1455:
924:
59:
899:
911:
1700:
In this particular example (but not always), bullet voting benefits one group of voters only if another group or groups do it as well. The example shows that, depending upon who does it, bullet voting may distort the outcome and could be counterproductive for some voters who do it (here, those from
1106:
In two states, it was found to violate the state constitution and overturned; in the remainder of states using it, it was repealed. In
Minnesota, it was ruled unconstitutional, in a decision that disallowed votes for multiple candidates, in opposition to some voters' single expressed preference, and
1074:
Bucklin was used for multiwinner elections. For multi-member districts, voters marked as many first choices as there are seats to be filled. Voters marked the same number of second and further choices. In some localities, the voter was required to mark a full set of first choices for his or her
1061:
like the
Majority Judgment. However, Bucklin's selection algorithm starts with the highest rated votes and adds lower ones until a median winner is reached, whereas Majority Judgment starts with the median votes and removes them until all but one candidate is eliminated. Due to this difference,
1041:
refers to the process of counting all votes on all ballots that are above some threshold, and then adjusting that threshold down until a majority is reached. In some variants which have been used, equal ranking was allowed at some or all ranks. Some variants had a predetermined number of ranks
1696:
If all
Memphis voters bullet vote, Chattanooga voters could cause their city to win by all bullet voting. However, if all Nashville voters also do the same, Memphis would win on the fourth and final round. In that case, Knoxville voters could do nothing to change the outcome.
1111:, the particular application required voters in multi-candidate elections to rank more than one candidate, or the vote would not be counted; and the preferential primary was therefore found unconstitutional. The canvassing method itself was not rejected in Oklahoma.
1676:
The first round has no majority winner. Therefore, the second rank votes are added. This moves
Nashville and Chattanooga above 50%, so a winner can be determined. Since Nashville is supported by a higher majority (68% versus 58%), Nashville is the winner.
1692:
In the above example, Memphis voters have the most first-place votes and might not offer a second preference in hopes of winning, but the strategy fails, unless other voters also bullet vote, because they are not a second-place choice of competitors.
1022:, that candidate wins. Otherwise the second choices are added to the first choices. Again, if a candidate with a majority vote is found, the winner is the candidate with the most votes accumulated. Lower rankings are added as needed.
1704:
To prevent bullet voting, voters could be required to rank all candidates on the ballot. This would provide the voter with a disincentive to bullet vote, as the vote would not be counted unless all candidates are ranked.
1689:(offer only one first-rank vote), in hopes that other voters will add enough votes to help their candidate win. This strategy is most secure if the supported candidate appears likely to gain many second-rank votes.
1029:
is determined based on the number of valid ballots. Since, after the first round, there may be more votes cast than voters, it is possible for more than one candidate to have majority support.
1095:
in 1793. It was re-invented under its current name and used in many political elections in the United States in the early 20th century, as were other experimental election methods during the
2595:
952:
1965:
1339:
1079:) could allow an organized 51%, or the largest minority in a contest with three or more slates, to win all three seats in the first round, so this method does not give
1143:
Predates traditional
Bucklin voting and is slightly modified: candidates could win with 40% of the vote. The idea may have been based on a proposed primary law for
1714:
1443:
2415:
2183:
643:
2610:
2600:
2311:
2163:
1394:
675:
537:
532:
2605:
2410:
2188:
1406:
945:
638:
1877:
2173:
1958:
320:
844:
2537:
984:, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the
95:
1894:
1049:
The
Bucklin procedure is one way to ensure that the winning candidate will be among those with the highest median vote. When used with a
2220:
938:
1933:
1951:
1810:
1436:
1108:
2555:
839:
2405:
2351:
1382:
829:
579:
550:
490:
2203:
2532:
1063:
561:
86:
1934:
Municipal Voting System Reform: Overcoming the Legal
Obstacles (History of use of Bucklin voting in Duluth, Minnesota in 1912)
2331:
624:
1775:
266:
251:
236:
2374:
2359:
2178:
1429:
882:
502:
425:
346:
2425:
2148:
2138:
1999:
1412:
If equal and skipped rankings are allowed, Bucklin passes or fails the same criteria as highest median rules like the
1363:
1080:
1058:
977:
314:
296:
137:
24:
867:
1786:
2390:
2081:
1938:
1249:
758:
741:
708:
688:
472:
460:
430:
231:
189:
122:
566:
2440:
2395:
2341:
2253:
1367:
1076:
614:
607:
91:
2430:
2316:
2274:
2193:
2118:
2054:
2012:
1749:
1159:
1100:
993:
668:
596:
585:
448:
435:
418:
395:
373:
336:
326:
2049:
2455:
2445:
2420:
2236:
2113:
1724:
1469:
1390:
794:
648:
331:
2496:
2435:
2298:
2241:
1488:
1371:
1309:
823:
703:
633:
440:
1858:
1774:
Hermann, J. R. "A Remembrance of James W. Bucklin". Single Tax Review, Vol. XIX, No.2, March-April 1919.
