
2895:
2893:
2892:
2887:
2882:
2877:
2872:
2867:
2862:
2857:
2852:
2847:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2806:
2804:
2800:
2799:
2797:
2796:
2791:
2786:
2784:Limited voting
2781:
2775:
2773:
2767:
2766:
2764:
2763:
2758:
2753:
2748:
2743:
2738:
2733:
2728:
2722:
2720:
2714:
2713:
2710:
2709:
2707:
2706:
2701:
2696:
2691:
2685:
2683:
2679:
2678:
2676:
2675:
2670:
2669:
2668:
2663:
2652:
2650:
2646:
2645:
2643:
2642:
2637:
2632:
2631:
2630:
2625:
2620:
2610:
2605:
2600:
2595:
2590:
2585:
2579:
2577:
2570:
2564:
2563:
2561:
2560:
2555:
2550:
2545:
2540:
2535:
2530:
2525:
2524:
2523:
2518:
2513:
2511:Coombs' method
2503:
2498:
2493:
2492:
2491:
2489:Schulze method
2486:
2481:
2476:
2471:
2466:
2461:
2451:
2449:Bucklin voting
2446:
2441:
2440:
2439:
2434:
2423:
2421:
2415:
2414:
2401:
2398:
2397:
2392:
2390:
2389:
2382:
2375:
2367:
2360:
2359:
2328:
2318:
2291:
2272:(3): 311â330.
2252:
2242:
2215:
2168:
2147:10.1086/256633
2122:
2103:(3): 469â489.
2080:
2069:(3): 469â489.
2049:
2014:
1977:
1927:
1877:
1875:
1872:
1871:
1870:
1864:
1859:
1853:
1852:
1838:
1822:
1819:
1818:
1817:
1811:
1805:. Holden-Day.
1795:
1789:
1773:
1751:
1748:
1737:
1736:
1733:
1730:
1727:
1723:
1722:
1719:
1716:
1713:
1709:
1708:
1705:
1702:
1699:
1695:
1694:
1691:
1688:
1685:
1681:
1680:
1677:
1674:
1671:
1668:
1665:
1652:Main article:
1649:
1646:
1614:Main article:
1611:
1608:
1603:
1602:
1599:
1596:
1586:Bucklin voting
1577:
1576:Bucklin/Median
1574:
1569:
1568:
1565:
1562:
1546:Main article:
1543:
1540:
1527:Main article:
1524:
1521:
1519:
1516:
1506:
1503:
1502:
1501:
1500:
1499:
1494:
1482:
1475:Bucklin voting
1472:
1467:
1454:ordinal voting
1452:The following
1449:
1446:
1438:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1396:Most sensible
1393:
1390:
1385:Main article:
1382:
1379:
1377:
1374:
1354:
1351:
1330:
1327:
1318:
1315:
1306:
1303:
1285:
1284:
1282:
1277:
1273:
1272:
1270:
1265:
1262:
1258:
1257:
1242:
1239:
1236:
1230:
1229:
1227:
1224:
1221:
1208:
1205:
1178:Ars Electionis
1155:
1152:
1144:highest median
1122:(often called
972:Voting systems
968:more than half
950:
949:
947:
946:
939:
932:
924:
921:
920:
908:
907:
895:
882:
879:
878:
875:
874:
869:
864:
859:
854:
842:
841:
836:
831:
826:
821:
810:
805:
804:
801:
800:
797:
796:
791:
786:
781:
766:
765:
763:Turkey-raising
760:
755:
750:
736:
735:
734:
733:
723:
718:
706:
705:
703:Center squeeze
700:
695:
690:
688:Spoiler effect
681:
676:
675:
672:
671:
668:
667:
662:
661:
660:
647:By ballot type
