921:
20:
56:
896:
908:
1613:(i.e. Condorcet methods) elect candidates who win a pairwise majority vote. In the race above, Jefferson would win against Adams 73-65, while Jefferson would likely defeat Burr in a one-on-one election, allowing Jefferson to safely secure the presidency. However, Condorcet methods have their own advantages and disadvantages; for example, they can suffer from
1404:
1336:
but would still have the same ideological center as the population. 100% bullet voting under
Approval Voting in a multi-winner election is unlikely, as voters are incentivized to vote for acceptable moderates in addition to their favorite candidates to avoid being locked out of the election entirely.
1987:
p.145 ("But the
Bucklin system was found to be defective, as it allowed a voter's second choice vote to help defeat a voter's first choice candidate. Under these circumstances, most voters refrained from giving second choices, and the intent of discovering which candidate was favored by the majority
1606:
lessens the Burr dilemma when some voters are either honest or willing to cooperate. In the real Burr election, honest electors might assign a score of 10/10 to
Jefferson, 9/10 to Burr, and 0/10 to Adams; or they might all agree ahead of time to use this strategy. This strategy gives Jefferson 73
1682:
4. Anti-single-shot provisions: These provisions compel voters to cast a vote for every open seat, even if voters do not want to support more than one candidate. A voter who casts a vote for less than the entire number of seats open (a "full slate") will not have their ballot counted. Requiring
1087:
as a ranked voting system where voters can rank as many candidates as they like, and the candidate with the most first-preference votes wins. As a result, plurality is "immune" to bullet voting or truncation as a strategy, but only by making every vote equivalent to a bullet vote.
1536:
If a
Republican voter supports both Jefferson and Burr, they are effectively casting no votes because they do not make a distinction between the top two candidates. If most Republicans support both, the election is also a near-tie, with the outcome being determined essentially by
994:
In systems that fail later-no-harm, voters who feel strongly about their favorite candidate can use bullet voting to maximize the chances their favorite candidate will be elected, at the cost of reducing the chances that one of their later preferences will win.
1623:
is a compromise between score and the ranked
Condorcet methods, which still maintains a "mostly score-based" system. Candidates give each candidate a score, and the top-two candidates face a runoff, where the candidate preferred by a majority
1151:(in other words, it accurately reflects a voter's honest ordering of candidates). In general, the optimal strategy for an approval voter is to approve of all above-average candidates, i.e. all candidates whose quality is higher than the
1441:
winner elections which can be distributed between multiple candidates or all given to one candidate. Effectively, this is one vote which can be fractionally divided among more than one candidate. This removes any penalty to
1607:
points and Burr 65.7 points. However, score voting systems can behave similarly to approval if voters act in a way that is individually strategic, suggesting score voting can only be a partial solution.
1466:
bullet voting in situations where adding additional preferences would hurt later candidates; in some situations, adding a later preference can cause that later-preference candidate to lose.
2033:
1115:
can suffer from an especially severe kind of strategic truncation, stronger than bullet voting, where voters cannot safely rank any candidates at all; such a situation is called a
1446:
voters, who support a single candidate, and it enables the possibility of a united minority to elect at least one winner despite a united majority voting for all other candidates.
949:
2189:
1590:
Ultimately the electors fell into the first trap, with all 73 Republicans (terrified by a possible Adams victory) supporting both
Jefferson and Burr. The resulting tie
1963:
1501:. According to Nagel, the electoral tie resulted from "a strategic tension built into approval voting, which forces two leaders appealing to the same voters to play a
1361:
assign multiple votes based on ranked ballots, like three votes for the first, two for the second, and one for the third choice. This encourages minority voters to
1006:), voters can sometimes strategically bullet-vote to hide their support for additional candidates; this strategy works because such systems can cause candidates to
2017:... This is a political predicament racial minorities find themselves. They must give up all of their other votes to have any hope of electing their first choice.
2639:
2407:
640:
1998:
1591:
1425:
mandatory, minimizing the power of a majority of voters to pick all the winners, and can work well if there are only a few more candidates as winners.
2535:
2387:
1553:
1498:
1041:
672:
534:
529:
2634:
2412:
942:
635:
1683:
minority voters to vote for a full slate dilutes their voting strength by preventing them from concentrating their support behind one candidate.
2397:
2182:
317:
2159:
2119:
1903:
2029:
1387:
winner elections. In this system, a voter who prefers a single candidate and is concerned his candidate will lose has a strong incentive to
841:
2761:
1829:
Single-shot voting is essentially a tactic used by voters ... choosing only one candidate or a lesser amount of candidates than open seats.
92:
1939:
2444:
935:
1059:, by allowing small groups to concentrate all their support on one candidate and win at least one seat on a city council. During the
2175:
2146:
1561:
2779:
1067:
voters from being able to achieve representation on city councils, creating a stigma that in some cases lasts to the present day.
836:
2629:
2575:
1525:
1108:
criterion as well; because instant-runoff fails participation, it encourages bullet voting or truncation in some circumstances.