2400:
2321:
2086:
1729:
1279:
1204:
1148:
1012:
731:
571:
455:
261:
240:
172:
150:
923:
789:
989:
2470:
2039:
1494:
1482:
1092:
862:
849:
817:
81:
1454:
2450:
2044:
1465:
1378:
1174:
768:
602:
255:
2491:
2101:
1476:
928:
799:
410:
194:
2059:
877:
1909:
1075:
ballot to be valid. However, allowing voters to cast three simultaneous votes for three seats (
1042:
available (usually 2 or 3), while others had unlimited ranks. There were also variants akin to
2460:
2369:
2326:
2246:
2168:
2091:
2076:
2034:
1831:
1806:
1800:
1413:
1398:
1324:
1219:
981:
834:
804:
726:
663:
497:
224:
199:
182:
50:
2501:
2133:
1989:
1974:
1402:
1264:
1189:
915:
872:
763:
751:
465:
341:
167:
161:
143:
132:
127:
115:
76:
38:
2549:
2465:
2306:
2284:
2096:
2017:
2007:
1985:
1734:
1096:
1050:
903:
736:
591:
556:
477:
388:
291:
214:
156:
34:
1879:
Primary
Elections: A Study of the History and Tendencies of Primary Election Legislation
1776:
http://cooperative-individualism.org/hermann-j-r_a-remembrance-of-james-bucklin-1919.htm
58:
2364:
2069:
773:
713:
698:
509:
378:
353:
204:
898:
2589:
2108:
1802:
A Right to
Representation: Proportional Election Systems for the Twenty-first Century
1719:
1386:
1054:
969:
782:
482:
270:
108:
71:
46:
20:
1103:, and then used in more than sixty other cities including Denver and San Francisco.
2123:
2064:
1739:
1043:
973:
522:
286:
279:
209:
2506:
2269:
2208:
2128:
2024:
1744:
1686:
400:
358:
301:
246:
2279:
2215:
2579:
All instances of this system were later abolished, but the dates are unknown.
1835:
2516:
2511:
1461:
1294:
1144:
368:
363:
910:
2336:
1026:
1019:
985:
619:
2198:
405:
2486:
1234:
1943:
1910:
Collective decisions and voting: the potential for public choice
1947:
1470:
All voters want the capital to be as close to them as possible.
1018:
First choice votes are first counted. If one candidate has a
57:
1479:, the largest city, but far from the others (42% of voters)
1468:. The population is concentrated around four major cities.
1685:
Voters supporting a strong candidate have an incentive to
1377:
Bucklin voting without equal rankings allowed fails the
1008:
Bucklin rules varied, but here is a typical example:
1057:, Bucklin's balloting method is the same as that of
972:
that can be used for single-member and multi-member
2525:
2479:
2383:
2350:
2297:
2262:
2229:
2156:
2147:
1998:
1407:independence of irrelevant alternatives criterion
1848:Brown v. Smallwood, 130 Minn. 492, 153 N. W. 953
2596:Non-proportional multi-winner electoral systems
1893:Mason, Haven A.; Locke, William James (1914).
1715:List of democracy and elections-related topics
1485:, near the center of the state (26% of voters)
1464:is holding an election on the location of its
1066:that Majority Judgment fails, and vice versa.
1959:
1501:The preferences of each region's voters are:
1437:
1046:in that lower-ranked votes counted for less.
946:
8:
2416:Independence of Smith-dominated alternatives
1805:. Ohio State University Press. p. 167.
