913:
955:
48:
888:
900:
1102:
1110:
Each voter casts their vote by selecting the candidates they support. The following table shows the results of the votes. Each row starts by saying how many voters voted in that way and marks each candidate that group of voters supported. The bottom row shows the number of votes each candidate received.
1013:
Each ballot is assigned a value equal to the reciprocal of one more than the number of candidates approved on that ballot who have been designated as elected. Each ballot is counted at its current value as a vote for all continuing candidates approved on that ballot. The candidate with the most votes
1109:
For this example, there is an election for a committee with 3 winners. There are six candidates from two main parties: A, B, and C from one party, and X, Y, and Z from another party. About 2/3 of the voters support the first party, and the other roughly 1/3 of the voters support the second party.
1498:, because not as many of the votes for Candidate X were halved. In round 3, anyone who voted for either Candidates C or X has their vote count 1/2, and anyone who voted for both has their vote count 1/3. If anyone had voted for neither, their vote would remain at 1. Below is that table.
1293:, and their vote is not counted in later rounds. For the second round, anyone who voted for Candidate C has their vote counted as only 1/2. Below is the chart for round 2. A second column on the left has been added to indicate the weight of each ballot.
1009:
Sequential
Proportional Approval Voting (SPAV) uses Approval Voting ballots to elect multiple winners equitably by selecting a candidate in each round and then reweighing the approvals for the subsequent rounds.
1954:
1050:
941:
2291:
2131:
1056:
is the number of candidates approved on that ballot who were already elected, until the required number of candidates is elected. This reweighting is based on the
2096:
Aziz, Haris; Serge
Gaspers, Joachim Gudmundsson, Simon Mackenzie, Nicholas Mattei, Toby Walsh (2014). "Computational Aspects of Multi-Winner Approval Voting".
2901:
2741:
1086:, permitting votes to be counted either by hand or by computer, rather than requiring a computer to determine the outcome of all but the simplest elections.
2509:
632:
1706:
had been used instead, the final committee would be all three candidates from the first party, as they had the highest three vote totals without scaling.
1105:
Illustration of the example election. Candidates with the most votes wins for each round. When a candidate is elected they are removed for the next round.
2080:
1093:, SPAV is better at selecting more central candidates, that represent all the voters, where STV is better at mimicking the distribution of the voters.
1001:
from 1909-1921, when it was replaced by a cruder "party-list" style system as it was easier to calculate, and is still used for some local elections.
1702:. The final result has 2/3 winners from the party that had about 2/3 of the votes, and 1/3 winner from the party that had about 1/3 of the votes. If
2637:
2489:
664:
526:
521:
2736:
934:
627:
2499:
2284:
2185:
Sánchez-Fernández, Luis; Elkind, Edith; Lackner, Martin; Fernández, Norberto; Fisteus, Jesús; Val, Pablo
Basanta; Skowron, Piotr (2017-02-10).
309:
2158:
2115:
2062:
833:
2863:
1952:
84:
2906:
2546:
927:
2277:
2254:
Aziz, H., Brill, M., Conitzer, V., et al. (2014): "Justified
Representation in Approval-Based Committee Voting", arXiv:1407.8269 p5
2234:
1014:
in the round is elected. The process continues until the number of elected candidates is equal to the number of seats to be filled.
2881:
1017:
At each stage, the unelected candidate with the highest approval score is elected. Then the value of each voter’s ballot is set at
828:
2731:
2677:
818:
568:
539:
479:
2529:
2858:
550:
75:
2657:
613:
2164:
255:
240:
225:
2700:
2685:
2504:
1874:
1869:
1803:
1083:
1076:
986:
871:
491:
414:
335:
2751:
2474:
2464:
2325:
303:
285:
126:
1951:
E. Phragmén (1899): "Till frågan om en proportionell valmetod." Statsvetenskaplig tidskrifts Vol. 2, No. 2: pp 87-95
856:
2716:
2407:
2028:
747:
730:
697:
677:
461:
449:
419:
220:
178:
111:
555:
2766:
2721:
2667:
2579:
603:
596:
80:
2911:
2756:
2642:
2600:
2519:
2444:
2380:
2338:
1889:
1715:
1090:
657:
585:
574:
437:
424:
407:
384:
362:
325:
315:
2375:
990:
2257:
2153:. AAMAS '19. Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems: 1946–1948.