643:
642:
641:
640:
635:
630:
620:
619:
618:
617:
616:
611:
601:
600:
599:
588:
565:
564:
563:
558:
553:
548:
530:
529:
524:
515:
510:
509:
506:
505:
502:
501:
499:Limited voting
496:
495:
494:
475:
474:
469:
464:
459:
458:
457:
452:
433:
432:
427:
422:
417:
403:
402:
397:
392:
387:
373:
372:
371:
370:
368:Localized list
365:
360:
355:
350:
340:
339:
338:
336:Biproportional
333:
328:
323:
307:
302:
301:
298:
297:
294:
293:
288:
283:
278:
264:
263:
248:
233:
209:
208:
207:
206:
201:
196:
191:
181:
167:
166:
165:
164:
153:
140:Instant-runoff
137:
136:
135:
127:Jungle primary
114:
103:Single vote -
101:
96:
95:
92:
91:
89:
88:
78:
73:
68:
63:
57:
54:
53:
43:
42:
32:
31:
15:
13:
10:
9:
6:
4:
3:
2:
3007:
2996:
2993:
2992:
2990:
2977:
2976:
2971:
2970:
2964:
2958:
2955:
2953:
2950:
2949:
2947:
2943:
2937:
2934:
2932:
2929:
2927:
2924:
2922:
2919:
2917:
2914:
2912:
2909:
2907:
2904:
2903:
2901:
2897:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2808:
2807:
2805:
2801:
2795:
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2776:
2774:
2772:
2768:
2762:
2759:
2757:
2754:
2752:
2749:
2747:
2744:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2723:
2721:
2719:
2715:
2705:
2702:
2700:
2697:
2695:
2692:
2690:
2687:
2686:
2684:
2680:
2674:
2671:
2667:
2664:
2662:
2659:
2658:
2657:
2654:
2653:
2651:
2647:
2641:
2638:
2636:
2633:
2629:
2626:
2624:
2621:
2619:
2616:
2615:
2614:
2611:
2609:
2606:
2604:
2601:
2599:
2596:
2594:
2591:
2589:
2586:
2584:
2581:
2580:
2578:
2574:
2571:
2569:
2565:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2522:
2519:
2517:
2514:
2512:
2509:
2508:
2507:
2504:
2502:
2499:
2497:
2494:
2490:
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2465:
2462:
2460:
2457:
2456:
2455:
2452:
2450:
2447:
2445:
2442:
2438:
2435:
2433:
2430:
2429:
2428:
2425:
2424:
2422:
2420:
2419:Single-winner
2416:
2412:
2410:
2406:
2399:
2395:
2388:
2383:
2381:
2376:
2374:
2369:
2368:
2365:
2355:
2351:
2347:
2343:
2339:
2332:
2329:
2322:
2319:
2314:
2310:
2306:
2302:
2295:
2292:
2287:
2283:
2279:
2275:
2271:
2267:
2266:Public Choice
2263:
2256:
2253:
2249:
2245:
2243:9789401148603
2239:
2235:
2234:
2229:
2225:
2224:Black, Duncan
2219:
2216:
2212:
2207:
2202:
2198:
2194:
2190:
2186:
2182:
2178:
2172:
2169:
2164:
2160:
2156:
2152:
2148:
2144:
2140:
2136:
2132:
2131:Black, Duncan
2126:
2123:
2118:
2114:
2110:
2106:
2102:
2098:
2094:
2090:
2084:
2081:
2076:
2072:
2068:
2064:
2060:
2053:
2050:
2045:
2041:
2037:
2033:
2030:(51): 29â48.