1099:. Bucklin voting was first used in 1909 in
1033:Variants and relationships to other methods
2153:
1966:
1952:
1944:
1444:
1430:
1113:
953:
939:
29:
23:variant with equal and skipped ranks, see
1503:
1070:Bucklin applied to multiwinner elections
2572:
2411:Independence of irrelevant alternatives
2189:Sequential proportional approval voting
1767:
45:
1497:, far to the northeast (17% of voters)
1787:Principles and problems of government
7:
1939:Grand Junction people: James Bucklin
1828:City government in the United States
2221:Indirect single transferable voting
14:
1912:, Nicolaus Tideman, 2006, p. 204
1876:Merriam, Charles Edward (1908).
1453:
1383:independence of clones criterion
922:
909:
897:
845:McKelvey–Schofield chaos theorem
491:Semi-proportional representation
123:First preference plurality (FPP)
2611:Non-monotonic electoral systems
2601:Single-winner electoral systems
1826:Kneier, Charles Mayard (1957).
1491:, somewhat east (15% of voters)
2606:Preferential electoral systems
2332:Mixed ballot transferable vote
1882:. University of Chicago Press.
1015:(first, second, third, etc.).
883:Harsanyi's utilitarian theorem
840:Moulin's impossibility theorem
805:Conflicting majorities paradox
1:
1362:Bucklin voting satisfies the
1358:Satisfied and failed criteria
709:Frustrated majorities paradox
2533:Comparison of voting systems
2375:Satisfaction approval voting
2360:Single non-transferable vote
2179:Proportional approval voting
1830:. Harper. pp. 365–370.
1799:Barber, Kathleen L. (2000).
1701:Chattanooga and Nashville).
878:Condorcet dominance theorems
818:Social and collective choice
2139:Graduated majority judgment
1615:
1091:The method was proposed by
1081:proportional representation
996:, and is also known as the
544:By mechanism of combination
315:Proportional representation
25:Graduated majority judgment
2627:
2391:Condorcet winner criterion
2082:First-past-the-post voting
742:Multiple districts paradox
473:Fractional approval voting
461:Interactive representation
18:
16:Class of electoral systems
2546:
2538:Voting systems by country
2441:Mutual majority criterion
2396:Condorcet loser criterion
2342:Vote linkage mixed system
2254:Largest remainders method
1981:
1527:
1520:
1513:
1506:
1403:Condorcet loser criterion
1368:mutual majority criterion
1350:
689:Paradoxes and pathologies
538:Mixed-member proportional
533:Mixed-member majoritarian
528:By results of combination
419:Approval-based committees
2431:Majority loser criterion
2317:Additional member system
2275:Hagenbach-Bischoff quota
2194:Single transferable vote
2119:Positional voting system
2055:Minimax Condorcet method
2013:Combined approval voting
1789:, Haines and Hanes, 1921
1750:Expanding Approvals Rule
1109:variant used in Oklahoma
1101:Grand Junction, Colorado
994:Grand Junction, Colorado
868:Condorcet's jury theorem
669:Double simultaneous vote
644:Rural–urban proportional
639:Dual-member proportional
601:
590:
557:Parallel (superposition)
449:Fractional social choice
436:Expanding approvals rule
265:
250:
235:
166:
155:
131:
2456:Resolvability criterion
2446:Participation criterion
2421:Later-no-harm criterion