2781:
2771:
2746:
2562:
2439:
2078:
1879:
783:
637:
320:
2822:
2761:
2624:
2567:
1743:
812:
692:
622:
429:
2726:
2647:
2412:
720:
560:
444:
250:
229:
161:
139:
912:
778:
1718:
whenever the committee size is at most 5, but might violate it when the committee size is at least 6.
1491:
Despite
Candidates A and B having so many votes in the first round, Candidate X is the second winner,
1071:
where a voter may withhold approval from candidates who are likely to be elected in any case, as with
1020:
2796:
2365:
851:
838:
806:
70:
2776:
2370:
1061:
757:
591:
244:
954:
2817:
2427:
2226:
2198:
2125:
2101:
2003:
1995:
1934:
994:
917:
788:
399:
183:
2385:
866:
2786:
2695:
2652:
2572:
2494:
2417:
2402:
2360:
2218:
2154:
2111:
2058:
2050:
1987:
1926:
1730:
1072:
1057:
823:
793:
715:
652:
486:
213:
188:
171:
39:
2827:
2459:
2315:
2300:
2208:
2151:
Proceedings of the 18th
International Conference on Autonomous Agents and MultiAgent Systems
2098:
Proceedings of the 2015 International
Conference on Autonomous Agents and Multiagent Systems
1979:
1918:
978:
904:
861:
752:
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454:
330:
156:
150:
132:
121:
116:
104:
65:
27:
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1884:
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1703:
1068:
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892:
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377:
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145:
23:
2186:
47:
2690:
2395:
2355:
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702:
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367:
342:
193:
887:
2895:
2434:
2007:
1911:"The Excess Method: A Multiwinner Approval Voting Procedure to Allocate Wasted Votes"
771:
471:
259:
97:
60:
35:
2230:
1938:
2449:
2390:
2145:
Faliszewski, Piotr; Skowron, Piotr; Szufa, Stanisław; Talmon, Nimrod (2019-05-08).
511:
275:
268:
198:
2146:
2832:
2595:
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389:
347:
290:
235:
2605:
2541:
2222:
2213:
1991:
1930:
2842:
2837:
2077:
Steven J. Brams, D. Marc
Kilgour (2009): "Satisfaction Approval Voting": p4
357:
352:
1910:
899:
2662:
1922:
608:
2022:
2524:
1999:
394:
997:
in the early 1900s. It was used (with adaptations for party lists) in
2812:
1286:
Because
Candidate C has the most support, they are the first winner,
998:
2269:
2106:
1983:
2203:
2255:
1100:
953:
1970:
Lewis, Edward G. (1950). "Review of Modern
Foreign Governments".
2273:
2191:
Proceedings of the AAAI Conference on Artificial Intelligence
1082:
It is a much computationally simpler algorithm than harmonic
985:
to a multiple winner election. It is a simplified version of
46:
2024:
Proportional Representation: A Study in Methods of Election
1089:
When comparing Sequential Proportional Approval Voting to
2147:"Proportional Representation in Elections: STV vs PAV"
1714:
Sequential-PAV satisfies the fairness property called
1060:(Jefferson method). Other weighting formulas such as
1023:
2053:. In Jean-François Laslier; M. Remzi Sanver (eds.).
2851:
2805:
2709:
2676:
2623:
2588:
2555:
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2473:
2324:
1064:may be used while still being referred to as SPAV.
1044:
2051:"Approval Balloting for Multi-winner Elections"
1751:Support monotonicity without additional voters
2285:
935:
8:
2742:Independence of Smith-dominated alternatives
2130:: CS1 maint: multiple names: authors list (
1695:Candidate B is the third and final winner,
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18:
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2202:
2105:
1024:
1022:
1723:
1500:
1295:
1112:
2737:Independence of irrelevant alternatives
2515:Sequential proportional approval voting
2187:"Proportional Justified Representation"
1901:
1835:Sequential Proportional Approval Voting
963:Sequential proportional approval voting
34:
2123:
1972:The American Political Science Review
1909:Brams, Steven; Brill, Markus (2018).
7:
2902:Semi-proportional electoral systems
2547:Indirect single transferable voting
993:, proposed by Danish statistician
14:
2021:Humphreys, John H. (2006-01-01).