826:
576:
547:
487:
2427:
2756:
1494:
1365:(not using all the rankings). If voters are required to rank all the candidates, it further encourages voters to (insincerely)
1037:
558:
83:
2555:
1984:
1662:
1317:
621:
2013:
At-large voting can discourage voters from supporting all the candidates they want to see on the council, a practice called
1143:
can be fairly common for voters who only feel one candidate adequately represents them. However, because approval satisfies
1694:
263:
248:
233:
2598:
2583:
2402:
1925:
1260:
879:
499:
422:
343:
2649:
2372:
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2223:
1814:"Ocean City Maryland News | OC MD Newspapers | Maryland Coast Dispatch » Merits Of Single-Shot Voting Questioned"
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1418:
1333:
1174:
1056:
311:
293:
134:
864:
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but allows more votes than winners. This results in a body that is less representative than a body elected under a
1144:
755:
738:
705:
685:
469:
457:
427:
228:
186:
119:
1813:
1568:. The candidate with the most votes would be president, and the one with the second-most would be vice-president.
563:
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2619:
2565:
2477:
1376:
1226:
611:
604:
88:
2654:
2540:
2498:
2417:
2342:
2278:
2236:
1451:
1296:
665:
593:
582:
445:
432:
415:
392:
370:
333:
323:
2273:
1123:
cast bullet-votes, although it suggested this had more to do with convenience than with strategic incentives.
2679:
2669:
2644:
2460:
2337:
2063:
1847:
1481:
1459:
1105:
1097:
999:
980:
791:
645:
328:
976:
is when a voter supports only a single candidate, typically to show strong support for a single favorite.
2720:
2659:
2522:
2465:
1521:
1517:
1007:
984:
820:
700:
630:
437:
2624:
2545:
2310:
1272:
1120:
1112:
1101:
1045:
1003:
988:
728:
568:
452:
258:
237:
169:
147:
1351:
refers to providing 100% support for one candidate and 0% for all other candidates, just like
Approval
920:
786:
2694:
2263:
1785:
1741:
859:
846:
814:
78:
2674:
2268:
1044:
after one
Jefferson-Burr elector forgot to truncate their ballot to exclude Burr, almost causing a
765:
599:
252:
2715:
2325:
2080:
1864:
1749:
1610:
1084:
925:
796:
407:
191:
2283:
2084:
2058:
1868:
1842:
874:
1711:
1391:
to avoid a second choice helping to eliminate the first choice. A united majority of voters in
2684:
2593:
2550:
2470:
2392:
2315:
2300:
2258:
2155:
2142:
2115:
1980:
1957:
1899:
1767:
1587:, with the intention of securing both the Presidency and the Vice-Presidency for their party.
1430:
1284:
1064:
1052:
831:
801:
723:
660:
494:
221:
196:
179:
47:
19:
1462:(after higher choices have been elected or eliminated). However, it creates an incentive for
2725:
2357:
2213:
2198:
2107:
2072:
1891:
1856:
1759:
1580:
1576:
1509:
1490:
1463:
1148:
1080:
1033:
912:
869:
760:
748:
462:
338:
164:
158:
140:
129:
124:
112:
73:
35:
2799:
2773:
2689:
2530:
2508:
2320:
2241:
2231:
2209:
1641:
1557:
1366:
1325:
1206:
1166:
1132:
1116:
900:
733:
588:
553:
474:
385:
288:
211:
153:
31:
55:
2588:
2293:
2253:
1614:
1502:
1455:
1238:
1158:
1152:
770:
710:
695:
506:
375:
350:
201:
1940:"Rate of "Bullet Voting" Depends on Candidate Strength, Party Cues, and Other Factors"
895:
2793:
2332:
2076:
1860:
1565:
1162:
1020:
Setups where voters may benefit from truncating their ballots are sometimes called a
779:
479:
267:
105:
68:
43:
1575:
held a majority in the
Electoral College that year, with 73 electors versus only 65
2347:
2288:
1603:
1358:
1340:
1214:
1210:
1178:
1136:
1063:, municipalities often banned or disparaged bullet voting in an attempt to prevent
1060:
519:
283:
276:
206:
2152:
Mathematics and
Democracy: Recent advances in Voting Systems and Collective choice
1763:
1670:
1508:
In a Burr scenario, a group of voters prefer two candidates (traditionally called
1479:
is a particular case in which bullet voting was considered. The term was used in
2730:
2493:
2432:
2352:
2248:
1620:
1170:
397:
355:
298:
243:
1055:, bullet voting is actively encouraged as a way for minority groups to achieve
2503:
2439:
1584:
1529:
1513:
1486:
1029:
2111:
1999:"Approval Voting is Better Than Plurality Voting, Even in Multi-Winner Races"
1977:
Democracy in Divided Societies: Electoral Engineering for Conflict Management
1895:
1771:
2740:
2735:
1161:
was infamous for its high vulnerability to bullet voting, due to its use of
365:
360:
2099:
1883:
1407:
Bullet voting in Cumulative voting allows multiple votes for one candidate.