2237:Highest averages method
1725:Plurality voting system
1013:rank preference ballots
795:Tyranny of the majority
572:Fusion (majority bonus)
389:Quota-remainder methods
2497:First-preference votes
2436:Monotonicity criterion
2406:Independence of clones
2109:Simple majoritarianism
1896:Pacific Municipalities
1372:monotonicity criterion
929:Mathematics portal
835:Majority impossibility
824:Impossibility theorems
620:Negative vote transfer
441:Method of equal shares
62:
2401:Consistency criterion
2322:Alternative vote plus
2087:Instant-runoff voting
1730:Instant-runoff voting
1115:Adoption by Location
998:Grand Junction system
732:Best-is-worst paradox
721:Pathological response
456:Direct representation
109:Single-winner methods
61:
2471:Seats-to-votes ratio
2242:Webster/Sainte-Laguë
1062:Bucklin passes some
1059:highest median rules
978:highest median rules
916:Economics portal
863:Median voter theorem
82:Comparative politics
2451:Plurality criterion
2050:Kemeny–Young method
1921:Tideman, 2006, ibid
1420:Example application
1379:Condorcet criterion
1149:Governor La Follete
1116:
1011:Voters are allowed
904:Politics portal
615:Vote linkage system
586:Seat linkage system
173:Ranked-choice (RCV)
2492:Election threshold
2426:Majority criterion
2102:Supplementary vote
1364:majority criterion
1114:
800:Discursive dilemma
759:Lesser evil voting
634:Supermixed systems
337:Largest remainders
195:Round-robin voting
63:
2563:
2562:
2461:Reversal symmetry
2370:Cumulative voting
2352:Semi-proportional
2327:Mixed single vote
2293:
2292:
2169:Mixed single vote
2077:Exhaustive ballot
2040:Copeland's method
2035:Condorcet methods
1975:Electoral systems
1859:"Dove v. Oglesby"
1673:
1672:
1610:
1609:
1532:
1525:
1518:
1511:
1472:The options are:
1414:Majority Judgment
1399:reversal symmetry
1355:
1354:
1087:History and usage
1053:scale instead of
982:majority judgment
963:
962:
850:Gibbard's theorem
790:Dominance paradox
727:Perverse response
431:Phragmen's method
297:Majority judgment
225:Positional voting
183:Condorcet methods
51:electoral systems
2618:
2580:
2577:
2502:Liquid democracy
2154:
2134:Two-round system
2045:Dodgson's method
1968:
1961:
1954:
1945:
1922:
1919:
1913:
1907:
1901:
1900:
1890:
1884:
1883:
1873:
1867:
1866:
1855:
1849:
1846:
1840:
1839:
1823:
1817:
1816:
1796:
1790:
1784:
1778:
1772:
1616:
1530:
1523:
1516:
1509:
1504:
1457:
1446:
1439:
1432:
1250:Colorado Springs
1151:a year earlier.
1137:State Primaries
1117:
990:James W. Bucklin
955:
948:
941:
927:
926:
914:
913:
902:
901:
857:Positive results
752:Strategic voting
649:Majority jackpot
606:
595:
466:Liquid democracy
342:National remnant
332:Highest averages
269:
254:
239:
171:
162:Alternative vote
160:
144:Partisan primary
136:
77:Mechanism design
30:
2626:
2625:
2621:
2620:
2619:
2617:
2616:
2615:
2586:
2585:
2584:
2583:
2578:
2574:
2569:
2564:
2559:
2542:
2521:
2475:
2466:Smith criterion
2379:
2346:
2307:Parallel voting
2289:
2285:Imperiali quota
2258:
2225:
2143:
2097:Contingent vote
2060:Nanson's method
2018:Unified primary
2008:Approval voting
1994:
1977:
1972:
1925:
1920:
1916:
1908:
1904:
1892:
1891:
1887:
1875:
1874:
1870:
1857:
1856:
1852:
1847:
1843:
1825:
1824:
1820:
1813:
1798:
1797:
1793:
1785:
1781:
1773:
1769:
1760:
1735:Approval voting
1711:
1683:
1674:
1612:
1529:
1522:
1515:
1508:
1451:
1450:
1422:
1360:
1097:progressive era
1089:
1072:
1064:voting criteria
1055:ordinal ranking
1051:cardinal voting
1035:
1006:
959:
921:
920:
908:
896:
888:
887:
854:
830:Arrow's theorem
820:
810:
809:
778:
748:
737:No-show paradox
718:
704:Cloning paradox
694:Spoiler effects
691:
681:
680:
655:
542:
525:
515:
514:
487:
478:Maximal lottery
445:
426:Thiele's method
415:
385:
317:
307:
306:
292:Approval voting
280:Cardinal voting
276:
221:
215:Maximal lottery
179:
111:
101:
28:
19:For the modern
17:
12:
11:
5:
2624:
2622:
2614:
2613:
2608:
2603:
2598:
2588:
2587:
2582:
2581:
2571:
2570:
2568:
2565:
2561:
2560:
2547:
2544:
2543:
2541:
2540:
2535:
2529:
2527:
2523:
2522:
2520:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2483:
2481:
2477:
2476:
2474:
2473:
2468:
2463:
2458:
2453:
2448:
2443:
2438:
2433:
2428:
2423:
2418:
2413:
2408:
2403:
2398:
2393:
2387:
2385:
2381:
2380:
2378:
2377:
2372:
2367:
2365:Limited voting
2362:
2356:
2354:
2348:
2347:
2345:
2344:
2339:
2334:
2329:
2324:
2319:
2314:
2309:
2303:
2301:
2295:
2294:
2291:
2290:
2288:
2287:
2282:
2277:
2272:
2266:
2264:
2260:
2259:
2257:
2256:
2251:
2250:
2249:
2244:
2233:
2231:
2227:
2226:
2224:
2223:
2218:
2213:
2212:
2211:
2206:
2201:
2191:
2186:
2181:
2176:
2171:
2166:
2160:
2158:
2151:
2145:
2144:
2142:
2141:
2136:
2131:
2126:
2121:
2116:
2111:
2106:
2105:
2104:
2099:
2094:
2092:Coombs' method
2084:
2079:
2074:
2073:
2072:
2070:Schulze method
2067:
2062:
2057:
2052:
2047:
2042:
2032:
2030:Bucklin voting
2027:
2022:
2021:
2020:
2015:
2004:
2002:
1996:
1995:
1982:
1979:
1978:
1973:
1971:
1970:
1963:
1956:
1948:
1942:
1941:
1936:
1930:
1929:
1924:
1923:
1914:
1902:
1885:
1868:
1850:
1841:
1818:
1811:
1791:
1779:
1766:
1765:
1764:
1759:
1756:
1755:
1754:
1753:
1752:
1747:
1742:
1737:
1732:
1727:
1717:
1710:
1707:
1682:
1681:Voter strategy
1679:
1671:
1670:
1667:
1664:
1660:
1659:
1656:
1653:
1649:
1648:
1645:
1642:
1638:
1637:
1634:
1631:
1627:
1626:
1623:
1620:
1614:
1608:
1607:
1606:
1605:
1602:
1599:
1596:
1589:
1588:
1587:
1584:
1581:
1578:
1571:
1570:
1569:
1566:
1563:
1560:
1553:
1552:
1551:
1548:
1545:
1542:
1534:
1533:
1526:
1519:
1512:
1499:
1498:
1492:
1486:
1480:
1449:
1448:
1441:
1434:
1426:
1425:
1421:
1418:
1359:
1356:
1353:
1352:
1348:
1347:
1345:
1342:
1337:
1333:
1332:
1330:
1327:
1322:
1318:
1317:
1315:
1312:
1307:
1303:
1302:
1300:
1297:
1292:
1288:
1287:
1285:
1282:
1277:
1276:New Hampshire
1273:
1272:
1270:
1267:
1262:
1258:
1257:
1255:
1252:
1247:
1243:
1242:
1240:
1237:
1232:
1228:
1227:
1225:
1222:
1217:
1213:
1212:
1210:
1207:
1202:
1198:
1197:
1195:
1192:
1187:
1183:
1182:
1180:
1177:
1172:
1168:
1167:
1165:
1162:
1160:Grand Junction
1157:
1153:
1152:
1141:
1138:
1135:
1131:
1130:
1127:
1124:
1121:
1088:
1085:
1071:
1068:
1039:Bucklin voting
1034:
1031:
1005:
1004:Voting process
1002:
970:voting methods
968:is a class of
966:Bucklin voting
961:
960:
958:
957:
950:
943:
935:
932:
931:
919:
918:
906:
893:
890:
889:
886:
885:
880:
875:
870:
865:
853:
852:
847:
842:
837:
832:
821:
816:
815:
812:
811:
808:
807:
802:
797:
792:
777:
776:
774:Turkey-raising
771:
766:
761:
747:
746:
745:
744:
734:
729:
717:
716:
714:Center squeeze
711:
706:
701:
699:Spoiler effect
692:
687:
686:
683:
682:
679:
678:
673:
672:
671:
658:By ballot type
654:
653:
652:
651:
646:
641:
631:
630:
629:
628:
627:
622:
612:
611:
610:
599:
576:
575:
574:
569:
564:
559:
541:
540:
535:
526:
521:
520:
517:
516:
513:
512:
510:Limited voting
507:
506:
505:
486:
485:
480:
475:
470:
469:
468:
463:
444:
443:
438:
433:
428:
414:
413:
408:
403:
398:
384:
383:
382:
381:
379:Localized list
376:
371:
366:
361:
351:
350:
349:
347:Biproportional
344:
339:
334:
318:
313:
312:
309:
308:
305:
304:
299:
294:
289:
275:
274:
259:
244:
220:
219:
218:
217:
212:
207:
202:
192:
178:
177:
176:
175:
164:
151:Instant-runoff
148:
147:
146:
138:Jungle primary
125:
114:Single vote -
112:
107:
106:
103:
102:
100:
99:
89:
84:
79:
74:
68:
65:
64:
54:
53:
43:
42:
15:
13:
10:
9:
6:
4:
3:
2:
2623:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2593:
2591:
2576:
2573:
2566:
2558:
2557:
2552:
2551:
2545:
2539:
2536:
2534:
2531:
2530:
2528:
2524:
2518:
2515:
2513:
2510:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2488:
2485:
2484:
2482:
2478:
2472:
2469:
2467:
2464:
2462:
2459:
2457:
2454:
2452:
2449:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
2397:
2394:
2392:
2389:
2388:
2386:
2382:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2358:
2357:
2355:
2353:
2349:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2304:
2302:
2300:
2296:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2267:
2265:
2261:
2255:
2252:
2248:
2245:
2243:
2240:
2239:
2238:
2235:
2234:
2232:
2228:
2222:
2219:
2217:
2214:
2210:
2207:
2205:
2202:
2200:
2197:
2196:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2161:
2159:
2155:
2152:
2150:
2146:
2140:
2137:
2135:
2132:
2130:
2127:
2125:
2122:
2120:
2117:
2115:
2112:
2110:
2107:
2103:
2100:
2098:
2095:
2093:
2090:
2089:
2088:
2085:
2083:
2080:
2078:
2075:
2071:
2068:
2066:
2063:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2041:
2038:
2037:
2036:
2033:
2031:
2028:
2026:
2023:
2019:
2016:
2014:
2011:
2010:
2009:
2006:
2005:
2003:
2001:
2000:Single-winner
1997:
1993:
1991:
1987:
1980:
1976:
1969:
1964:
1962:
1957:
1955:
1950:
1949:
1946:
1940:
1937:
1935:
1932:
1931:
1927:
1926:
1918:
1915:
1911:
1906:
1903:
1898:
1897:
1889:
1886:
1881:
1880:
1872:
1869:
1864:
1860:
1854:
1851:
1845:
1842:
1837:
1833:
1829:
1822:
1819:
1814:
1812:9780814208540
1808:
1804:
1803:
1795:
1792:
1788:
1783:
1780:
1777:
1771:
1768:
1762:
1761:
1757:
1751:
1748:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1722:
1721:
1720:Voting system
1718:
1716:
1713:
1712:
1708:
1706:
1702:
1698:
1694:
1690:
1688:
1680:
1678:
1668:
1665:
1662:
1661:
1657:
1654:
1651:
1650:
1646:
1643:
1640:
1639:
1635:
1632:
1629:
1628:
1624:
1621:
1618:
1617:
1613:
1603:
1600:
1597:
1595:
1592:
1591:
1590:
1585:
1582:
1579:
1577:
1574:
1573:
1572:
1567:
1564:
1561:
1559:
1556:
1555:
1554:
1549:
1546:
1543:
1541:
1538:
1537:
1536:
1535:
1528:17% of voters
1521:15% of voters
1514:26% of voters
1507:42% of voters
1505:
1502:
1496:
1493:
1490:
1487:
1484:
1481:
1478:
1475:
1474:
1473:
1471:
1467:
1463:
1460:Suppose that
1458:
1456:
1447:
1442:
1440:
1435:
1433:
1428:
1427:
1424:
1419:
1417:
1415:
1410:
1408:
1404:
1400:
1396:
1392:
1391:participation
1388:
1387:later-no-harm
1384:
1380:
1375:
1373:
1369:
1365:
1357:
1349:
1346:
1343:
1341:
1340:San Francisco
1338:
1335:
1334:
1331:
1328:
1326:
1323:
1320:
1319:
1316:
1313:
1311:
1308:
1305:
1304:
1301:
1298:
1296:
1293:
1290:
1289:
1286:
1283:
1281:
1278:
1275:
1274:
1271:
1268:
1266:
1263:
1260:
1259:
1256:
1253:
1251:
1248:
1245:
1244:
1241:
1238:
1236:
1233:
1230:
1229:
1226:
1223:
1221:
1218:
1215:
1214:
1211:
1208:
1206:
1203:
1200:
1199:
1196:
1193:
1191:
1188:
1185:
1184:
1181:
1178:
1176:
1173:
1170:
1169:
1166:
1163:
1161:
1158:
1155:
1154:
1150:
1147:suggested by
1146:
1142:
1139:
1136:
1133:
1132:
1128:
1126:Year Adopted
1125:
1122:
1119:
1118:
1112:
1110:
1104:
1102:
1098:
1094:
1086:
1084:
1082:
1078:
1069:
1067:
1065:
1060:
1056:
1052:
1047:
1045:
1040:
1032:
1030:
1028:
1023:
1021:
1016:
1014:
1009:
1003:
1001:
999:
995:
991:
987:
983:
979:
975:
971:
967:
956:
951:
949:
944:
942:
937:
936:
934:
933:
930:
925:
917:
912:
907:
905:
900:
895:
894:
892:
891:
884:
881:
879:
876:
874:
873:May's theorem
871:
869:
866:
864:
861:
860:
859:
858:
851:
848:
846:
843:
841:
838:
836:
833:
831:
828:
827:
826:
825:
819:
814:
813:
806:
803:
801:
798:
796:
793:
791:
788:
787:
786:
785:
784:
783:majority rule
781:Paradoxes of
775:
772:
770:
767:
765:
762:
760:
757:
756:
755:
754:
753:
743:
740:
739:
738:
735:
733:
730:
728:
725:
724:
723:
722:
715:
712:
710:
707:
705:
702:
700:
697:
696:
695:
690:
685:
684:
677:
674:
670:
667:
666:
665:
662:
661:
660:
659:
650:
647:
645:
642:
640:
637:
636:
635:
632:
626:
623:
621:
618:
617:
616:
613:
609:
604:
600:
598:
593:
589:
588:
587:
584:
583:
582:
581:
577:
573:
570:
568:
565:
563:
560:
558:
555:
554:
553:
552:
547:
546:
545:
539:
536:
534:
531:
530:
529:
524:
523:Mixed systems
519:
518:
511:
508:
504:
501:
500:
499:
496:
495:
494:
493:
492:
484:
483:Random ballot
481:
479:
476:
474:
471:
467:
464:
462:
459:
458:
457:
454:
453:
452:
451:
450:
442:
439:
437:
434:
432:
429:
427:
424:
423:
422:
421:
420:
412:
409:
407:
404:
402:
399:
397:
394:
393:
392:
391:
390:
380:
377:
375:
372:
370:
367:
365:
362:
360:
357:
356:
355:
352:
348:
345:
343:
340:
338:
335:
333:
330:
329:
328:
327:Apportionment
325:
324:
323:
322:
316:
311:
310:
303:
300:
298:
295:
293:
290:
288:
285:
284:
283:
282:
281:
272:
268:
263:
262:Antiplurality
260:
257:
253:
248:
245:
242:
238:
233:
230:
229:
228:
227:
226:
216:
213:
211:
208:
206:
203:
201:
198:
197:
196:
193:
191:
190:Condorcet-IRV
188:
187:
186:
185:
184:
174:
169:
165:
163:
158:
154:
153:
152:
149:
145:
142:
141:
139:
134:
129:
126:
124:
121:
120:
119:
117:
110:
105:
104:
97:
93:
90:
88:
85:
83:
80:
78:
75:
73:
72:Social choice
70:
69:
67:
66:
60:
56:
55:
52:
48:
47:Social choice
44:
40:
36:
32:
31:
26:
22:
21:graded voting
2575:
2554:
2548:
2164:Mixed-member
2149:Proportional