2029:
2025:
2018:
2015:
2010:
2004:
1990:
1989:
1981:
1978:
1973:
1969:
1965:
1961:
1957:
1953:
1949:
1945:
1941:
1934:
1932:
1928:
1923:
1919:
1915:
1911:
1906:
1901:
1897:
1893:
1889:
1882:
1879:
1873:
1868:
1865:
1863:
1860:
1858:
1855:
1854:
1850:
1844:
1839:
1836:
1830:
1825:
1820:
1814:
1808:
1804:
1800:
1796:
1792:
1790:0-631-12460-8
1786:
1782:
1778:
1774:
1770:
1765:
1764:
1758:
1757:Black, Duncan
1754:
1753:
1749:
1747:
1745:
1734:
1731:
1728:
1725:
1724:
1720:
1717:
1714:
1711:
1710:
1706:
1703:
1700:
1697:
1696:
1692:
1689:
1686:
1683:
1682:
1678:
1675:
1672:
1664:
1663:
1660:
1655:
1647:
1645:
1643:
1639:
1635:
1631:
1627:
1622:
1617:
1609:
1607:
1600:
1597:
1594:
1593:
1592:
1587:
1583:
1575:
1573:
1566:
1563:
1560:
1559:
1558:
1554:
1549:
1541:
1539:
1535:
1530:
1522:
1517:
1515:
1512:
1504:
1498:
1495:
1493:
1490:
1489:
1488:, including:
1487:
1484:All kinds of
1483:
1480:
1479:median voting
1476:
1473:
1471:
1468:
1466:
1463:
1462:
1461:
1459:
1455:
1447:
1445:
1443:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1411:
1408:
1406:
1403:
1402:
1401:
1399:
1391:
1388:
1380:
1375:
1373:
1371:
1368:
1364:
1360:
1352:
1350:
1348:
1344:
1340:
1336:
1329:Participation
1328:
1326:
1324:
1316:
1314:
1312:
1304:
1302:
1300:
1295:
1293:
1281:
1278:
1274:
1271:
1269:
1266:
1263:
1259:
1256:
1246:
1243:
1240:
1237:
1235:
1231:
1228:
1225:
1222:
1220:
1219:
1216:
1214:
1206:
1204:
1202:
1198:
1197:mathematician
1194:
1190:
1186:
1185:voting theory
1181:
1179:
1175:
1171:
1168:
1164:
1161:
1153:
1151:
1149:
1145:
1141:
1137:
1136:rated systems
1133:
1129:
1125:
1121:
1117:
1113:
1109:
1105:
1100:
1098:
1094:
1090:
1085:
1083:
1079:
1075:
1071:
1067:
1063:
1059:
1053:
1016:
1008:
1007:
1003:âis called a
1002:
998:
996:
992:
986:
984:
983:majority rule
980:
978:
977:majority-rule
973:
969:
965:
961:
957:
945:
940:
938:
933:
931:
926:
925:
923:
922:
919:
914:
906:
901:
896:
894:
889:
884:
883:
881:
880:
873:
870:
868:
865:
863:
862:May's theorem
860:
858:
855:
853:
850:
849:
848:
847:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
816:
815:
814:
808:
803:
802:
795:
792:
790:
787:
785:
782:
780:
777:
776:
775:
774:
773:
772:majority rule
770:Paradoxes of
764:
761:
759:
756:
754:
751:
749:
746:
745:
744:
743:
742:
732:
729:
728:
727:
724:
722:
719:
717:
714:
713:
712:
711:
704:
701:
699:
696:
694:
691:
689:
686:
685:
684:
679:
674:
673:
666:
663:
659:
656:
655:
654:
651:
650:
649:
648:
639:
636:
634:
631:
629:
626:
625:
624:
621:
615:
612:
610:
607:
606:
605:
602:
598:
593:
589:
587:
582:
578:
577:
576:
573:
572:
571:
570:
566:
562:
559:
557:
554:
552:
549:
547:
544:
543:
542:
541:
536:
535:
534:
528:
525:
523:
520:
519:
518:
513:
512:Mixed systems
508:
507:
500:
497:
493:
490:
489:
488:
485:
484:
483:
482:
481:
473:
472:Random ballot
470:
468:
465:
463:
460:
456:
453:
451:
448:
447:
446:
443:
442:
441:
440:
439:
431:
428:
426:
423:
421:
418:
416:
413:
412:
411:
410:
409:
401:
398:
396:
393:
391:
388:
386:
383:
382:
381:
380:
379:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
345:
344:
341:
337:
334:
332:
329:
327:
324:
322:
319:
318:
317:
316:Apportionment
314:
313:
312:
311:
305:
300:
299:
292:
289:
287:
284:
282:
279:
277:
274:
273:
272:
271:
270:
261:
257:
252:
251:Antiplurality
249:
246:
242:
237:
234:
231:
227:
222:
219:
218:
217:
216:
215:
205:
202:
200:
197:
195:
192:
190:
187:
186:
185:
182:
180:
179:Condorcet-IRV
177:
176:
175:
174:
173:
163:
158:
154:
152:
147:
143:
142:
141:
138:
134:
131:
130:
128:
123:
118:
115:
113:
110:
109:
108:
106:
99:
94:
93:
86:
82:
79:
77:
74:
72:
69:
67:
64:
62:
61:Social choice
59:
58:
56:
55:
49:
45:
44:
41:
37:
36:Social choice
33:
29:
25:
21:
20:
2973:
2967:
2809:
2583:Mixed-member
2568:Proportional
2543:Score voting
2484:Ranked pairs
2403:Part of the
2402:
2348:(1): 59â77.