1181:, which allow voters to skip ratings to show weak support for a candidate.
907:
2560:
1309:
Multiple votes are often allowed in elections with more than one winner.
616:
1742:"An Examination of Ranked-Choice Voting in the United States, 2004–2022"
2422:
1403:
402:
2710:
1564:
was allowed to vote for two candidates, with all votes being counted
1516:) from the same political party or faction (traditionally called the
1347:
where voters can give gradations of support for each candidate. Here
2167:
2030:"Black candidate for Euclid school board to test new voting system"
1754:
1402:
1528:). These candidates face a unified opposition (the supporters of
991:) will encourage bullet voting or truncation in some situations.
2171:
1313:
can help a first choice be elected, depending on the system:
54:
1786:"Does "Bullet Voting" Really Work? - Philadelphia Magazine"
2139:
Behind the Ballot Box: A Citizen's guide to voting systems
1579:. Most of these electors were instructed to vote for both
1294:
1282:
1270:
1258:
1236:
1224:
1204:
1617:, which do not occur in honest approval and score voting.
23:
A voter marking a ballot for a single favorite candidate.
2154:, Bruno Simeone and Friedrich Pukelsheim Editors, 2006.
2104:
Mathematics and Democracy. Studies in Choice and Welfare
1888:
Mathematics and Democracy. Studies in Choice and Welfare
1328:
used in a multi-winner election works the same way as
1188:
1104:
are not immune to truncation, unless they satisfy the
2749:
2703:
2607:
2574:
2521:
2486:
2453:
2380:
2371:
2222:
1594:when the tiebreaking mechanism deadlocked as well.
2106:. Berlin, Heidelberg: Springer. pp. 133–150.
1890:. Berlin, Heidelberg: Springer. pp. 133–150.
1395:can control all the winners despite any strategic
1740:Graham-Squire, Adam; McCune, David (2023-06-12).
1560:, though not quite identical. Each member of the
1119:. A 2021 study found roughly 32% of voters under
979:Every voting method that does not satisfy either
1926:Decision 1997: Constitutional Change in New York
1421:limits everyone to one vote, effectively making
1695:EDITORIAL: To plump, or not to plump your vote
1458:strategic bullet voting, since lower rankings
2183:
1556:was conducted using a voting-rule similar to
1540:On the other hand, if too many electors vote
943:
8:
2640:Independence of Smith-dominated alternatives
1962:: CS1 maint: multiple names: authors list (
1485:(2007) by Jack H. Nagel, who named it after
1499:United States presidential election of 1800
2377:
2190:
2176:
2168:
950:
936:
26:
1886:. In Simeone, B.; Pukelsheim, F. (eds.).
1753:
2102:. In Simeone, B.; Pukelheim, F. (eds.).
2100:"A Strategic Problem in Approval Voting"
1884:"A Strategic Problem in Approval Voting"
1554:1800 United States presidential election
1371:strongest rivals at the lowest rankings.
18:
2635:Independence of irrelevant alternatives
2413:Sequential proportional approval voting
1634:
42:
16:Vote supporting only a single candidate
2052:
2050:
1955:
1938:Zawora, Deb Otis, Chris (2021-08-16).
2059:"The Burr Dilemma in Approval Voting"
1921:
1919:
1917:
1915:
1843:"The Burr Dilemma in Approval Voting"
1592:nearly caused a constitutional crisis
7:
1808:
1806:
1735:
1733:
1731:
1706:
1704:
1702:
1657:
1655:
1653:
1651:
1649:
1096:Contrary to a common misconception,
2445:Indirect single transferable voting
1111:Graham-Squire and McCune note that
14:
2085:10.1111/j.1468-2508.2007.00493.x
2077:10.1111/j.1468-2508.2007.00493.x
2057:Nagel, Jack H. (February 2007).
1869:10.1111/j.1468-2508.2007.00493.x
1861:10.1111/j.1468-2508.2007.00493.x
1841:Nagel, Jack H. (February 2007).
1548:for Burr, Adams will be elected.