1045:{\displaystyle {\frac {1}{s+1}}}
911:
898:
886:
834:McKelvey–Schofield chaos theorem
480:Semi-proportional representation
112:First preference plurality (FPP)
16:Multiple-winner electoral system
2237:from the original on 2021-06-24
2167:from the original on 2022-05-11
2031:from the original on 2022-05-11
2658:Mixed ballot transferable vote
2057:. Springer. pp. 105–124.
1067:There is an incentive towards
958:Flow chart of SPAV calculation
872:Harsanyi's utilitarian theorem
829:Moulin's impossibility theorem
794:Conflicting majorities paradox
1:
698:Frustrated majorities paradox
2859:Comparison of voting systems
2701:Satisfaction approval voting
2686:Single non-transferable vote
2505:Proportional approval voting
1875:Satisfaction approval voting
1870:Proportional approval voting
1804:Proportional approval voting
1761:inclusion- strategyproofness
1084:proportional approval voting
1077:single non-transferable vote
987:proportional approval voting
981:that extends the concept of
867:Condorcet dominance theorems
807:Social and collective choice
2465:Graduated majority judgment
2055:Handbook on Approval Voting
533:By mechanism of combination
304:Proportional representation
2928:
2907:Cardinal electoral systems
2717:Condorcet winner criterion
2408:First-past-the-post voting
989:. It is a special case of
971:reweighted approval voting
731:Multiple districts paradox
462:Fractional approval voting
450:Interactive representation
2872:
2864:Voting systems by country
2767:Mutual majority criterion
2722:Condorcet loser criterion
2668:Vote linkage mixed system
2580:Largest remainders method
2307:
2049:Kilgour, D. Marc (2010).
678:Paradoxes and pathologies
527:Mixed-member proportional
522:Mixed-member majoritarian
517:By results of combination
408:Approval-based committees
2757:Majority loser criterion
2643:Additional member system
2601:Hagenbach-Bischoff quota
2520:Single transferable vote
2445:Positional voting system
2381:Minimax Condorcet method
2339:Combined approval voting
2214:10.1609/aaai.v31i1.10611
1890:Single transferable vote
1766:Computational complexity
1716:justified representation
1091:Single Transferable Vote
857:Condorcet's jury theorem
658:Double simultaneous vote
633:Rural–urban proportional
628:Dual-member proportional
590:
579:
546:Parallel (superposition)
438:Fractional social choice
425:Expanding approvals rule
254:
239:
224:
155:
144:
120:
2782:Resolvability criterion
2772:Participation criterion
2747:Later-no-harm criterion
2563:Highest averages method
1915:SSRN Electronic Journal
1880:Reweighted range voting
784:Tyranny of the majority
561:Fusion (majority bonus)
378:Quota-remainder methods
2823:First-preference votes
2762:Monotonicity criterion
2732:Independence of clones
2435:Simple majoritarianism
1746:with additional voters
1737:Committee monotonicity
1114:Votes from 200 voters
1106:
1046:
959:
918:Mathematics portal
824:Majority impossibility
813:Impossibility theorems
609:Negative vote transfer
430:Method of equal shares
51:
2727:Consistency criterion
2648:Alternative vote plus
2413:Instant-runoff voting
1297:Second Round Results
1104:
1047:
991:Thiele's voting rules
957:
721:Best-is-worst paradox
710:Pathological response
445:Direct representation
98:Single-winner methods
50:
2797:Seats-to-votes ratio
2568:Webster/Sainte-Laguë
2100:. pp. 107–115.