2345:
2341:
2331:
2321:
2304:
2294:
2269:
2265:
2255:
2247:
2232:
2218:
2210:
2188:
2184:
2171:
2141:(1): 23â34.
2138:
2134:
2125:
2100:
2096:
2083:
2066:
2062:
2052:
2027:
2017:
1993:, retrieved
1987:
1980:
1947:
1943:
1895:
1892:Econometrica
1891:
1881:
1802:
1780:
1762:
1740:
1657:
1654:Score voting
1648:Score voting
1619:
1604:
1589:
1570:
1555:
1551:
1536:
1532:
1511:rated voting
1508:
1505:Rated voting
1470:Coombs' rule
1457:
1451:
1439:
1420:Ranked pairs
1410:Kemeny-Young
1395:
1366:
1356:
1343:ranked pairs
1339:ranked pairs
1332:
1320:
1308:
1296:
1288:
1247:
1233:
1210:
1182:
1177:
1157:
1140:score voting
1115:
1104:Ranked Pairs
1101:
1086:
1061:
1057:
1004:
994:
990:
987:
975:
963:
959:
953:
845:
844:
811:
769:
768:
753:Exaggeration
739:
738:
709:
708:
697:
682:
646:
645:
614:Mixed ballot
569:Compensatory
567:
540:compensatory
537:
532:
516:
478:
477:
436:
435:
406:
405:
376:
375:
363:List-free PR
308:
276:Score voting
267:
266:
212:
211:
199:Ranked pairs
170:
169:
102:
2926:Spoilt vote
2689:Droop quota
2628:Schulze STV
2603:Ruralâurban
2548:STAR voting
2444:Borda count
2326:2877-2879).
2206:1765/111247
1642:Ralph Nader
1638:George Bush
1529:Borda count
1523:Borda count
1492:Borda count
1456:methods do
1276:Spend more
1170:Ramon Llull
1163:philosopher
1082:probability
1001:abstentions
653:Single vote
556:Conditional
551:Coexistence
400:Quota Borda
390:Schulze STV
348:Closed list
291:STAR voting
236:Borda count
2945:Comparison
2699:Hare quota
2649:Allocation
2635:Spare vote
2623:Hare-Clark
2593:Party-list
1995:2024-04-21
1905:1503.00694
1874:References
1666:Candidates
1444:for more.
1370:indirectly
1261:Cut taxes
1167:theologian
1130:, and the
1110:, and the
1021:English:
758:Truncation
487:Cumulative
310:Party-list
85:By country
76:Comparison
2936:Unseating
2931:Sortition
2533:Plurality
2409:Economics
2286:1573-7101
2191:: 56â71.