1177:that this can be fixed by using
919:
906:
894:
842:McKelvey–Schofield chaos theorem
488:Semi-proportional representation
120:First preference plurality (FPP)
2036:from the original on 2011-06-07
1716:The Center for Election Science
2556:Mixed ballot transferable vote
1566:anonymously and simultaneously
1524:, not to be confused with the
1318:Multiple non-transferable vote
880:Harsanyi's utilitarian theorem
837:Moulin's impossibility theorem
802:Conflicting majorities paradox
1:
1764:10.1080/00344893.2023.2221689
706:Frustrated majorities paradox
2757:Comparison of voting systems
2599:Satisfaction approval voting
2584:Single non-transferable vote
2403:Proportional approval voting
1261:Single non-transferable vote
875:Condorcet dominance theorems
815:Social and collective choice
2363:Graduated majority judgment
1667:Southern Poverty Law Center
1532:). This creates a dilemma:
1419:single nontransferable vote
1379:(Bloc-voting) allows up to
1057:proportional representation
541:By mechanism of combination
312:Proportional representation
2816:
2615:Condorcet winner criterion
2306:First-past-the-post voting
1489:, who initially tied with
1454:removes the incentive for
1334:proportional voting method
1159:Traditional Bucklin voting
1081:First-preference plurality
739:Multiple districts paradox
470:Fractional approval voting
458:Interactive representation
2770:
2762:Voting systems by country
2665:Mutual majority criterion
2620:Condorcet loser criterion
2566:Vote linkage mixed system
2478:Largest remainders method
2205:
1928:By Henrik N. Dullea, 1997
1712:"Later-No-Harm Criterion"
1383:votes for elections with
1377:Plurality-at-large voting
1227:Plurality-at-large voting
1185:Multiple winner elections
1173:showed in their study of
686:Paradoxes and pathologies
535:Mixed-member proportional
530:Mixed-member majoritarian
525:By results of combination
416:Approval-based committees
2655:Majority loser criterion
2541:Additional member system
2499:Hagenbach-Bischoff quota
2418:Single transferable vote
2343:Positional voting system
2279:Minimax Condorcet method
2237:Combined approval voting
2112:10.1007/3-540-35605-3_10
1979:, Benjamin Reiley, 2001
1896:10.1007/3-540-35605-3_10
1452:Single transferable vote
1297:Single transferable vote
865:Condorcet's jury theorem
666:Double simultaneous vote
641:Rural–urban proportional
636:Dual-member proportional
598:
587:
554:Parallel (superposition)
446:Fractional social choice
433:Expanding approvals rule
262:
247:
232:
163:
152:
128:
2680:Resolvability criterion
2670:Participation criterion
2645:Later-no-harm criterion
2461:Highest averages method
2141:, Douglas J Amy, 2000.
2098:Nagel, Jack H. (2006).
2064:The Journal of Politics
1882:Nagel, Jack H. (2006).
1848:The Journal of Politics
1642:Bullet Voting Explained
1482:The Journal of Politics
1343:is a generalization of
1300:(Implicit divided vote)
1288:(Explicit divided vote)
1071:Single winner elections
1028:. This name comes from
1008:lose when they receive
792:Tyranny of the majority
569:Fusion (majority bonus)
386:Quota-remainder methods
2721:First-preference votes
2660:Monotonicity criterion
2630:Independence of clones
2333:Simple majoritarianism
1573:Democratic-Republicans
1522:Democratic-Republicans
1408:
926:Mathematics portal
832:Majority impossibility
821:Impossibility theorems
617:Negative vote transfer
438:Method of equal shares
59:
24:
2625:Consistency criterion
2546:Alternative vote plus
2311:Instant-runoff voting
1790:Philadelphia Magazine
1406:
1399:by a united minority.
1273:Instant-runoff voting
1147:, such voting is not
1046:constitutional crisis
989:instant-runoff voting
729:Best-is-worst paradox
718:Pathological response
453:Direct representation
106:Single-winner methods
58:
22:
2695:Seats-to-votes ratio
2466:Webster/Sainte-Laguë
1412:Limited-Vote Systems
1175:highest median rules
1145:no favorite betrayal
913:Economics portal
860:Median voter theorem
79:Comparative politics
2675:Plurality criterion
2274:Kemeny–Young method
1818:mdcoastdispatch.com
1460:are only used later
1194:
1015:support from voters
901:Politics portal
612:Vote linkage system
583:Seat linkage system
170:Ranked-choice (RCV)
2716:Election threshold
2650:Majority criterion
2326:Supplementary vote
2087:– via JSTOR.
2011:Amy (2000) p.60 ('
1871:– via JSTOR.
1663:"Drawing the Line"
1611:Paired tournaments
1409:
1393:plurality-at-large
1330:Plurality-at-large
1189:
1022:truncation paradox
983:(most methods) or
797:Discursive dilemma
756:Lesser evil voting
631:Supermixed systems
334:Largest remainders
192:Round-robin voting
60:
25:
2787:
2786:
2685:Reversal symmetry
2594:Cumulative voting
2576:Semi-proportional
2551:Mixed single vote
2517:
2516:
2393:Mixed single vote
2301:Exhaustive ballot
2264:Copeland's method
2259:Condorcet methods
2199:Electoral systems
2160:978-3-540-35603-5
2121:978-3-540-35603-5
1905:978-3-540-35603-5
1820:. 22 October 2008
1562:Electoral College
1544:for Jefferson or
1495:Electoral College
1431:Cumulative voting
1307:
1306:
1285:Cumulative voting
1053:cumulative voting
1038:Electoral College
1002:systems (such as
1000:non-participatory
960:
959:
847:Gibbard's theorem
787:Dominance paradox
724:Perverse response
428:Phragmen's method
294:Majority judgment
222:Positional voting
180:Condorcet methods
48:electoral systems
2807:
2726:Liquid democracy
2378:
2358:Two-round system
2269:Dodgson's method
2192:
2185:
2178:
2169:
2126:
2125:
2095:
2089:
2088:
2054:
2045:
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2042:
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2026:
2020:
2009:
2003:
2002:
1995:
1989:
1974:
1968:
1967:
1961:
1953:
1951:
1950:
1935:
1929:
1923:
1910:
1909:
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1679:
1678:
1669:. Archived from
1659:
1644:
1639:
1526:Republican Party
1491:Thomas Jefferson
1195:
1155:of the winner.