1923:10.2139/ssrn.3274796
1502:Third Round Results
1021:
905:Economics portal
852:Median voter theorem
71:Comparative politics
2777:Plurality criterion
2376:Kemeny–Young method
1503:
1298:
1115:
1062:Sainte-Lague method
893:Politics portal
604:Vote linkage system
575:Seat linkage system
162:Ranked-choice (RCV)
2818:Election threshold
2752:Majority criterion
2428:Supplementary vote
2260:2017-04-13 at the
2083:2012-06-28 at the
1957:2015-06-18 at the
1501:
1296:
1113:
1107:
1042:
995:Thorvald N. Thiele
960:
789:Discursive dilemma
748:Lesser evil voting
623:Supermixed systems
326:Largest remainders
184:Round-robin voting
52:
2889:
2888:
2787:Reversal symmetry
2696:Cumulative voting
2678:Semi-proportional
2653:Mixed single vote
2619:
2618:
2495:Mixed single vote
2403:Exhaustive ballot
2366:Copeland's method
2361:Condorcet methods
2301:Electoral systems
2160:978-1-4503-6309-9
2117:978-1-4503-3413-6
2064:978-3-642-02839-7
1861:
1860:
1731:Pareto efficiency
1693:
1692:
1489:
1488:
1284:
1283:
1073:cumulative voting
1040:
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
2919:
2828:Liquid democracy
2480:
2460:Two-round system
2371:Dodgson's method
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1116:
1051:
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979:electoral system
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930:
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846:Positive results
741:Strategic voting
638:Majority jackpot
595:
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455:Liquid democracy
331:National remnant
321:Highest averages
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151:Alternative vote
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133:Partisan primary
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66:Mechanism design
19:
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2792:Smith criterion
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2633:Parallel voting
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2611:Imperiali quota
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2423:Contingent vote
2386:Nanson's method
2344:Unified primary
2334:Approval voting
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2262:Wayback Machine
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2085:Wayback Machine
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2015:
1984:10.2307/1950372
1969:
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1959:Wayback Machine
1950:
1946:
1908:
1907:
1903:
1898:
1885:Approval voting
1866:
1773:Approval voting
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1704:approval voting
1700:
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1291:
1099:
1069:tactical voting
1029:
1019:
1018:
1007:
983:approval voting
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:
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467:Maximal lottery
434:
415:Thiele's method
404:
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295:
281:Approval voting
269:Cardinal voting
265:
210:
204:Maximal lottery
168:
100:
90:
17:
12:
11:
5:
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1978:(1): 209–211.
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1289:
1282:
1281:
1278:
1275:
1272:
1269:
1266:
1263:
1259:
1258:
1256:
1253:
1250:
1248:
1246:
1244:
1240:
1239:
1236:
1233:
1230:
1227:
1225:
1223:
1219:
1218:
1215:
1212:
1209:
1207:
1205:
1203:
1199:
1198:
1196:
1194:
1191:
1188:
1185:
1182:
1178:
1177:
1175:
1173:
1171:
1168:
1165:
1163:
1159:
1158:
1156:
1154:
1152:
1149:
1146:
1143:
1139:
1138:
1135:
1132:
1129:
1126:
1123:
1120:
1098:
1095:
1058:D'Hondt method
1038:
1035:
1032:
1028:
1006:
1003:
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:
2924:
2913:
2910:
2908:
2905:
2903:
2900:
2899:
2897:
2884:
2883:
2878:
2877:
2871:
2865:
2862:
2860:
2857:
2856:
2854:
2850:
2844:
2841:
2839:
2836:
2834:
2831:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2810:
2808:
2804:
2798:
2795:
2793:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2728:
2725:
2723:
2720:
2718:
2715:
2714:
2712:
2708:
2702:
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2683:
2681:
2679:
2675:
2669:
2666:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2636:
2634:
2631:
2630:
2628:
2626:
2622:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2593:
2591:
2587:
2581:
2578:
2574:
2571:
2569:
2566:
2565:
2564:
2561:
2560:
2558:
2554:
2548:
2545:
2543:
2540:
2536:
2533:
2531:
2528:
2526:
2523:
2522:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2493:
2491:
2488:
2487:
2485:
2481:
2478:
2476:
2472:
2466:
2463:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2436:
2433:
2429:
2426:
2424:
2421:
2419:
2416:
2415:
2414:
2411:
2409:
2406:
2404:
2401:
2397:
2394:
2392:
2389:
2387:
2384:
2382:
2379:
2377:
2374:
2372:
2369:
2367:
2364:
2363:
2362:
2359:
2357:
2354:
2352:
2349:
2345:
2342:
2340:
2337:
2336:
2335:
2332:
2331:
2329:
2327:
2326:Single-winner
2323:
2319:
2317:
2313:
2306:
2302:
2295:
2290:
2288:
2283:
2281:
2276:
2275:
2272:
2263:
2259:
2256:
2251:
2248:
2236:
2232:
2228:
2224:
2220:
2215:
2210:
2205:
2200:
2196:
2192:
2188:
2181:
2178:
2166:
2162:
2156:
2152:
2148:
2141:
2138:
2133:
2127:
2119:
2113:
2108:
2103:
2099:
2092:
2089:
2086:
2082:
2079:
2074:
2071:
2066:
2060:
2056:
2052:
2045:
2042:
2030:
2026:
2025:
2017:
2014:
2009:
2005:
2001:
1997:
1993:
1989:
1985:
1981:
1977:
1973:
1966:
1963:
1960:
1956:
1953:
1948:
1945:
1940:
1936:
1932:
1928:
1924:
1920:
1916:
1912:
1905:
1902:
1895:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1867:
1863:
1856:
1853:
1850:
1847:
1844:
1841:
1838:
1836:
1833:
1832:
1828:
1825:
1822:
1819:
1816:
1813:
1811:
1808:
1806:
1805:
1801:
1800:
1796:
1793:
1790:
1787:
1784:
1781:
1779:
1776:
1774:
1771:
1770:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1749:
1747:
1745:
1740:
1738:
1735:
1733:
1732:
1728:
1726:
1725:
1722:
1719:
1717:
1709:
1707:
1705:
1701:
1688:
1685:
1683:
1681:
1678:
1675:
1673:
1670:
1669:
1666:
1663:
1660:
1658:
1656:
1654:
1651:
1648:
1647:
1643:
1640:
1637:
1634:
1632:
1630:
1627:
1624:
1623:
1619:
1616:
1613:
1611:
1609:
1607:
1604:
1601:
1600:
1597:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1576:
1573:
1571:
1569:
1566:
1563:
1561:
1558:
1555:
1554:
1551:
1549:
1547:
1544:
1541:
1538:
1535:
1532:
1531:
1527:
1524:
1521:
1518:
1515:
1512:
1509:
1506:
1505:
1499:
1497:
1484:
1481:
1478:
1476:
1473:
1470:
1468:
1465:
1464:
1461:
1458:
1455:
1453:
1451:
1449:
1446:
1443:
1442:
1438:
1435:
1432:
1429:
1427:
1425:
1422:
1419:
1418:
1414:
1411:
1408:
1406:
1404:
1402:
1399:
1396:
1395:
1392:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1371:
1368:
1366:
1364:
1361:
1358:
1356:
1353:
1350:
1349:
1346:
1344:
1342:
1339:
1336:
1333:
1330:
1327:
1326:
1322:
1319:
1316:
1313:
1310:
1307:
1304:
1301:
1300:
1294:
1292:
1279:
1276:
1273:
1270:
1267:
1264:
1261:
1260:
1257:
1254:
1251:
1249:
1247:
1245:
1242:
1241:
1237:
1234:
1231:
1228:
1226:
1224:
1221:
1220:
1216:
1213:
1210:
1208:
1206:
1204:
1201:
1200:
1197:
1195:
1192:
1189:
1186:
1183:
1180:
1179:
1176:
1174:
1172:
1169:
1166:
1164:
1161:
1160:
1157:
1155:
1153:
1150:
1147:
1144:
1141:
1140:
1136:
1133:
1130:
1127:
1124:
1121:
1118:
1117:
1111:
1103:
1096:
1094:
1092:
1087:
1085:
1080:
1078:
1074:
1070:
1065:
1063:
1059:
1055:
1036:
1033:
1030:
1026:
1015:
1011:
1004:
1002:
1000:
996:
992:
988:
984:
980:
976:
972:
968:
964:
956:
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:
2880:
2874:
2514:
2490:Mixed-member
2475:Proportional
2450:Score voting
2391:Ranked pairs
2310:Part of the
2309:
2250:
2239:. Retrieved
2194:
2190:
2180:
2169:. Retrieved
2150:
2140:
2097:
2091:
2073:
2054:
2044:
2033:. Retrieved
2023:
2016:
1975:
1971:
1965:
1947:
1914:
1904:
1834:
1809:
1802:
1777:
1765:
1760:
1755:
1750:
1744:monotonicity
1741:
1736:
1729:
1720:
1713:
1696:
1694:
1528:Candidate Z
1492:
1490:
1323:Candidate Z
1287:
1285:
1137:Candidate Z
1108:
1088:
1081:
1066:
1053:
1016:
1012:
1008:
974:
970:
966:
962:
961:
845:
844:
811:
769:
768:
753:Exaggeration
739:
738:
709:
708:
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:
2833:Spoilt vote
2596:Droop quota
2535:Schulze STV
2510:Rural–urban
2455:STAR voting
2351:Borda count
2107:1407.3247v1
1756:Consistency
1525:Candidate Y
1522:Candidate X
1519:Candidate C
1516:Candidate B
1513:Candidate A
1320:Candidate Y
1317:Candidate X
1314:Candidate C
1311:Candidate B
1308:Candidate A
1262:Total Votes
1134:Candidate Y
1131:Candidate X
1128:Candidate C
1125:Candidate B
1122:Candidate A
1005:Description
653:Single vote
556:Conditional
551:Coexistence
400:Quota Borda
390:Schulze STV
348:Closed list
291:STAR voting
236:Borda count
2896:Categories
2852:Comparison
2606:Hare quota
2556:Allocation
2542:Spare vote
2530:Hare-Clark
2500:Party-list
2241:2021-06-24
2204:1611.09928
2171:2022-05-11
2035:2022-05-11
1896:References
1710:Properties
1507:# of votes
1302:# of votes
1119:# of votes
758:Truncation
487:Cumulative
310:Party-list
85:By country
76:Comparison
2843:Unseating
2838:Sortition
2440:Plurality
2316:Economics
2223:2374-3468
2126:cite book
2008:152254976
1992:0003-0554
1931:1556-5068
665:Dual-vote
358:Panachage
353:Open list
343:List type
221:Plurality
117:Two-round
105:plurality
28:Economics
2710:Criteria
2663:Scorporo
2312:politics
2258:Archived
2235:Archived
2231:17538641
2165:Archived
2081:Archived
2029:Archived
1955:Archived
1939:53600917
1864:See also
1829:NP-hard
1742:Support
1075:and the
977:) is an
385:Hare STV
24:Politics
22:A joint
2882:Project
2573:D'Hondt
2525:CPO-STV
2483:Systems
2000:1950372
1689:37 5/6
1097:Example
395:CPO-STV
245:Baldwin
194:Schulze
189:Minimax
107:methods
2876:Portal
2813:Ballot
2589:Quotas
2318:series
2229:
2221:
2157:
2114:
2061:
2006:
1998:
1990:
1937:
1929:
1810:strong
1778:strong
1686:38 1/3
1679:60 1/3
1676:57 1/3
1052:where
999:Sweden
260:Coombs
30:series
2806:Other
2625:Mixed
2227:S2CID
2199:arXiv
2197:(1).
2102:arXiv
2004:S2CID
1996:JSTOR
1935:S2CID
1848:cand
1845:cand
1820:cand
969:) or
597:'MMP'
586:'AMS'
2314:and
2219:ISSN
2155:ISBN
2132:link
2112:ISBN
2059:ISBN
1988:ISSN
1927:ISSN
1652:1/2
1628:1/3
1605:1/2
1581:1/3
1559:1/2
1536:1/2
1423:1/2
1376:1/2
1354:1/2
1331:1/2
1142:112
967:SPAV
538:Non-
492:SNTV
81:List
38:and
26:and
2638:MMP
2209:doi
1980:doi
1919:doi
1533:112
1485:75
1328:112
1280:77
1271:126
1268:122
1265:116
1202:73
975:RAV
256:el.
241:el.
230:IRV
226:el.
2898::
2879:—
2233:.
2225:.
2217:.
2207:.
2195:31
2193:.
2189:.
2163:.
2149:.
2128:}}
2124:{{
2110:.
2027:.
2002:.
1994:.
1986:.
1976:44
1974:.
1933:.
1925:.
1917:.
1913:.
1857:P
1854:×
1851:×
1842:✓
1839:×
1826:×
1823:✓
1817:✓
1814:×
1797:P
1794:✓
1791:✓
1788:✓
1785:✓
1782:✓
1644:✓
1620:✓
1602:73
1482:76
1479:78
1474:61
1471:58
1447:1
1439:✓
1415:✓
1400:1
1397:73
1277:78
1274:82
1243:1
1238:✓
1222:4
1217:✓
1181:4
1162:6
1079:.
592:NZ
581:UK
157:US
146:UK
129:)
122:US
2293:e
2286:t
2279:v
2244:.
2211::
2201::
2174:.
2134:)
2120:.
2104::
2067:.
2038:.
2010:.
1982::
1941:.
1921::
1699:3
1697:w
1664:✓
1661:✓
1649:1
1641:✓
1638:✓
1635:✓
1625:4
1617:✓
1614:✓
1593:✓
1590:✓
1587:✓
1584:✓
1578:4
1567:✓
1564:✓
1556:6
1545:✓
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