2163:153953456
2117:0036-1399
2075:0036-1399
2044:0769-489X
1964:0176-1714
1922:0012-9682
1376:By method
1363:top cycle
1080:known in
1058:beats-all
1006:Condorcet
979:principle
665:Dual-vote
358:Panachage
353:Open list
343:List type
221:Plurality
117:Two-round
105:plurality
28:Economics
2989:Category
2803:Criteria
2756:Scorporo
2405:politics
2091:(1977).
2003:citation
1972:45286016
1821:See also
1801:(1970).
1779:(1969).
1759:(1958).
1726:Average
1518:Examples
1349:family.
1299:rankings
1264:522â186
1241:496â212
1238:403â305
1234:Pay debt
1118:include
997:majority
995:relative
956:election
385:Hare STV
24:Politics
22:A joint
2975:Project
2666:D'Hondt
2618:CPO-STV
2576:Systems
2155:1825026
1634:Al Gore
1425:Schulze
1415:Minimax
1347:minimax
1207:Example
1160:Spanish
1154:History
1138:, like
1134:. Most
1011:French:
395:CPO-STV
245:Baldwin
194:Schulze
189:Minimax
107:methods
2969:Portal
2906:Ballot
2682:Quotas
2411:series
2284:
2240:
2161:
2153:
2115:
2073:
2042:
1970:
1962:
1920:
1809:
1787:
991:simple
954:In an
260:Coombs
30:series
2899:Other
2718:Mixed
2159:S2CID
2151:JSTOR
1968:JSTOR
1900:arXiv
1729:2.55
1669:Votes
1405:Black
1060:, or
597:'MMP'
586:'AMS'
2407:and
2282:ISSN
2238:ISBN
2113:ISSN
2071:ISSN
2040:ISSN
2009:link
1960:ISSN
1918:ISSN
1807:ISBN
1785:ISBN
1735:2.6
1732:1.6
1721:4/5
1718:5/5
1715:2/5
1707:5/5
1704:1/5
1701:0/5
1693:0/5
1690:1/5
1687:5/5
1584:and
1448:Fail
1440:See
1392:Pass
1381:List
1357:The
1199:and
1195:, a
1165:and
1142:and
538:Non-
492:SNTV
81:List
38:and
26:and
2731:MMP
2350:doi
2309:doi
2274:doi
2270:158
2201:hdl
2193:doi
2143:doi
2105:doi
2032:doi
1952:doi
1910:doi
1712:15
1698:40
1684:45
1636:to
1458:not
1280:0â2
1268:1â1
1245:2â0
1191:by
1150:).
1126:),
1116:not
1056:),
1040:ÉËr
993:or
966:if
962:or
256:el.
241:el.
230:IRV
226:el.
2991::
2972:â
2346:75
2344:.
2340:.
2307:.
2303:.
2280:.
2268:.
2264:.
2246:.
2209:.
2199:.
2189:39
2187:.
2183:.
2157:.
2149:.
2139:56
2137:.
2111:.
2101:33
2099:.
2095:.
2067:33
2065:.
2061:.
2038:.
2026:.
2005:}}
2001:{{
1966:.
1958:.
1948:54
1946:.
1942:.
1930:^
1916:.
1908:.
1896:84
1894:.
1890:.
1767:.
1679:C
1676:B
1673:A
1644:.
1367:or
1313:.
1203:.
1106:,
1084:.
1049:eÉȘ
1018:,
592:NZ
581:UK
157:US
146:UK
129:)
122:US
2386:e
2379:t
2372:v
2356:.
2352::
2315:.
2311::
2288:.
2276::
2203::
2195::
2165:.
2145::
2119:.
2107::
2077:.
2046:.
2034::
2011:)
1974:.
1954::
1924:.
1912::
1902::
1815:.
1793:.
1771:.
1481:)
1345:-
1254:Y
1052:/
1046:s
1043:Ë
1037:d
1034:n
1031:É
1028:k
1025:/
1009:(
943:e
936:t
929:v
594::
583::
262:)
253:(
247:)
238:(
232:)
223:(
159::
148::
124::
119:(
87:)
83:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