1131:By contrast, in
1051:In systems like
1034:Thomas Jefferson
1032:, who tied with
952:
945:
938:
924:
923:
911:
910:
899:
898:
854:Positive results
749:Strategic voting
646:Majority jackpot
603:
592:
463:Liquid democracy
339:National remnant
329:Highest averages
266:
251:
236:
168:
159:Alternative vote
157:
141:Partisan primary
133:
74:Mechanism design
27:
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2790:
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2745:
2699:
2690:Smith criterion
2603:
2570:
2531:Parallel voting
2513:
2509:Imperiali quota
2482:
2449:
2367:
2321:Contingent vote
2284:Nanson's method
2242:Unified primary
2232:Approval voting
2218:
2201:
2196:
2165:
2135:
2133:Further reading
2130:
2129:
2122:
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2096:
2092:
2056:
2055:
2048:
2039:
2037:
2028:
2027:
2023:
2010:
2006:
1997:
1996:
1992:
1988:was thwarted.)"
1975:
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1937:
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1932:
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1640:
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1631:
1615:spoiler effects
1600:
1558:approval voting
1503:game of Chicken
1473:
1345:Approval voting
1326:Approval voting
1299:
1287:
1275:
1263:
1254:
1249:
1241:
1220:
1213:
1209:
1207:Approval voting
1193:seat elections
1187:
1129:
1127:Cardinal voting
1117:no-show paradox
1094:
1078:
1073:
956:
918:
917:
905:
893:
885:
884:
851:
827:Arrow's theorem
817:
807:
806:
775:
745:
734:No-show paradox
715:
701:Cloning paradox
691:Spoiler effects
688:
678:
677:
652:
539:
522:
512:
511:
484:
475:Maximal lottery
442:
423:Thiele's method
412:
382:
314:
304:
303:
289:Approval voting
277:Cardinal voting
273:
218:
212:Maximal lottery
176:
108:
98:
17:
12:
11:
5:
2813:
2811:
2803:
2802:
2792:
2791:
2785:
2784:
2771:
2768:
2767:
2765:
2764:
2759:
2753:
2751:
2747:
2746:
2744:
2743:
2738:
2733:
2728:
2723:
2718:
2713:
2707:
2705:
2701:
2700:
2698:
2697:
2692:
2687:
2682:
2677:
2672:
2667:
2662:
2657:
2652:
2647:
2642:
2637:
2632:
2627:
2622:
2617:
2611:
2609:
2605:
2604:
2602:
2601:
2596:
2591:
2589:Limited voting
2586:
2580:
2578:
2572:
2571:
2569:
2568:
2563:
2558:
2553:
2548:
2543:
2538:
2533:
2527:
2525:
2519:
2518:
2515:
2514:
2512:
2511:
2506:
2501:
2496:
2490:
2488:
2484:
2483:
2481:
2480:
2475:
2474:
2473:
2468:
2457:
2455:
2451:
2450:
2448:
2447:
2442:
2437:
2436:
2435:
2430:
2425:
2415:
2410:
2405:
2400:
2395:
2390:
2384:
2382:
2375:
2369:
2368:
2366:
2365:
2360:
2355:
2350:
2345:
2340:
2335:
2330:
2329:
2328:
2323:
2318:
2316:Coombs' method
2308:
2303:
2298:
2297:
2296:
2294:Schulze method
2291:
2286:
2281:
2276:
2271:
2266:
2256:
2254:Bucklin voting
2251:
2246:
2245:
2244:
2239:
2228:
2226:
2220:
2219:
2206:
2203:
2202:
2197:
2195:
2194:
2187:
2180:
2172:
2163:
2162:
2149:
2134:
2131:
2128:
2127:
2120:
2090:
2046:
2021:
2004:
2001:. 7 June 2020.
1990:
1969:
1930:
1911:
1904:
1874:
1833:
1802:
1777:
1746:Representation
1727:
1698:
1687:
1645:
1633:
1632:
1630:
1627:
1626:
1625:
1618:
1608:
1599:
1596:
1550:
1549:
1538:
1472:
1469:
1468:
1467:
1448:
1447:
1427:
1426:
1414:
1413:
1401:
1400:
1374:
1373:
1372:
1356:
1322:
1321:
1305:
1304:
1301:
1293:
1292:
1289:
1281:
1280:
1277:
1269:
1268:
1265:
1257:
1256:
1243:
1239:Limited voting
1235:
1234:
1229:
1223:
1222:
1217:
1203:
1202:
1199:
1186:
1183:
1163:ranked ballots
1153:expected value
1128:
1125:
1121:instant-runoff
1113:instant-runoff
1102:instant-runoff
1093:
1092:Instant-runoff
1090:
1077:
1074:
1072:
1069:
1004:instant-runoff
958:
957:
955:
954:
947:
940:
932:
929:
928:
916:
915:
903:
890:
887:
886:
883:
882:
877:
872:
867:
862:
850:
849:
844:
839:
834:
829:
818:
813:
812:
809:
808:
805:
804:
799:
794:
789:
774:
773:
771:Turkey-raising
768:
763:
758:
744:
743:
742:
741:
731:
726:
714:
713:
711:Center squeeze
708:
703:
698:
696:Spoiler effect
689:
684:
683:
680:
679:
676:
675:
670:
669:
668:
655:By ballot type
651:
650:
649:
648:
643:
638:
628:
627:
626:
625:
624:
619:
609:
608:
607:
596:
573:
572:
571:
566:
561:
556:
538:
537:
532:
523:
518:
517:
514:
513:
510:
509:
507:Limited voting
504:
503:
502:
483:
482:
477:
472:
467:
466:
465:
460:
441:
440:
435:
430:
425:
411:
410:
405:
400:
395:
381:
380:
379:
378:
376:Localized list
373:
368:
363:
358:
348:
347:
346:
344:Biproportional
341:
336:
331:
315:
310:
309:
306:
305:
302:
301:
296:
291:
286:
272:
271:
256:
241:
217:
216:
215:
214:
209:
204:
199:
189:
175:
174:
173:
172:
161:
148:Instant-runoff
145:
144:
143:
135:Jungle primary
122:
111:Single vote -
109:
104:
103:
100:
99:
97:
96:
86:
81:
76:
71:
65:
62:
61:
51:
50:
40:
39:
15:
13:
10:
9:
6:
4:
3:
2:
2812:
2801:
2798:
2797:
2795:
2782:
2781:
2776:
2775:
2769:
2763:
2760:
2758:
2755:
2754:
2752:
2748:
2742:
2739:
2737:
2734:
2732:
2729:
2727:
2724:
2722:
2719:
2717:
2714:
2712:
2709:
2708:
2706:
2702:
2696:
2693:
2691:
2688:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2626:
2623:
2621:
2618:
2616:
2613:
2612:
2610:
2606:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2582:
2581:
2579:
2577:
2573:
2567:
2564:
2562:
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2542:
2539:
2537:
2534:
2532:
2529:
2528:
2526:
2524:
2520:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2491:
2489:
2485:
2479:
2476:
2472:
2469:
2467:
2464:
2463:
2462:
2459:
2458:
2456:
2452:
2446:
2443:
2441:
2438:
2434:
2431:
2429:
2426:
2424:
2421:
2420:
2419:
2416:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2385:
2383:
2379:
2376:
2374:
2370:
2364:
2361:
2359:
2356:
2354:
2351:
2349:
2346:
2344:
2341:
2339:
2336:
2334:
2331:
2327:
2324:
2322:
2319:
2317:
2314:
2313:
2312:
2309:
2307:
2304:
2302:
2299:
2295:
2292:
2290:
2287:
2285:
2282:
2280:
2277:
2275:
2272:
2270:
2267:
2265:
2262:
2261:
2260:
2257:
2255:
2252:
2250:
2247:
2243:
2240:
2238:
2235:
2234:
2233:
2230:
2229:
2227:
2225:
2224:Single-winner
2221:
2217:
2215:
2211:
2204:
2200:
2193:
2188:
2186:
2181:
2179:
2174:
2173:
2170:
2166:
2161:
2157:
2153:
2150:
2148:
2147:0-275-96585-6
2144:
2140:
2137:
2136:
2132:
2123:
2117:
2113:
2109:
2105:
2101:
2094:
2091:
2086:
2082:
2078:
2074:
2070:
2066:
2065:
2060:
2053:
2051:
2047:
2035:
2031:
2025:
2022:
2018:
2015:bullet voting
2014:
2008:
2005:
2000:
1994:
1991:
1986:
1982:
1978:
1973:
1970:
1965:
1959:
1945:
1941:
1934:
1931:
1927:
1922:
1920:
1918:
1916:
1912:
1907:
1901:
1897:
1893:
1889:
1885:
1878:
1875:
1870:
1866:
1862:
1858:
1854:
1850:
1849:
1844:
1837:
1834:
1830:
1819:
1815:
1809:
1807:
1803:
1791:
1787:
1781:
1778:
1773:
1769:
1765:
1761:
1756:
1751:
1747:
1743:
1736:
1734:
1732:
1728:
1717:
1713:
1707:
1705:
1703:
1699:
1696:
1691:
1688:
1684:
1673:on 2017-02-21
1672:
1668:
1664:
1658:
1656:
1654:
1652:
1650:
1646:
1643:
1638:
1635:
1628:
1622:
1619:
1616:
1612:
1609:
1605:
1602:
1601:
1597:
1595:
1593:
1588:
1586:
1582:
1578:
1574:
1569:
1567:
1563:
1559:
1555:
1547:
1543:
1539:
1535:
1534:
1533:
1531:
1527:
1523:
1519:
1515:
1511:
1506:
1504:
1500:
1497:votes in the
1496:
1492:
1488:
1484:
1483:
1478:
1470:
1465:
1461:
1457:
1453:
1450:
1449:
1445:
1440:
1436:
1433:allows up to
1432:
1429:
1428:
1424:
1423:bullet voting
1420:
1416:
1415:
1411:
1410:
1405:
1398:
1397:bullet voting
1394:
1390:
1386:
1382:
1378:
1375:
1370:
1369:
1364:
1360:
1357:
1354:
1353:bullet voting
1350:
1349:bullet voting
1346:
1342:
1339:
1338:
1335:
1331:
1327:
1324:
1323:
1319:
1316:
1315:
1314:
1312:
1311:Bullet voting
1302:
1298:
1295:
1290:
1286:
1283:
1278:
1274:
1271:
1266:
1262:
1259:
1252:
1247:
1244:
1240:
1237:
1233:
1230:
1228:
1225:
1218:
1216:
1212:
1208:
1205:
1200:
1197:
1196:
1192:
1184:
1182:
1180:
1179:rated ballots
1176:
1172:
1168:
1164:
1160:
1156:
1154:
1150:
1146:
1142:
1141:bullet voting
1138:
1134:
1126:
1124:
1122:
1118:
1114:
1109:
1107:
1106:participation
1103:
1100:systems like
1099:
1098:later-no-harm
1091:
1089:
1086:
1082:
1075:
1070:
1068:
1066:
1062:
1058:
1054:
1049:
1047:
1043:
1042:1800 election
1039:
1035:
1031:
1027:
1023:
1018:
1016:
1014:
1011:
1005:
1001:
996:
992:
990:
986:
982:
981:later-no-harm
977:
975:
971:
968:
964:
953:
948:
946:
941:
939:
934:
933:
931:
930:
927:
922:
914:
909:
904:
902:
897:
892:
891:
889:
888:
881:
878:
876:
873:
871:
870:May's theorem
868:
866:
863:
861:
858:
857:
856:
855:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
824:
823:
822:
816:
811:
810:
803:
800:
798:
795:
793:
790:
788:
785:
784:
783:
782:
781:
780:majority rule
778:Paradoxes of
772:
769:
767:
764:
762:
759:
757:
754:
753:
752:
751:
750:
740:
737:
736:
735:
732:
730:
727:
725:
722:
721:
720:
719:
712:
709:
707:
704:
702:
699:
697:
694:
693:
692:
687:
682:
681:
674:
671:
667:
664:
663:
662:
659:
658:
657:
656:
647:
644:
642:
639:
637:
634:
633:
632:
629:
623:
620:
618:
615:
614:
613:
610:
606:
601:
597:
595:
590:
586:
585:
584:
581:
580:
579:
578:
574:
570:
567:
565:
562:
560:
557:
555:
552:
551:
550:
549:
544:
543:
542:
536:
533:
531:
528:
527:
526:
521:
520:Mixed systems
516:
515:
508:
505:
501:
498:
497:
496:
493:
492:
491:
490:
489:
481:
480:Random ballot
478:
476:
473:
471:
468:
464:
461:
459:
456:
455:
454:
451:
450:
449:
448:
447:
439:
436:
434:
431:
429:
426:
424:
421:
420:
419:
418:
417:
409:
406:
404:
401:
399:
396:
394:
391:
390:
389:
388:
387:
377:
374:
372:
369:
367:
364:
362:
359:
357:
354:
353:
352:
349:
345:
342:
340:
337:
335:
332:
330:
327:
326:
325:
324:Apportionment
322:
321:
320:
319:
313:
308:
307:
300:
297:
295:
292:
290:
287:
285:
282:
281:
280:
279:
278:
269:
265:
260:
259:Antiplurality
257:
254:
250:
245:
242:
239:
235:
230:
227:
226:
225:
224:
223:
213:
210:
208:
205:
203:
200:
198:
195:
194:
193:
190:
188:
187:Condorcet-IRV
185:
184:
183:
182:
181:
171:
166:
162:
160:
155:
151:
150:
149:
146:
142:
139:
138:
136:
131:
126:
123:
121:
118:
117:
116:
114:
107:
102:
101:
94:
90:
87:
85:
82:
80:
77:
75:
72:
70:
69:Social choice
67:
66:
64:
63:
57:
53:
52:
49:
45:
44:Social choice
41:
37:
33:
29:
28:
21:
2778:
2772:
2388:Mixed-member
2373:Proportional
2348:Score voting
2289:Ranked pairs
2208:Part of the
2207:
2164:
2151:
2138:
2103:
2093:
2071:(1): 43–58.
2068:
2062:
2038:. Retrieved
2024:
2016:
2012:
2007:
1993:
1976:
1972:
1947:. Retrieved
1943:
1933:
1887:
1877:
1855:(1): 43–58.
1852:
1846:
1836:
1828:
1822:. Retrieved
1817:
1794:. Retrieved
1792:. 2015-10-27
1789:
1780:
1745:
1719:. Retrieved
1715:
1690:
1681:
1675:. Retrieved
1671:the original
1666:
1637:
1604:Score voting
1589:
1570:
1551:
1545:
1541:
1507:
1480:
1477:Burr dilemma
1476:
1474:
1471:Burr dilemma
1443:
1438:
1434:
1422:
1396:
1392:
1388:
1384:
1380:
1367:
1362:
1359:Borda voting
1352:
1348:
1344:
1341:Range voting
1329:
1310:
1308:
1276:(Whole vote)
1264:(Whole vote)
1250:
1245:
1231:
1215:Borda voting
1211:Range voting
1190:
1157:
1140:
1137:score voting
1130:
1110:
1095:
1079:
1061:Jim Crow era
1050:
1026:Burr dilemma
1025:
1021:
1019:
1012:
1009:
997:
993:
985:monotonicity
978:
974:plump voting
973:
970:
966:
962:
961:
853:
852:
819:
777:
776:
761:Exaggeration
747:
746:
717:
716:
690:
654:
653:
622:Mixed ballot
577:Compensatory
575:
548:compensatory
545:
540:
524:
486:
485:
444:
443:
414:
413:
384:
383:
371:List-free PR
316:
284:Score voting
275:
274:
220:
219:
207:Ranked pairs
178:
177:
110:
2731:Spoilt vote
2494:Droop quota
2433:Schulze STV
2408:Rural–urban
2353:STAR voting
2249:Borda count
1621:STAR voting
1577:Federalists
1518:Republicans
1389:bullet vote
1363:bullet vote
1165:; however,
1083:is usually
1040:during the
967:single-shot
661:Single vote
564:Conditional
559:Coexistence
408:Quota Borda
398:Schulze STV
356:Closed list
299:STAR voting
244:Borda count
2750:Comparison
2504:Hare quota
2454:Allocation
2440:Spare vote
2428:Hare-Clark
2398:Party-list
2040:2011-06-07
1985:0521797306
1949:2024-05-13
1824:2017-07-13
1796:2017-07-12
1755:2301.12075
1721:2024-02-02
1677:2017-07-13
1629:References
1487:Aaron Burr
1437:votes for
1030:Aaron Burr
766:Truncation
495:Cumulative
318:Party-list
93:By country
84:Comparison
2741:Unseating
2736:Sortition
2338:Plurality
2214:Economics
1772:0034-4893
1598:Solutions
1581:Jefferson
1510:Jefferson
1464:insincere
1149:deceptive
1076:Plurality
987:(such as
673:Dual-vote
366:Panachage
361:Open list
351:List type
229:Plurality
125:Two-round
113:plurality
36:Economics
2794:Category
2608:Criteria
2561:Scorporo
2210:politics
2034:Archived
1958:cite web
1944:FairVote
1748:: 1–19.
1167:Balinski
1133:approval
393:Hare STV
32:Politics
30:A joint
2780:Project
2471:D'Hondt
2423:CPO-STV
2381:Systems
1537:chance.
1456:sincere
1320:methods
1221:scores
1085:modeled
1036:in the
403:CPO-STV
253:Baldwin
202:Schulze
197:Minimax
115:methods
2800:Voting
2774:Portal
2711:Ballot
2487:Quotas
2216:series
2158:
2145:
2118:
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1983:
1902:
1867:
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1444:bullet
1242:
1201:Votes
1198:System
1171:Laraki
963:Bullet
268:Coombs
38:series
2704:Other
2523:Mixed
2081:JSTOR
1865:JSTOR
1750:arXiv
1624:wins.
1530:Adams
1219:Point
1065:black
605:'MMP'
594:'AMS'
2212:and
2156:ISBN
2143:ISBN
2116:ISBN
1981:ISBN
1964:link
1900:ISBN
1768:ISSN
1585:Burr
1583:and
1571:The
1552:The
1546:only
1542:only
1514:Burr
1512:and
1505:."
1493:for
1475:The
1368:bury
1255:...
1169:and
1135:and
1013:much
546:Non-
500:SNTV
89:List
46:and
34:and
2536:MMP
2108:doi
2073:doi
1892:doi
1857:doi
1760:doi
1520:or
1024:or
1010:too
998:In
972:or
264:el.
249:el.
238:IRV
234:el.
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600:NZ
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1439:N
1435:N
1385:N
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1191:N
969:,
951:e
944:t
937:v
602::
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