2124:Score voting
2065:Ranked pairs
2029:
1984:Part of the
1983:
1917:
1905:
1895:
1888:
1878:
1871:
1862:
1853:
1844:
1827:
1821:
1801:
1794:
1782:
1770:
1740:Score voting
1703:
1699:
1695:
1691:
1684:
1675:
1652:Chattanooga
1611:
1598:Chattanooga
1593:
1575:
1562:Chattanooga
1557:
1547:Chattanooga
1539:
1500:
1459:
1452:
1423:
1411:
1376:
1361:
1310:Fort Collins
1105:
1090:
1077:block voting
1073:
1048:
1044:Borda voting
1038:
1036:
1024:
1017:
1010:
1007:
997:
965:
964:
856:
855:
822:
780:
779:
764:Exaggeration
750:
749:
720:
719:
693:
657:
656:
625:Mixed ballot
580:Compensatory
578:
551:compensatory
548:
543:
527:
489:
488:
447:
446:
417:
416:
387:
386:
374:List-free PR
319:
287:Score voting
278:
277:
223:
222:
210:Ranked pairs
181:
180:
113:
2507:Spoilt vote
2270:Droop quota
2209:Schulze STV
2184:Rural–urban
2129:STAR voting
2025:Borda count
1745:Borda count
1687:bullet vote
1576:Chattanooga
1524:Center-East
1489:Chattanooga
1395:consistency
1336:California
1171:Washington
1134:Washington
988:politician
664:Single vote
567:Conditional
562:Coexistence
411:Quota Borda
401:Schulze STV
359:Closed list
302:STAR voting
247:Borda count
2590:Categories
2526:Comparison
2280:Hare quota
2230:Allocation
2216:Spare vote
2204:Hare-Clark
2174:Party-list
1758:References
1663:Knoxville
1641:Nashville
1601:Nashville
1583:Nashville
1580:Knoxville
1565:Knoxville
1550:Knoxville
1544:Nashville
1216:Minnesota
1205:New Iberia
1201:Louisiana
769:Truncation
498:Cumulative
321:Party-list
96:By country
87:Comparison
2517:Unseating
2512:Sortition
2114:Plurality
1990:Economics
1836:610214970
1594:Knoxville
1558:Nashville
1495:Knoxville
1483:Nashville
1462:Tennessee
1325:La Grande
1306:Colorado
1295:Cleveland
1246:Colorado
1231:Colorado
1186:Colorado
1156:Colorado
1145:Wisconsin
1123:Election
1093:Condorcet
1037:The term
980:like the
974:districts
676:Dual-vote
369:Panachage
364:Open list
354:List type
232:Plurality
128:Two-round
116:plurality
39:Economics
2384:Criteria
2337:Scorporo
1986:politics
1863:oscn.net
1763:Specific
1709:See also
1630:Memphis
1625:Round 2
1622:Round 1
1604:Memphis
1586:Memphis
1568:Memphis
1531:Far-East
1510:Far-West
1405:and the
1370:and the
1351:Sources
1265:Portland
1027:majority
1020:majority
986:Georgist
976:. As in
396:Hare STV
35:Politics
33:A joint
2556:Project
2247:D'Hondt
2199:CPO-STV
2157:Systems
1928:General
1540:Memphis
1477:Memphis
1466:capital
1321:Oregon
1261:Oregon
1175:Spokane
406:CPO-STV
256:Baldwin
205:Schulze
200:Minimax
118:methods
2550:Portal
2487:Ballot
2263:Quotas
1992:series
1834:
1809:
1517:Center
1401:, the
1366:, the
1280:Nashua
1235:Denver
1220:Duluth
1190:Pueblo
1129:Notes
1120:State
271:Coombs
41:series
2567:Notes
2480:Other
2299:Mixed
1619:City
1344:1917
1329:1913
1314:1913
1299:1913
1291:Ohio
1284:1913
1269:1913
1254:1913
1239:1913
1224:1913
1209:1912
1194:1911
1179:1910
1164:1909
1140:1907
1107:in a
608:'MMP'
597:'AMS'
1988:and
1832:OCLC
1807:ISBN
549:Non-
503:SNTV
92:List
49:and
37:and
2312:MMP
1669:32
1666:17
1658:58
1655:15
1647:68
1644:26
1636:42
1633:42
992:of
267:el.
252:el.
241:IRV
237:el.
2592::
2553:—
1861:.
1416:.
1409:.
1397:,
1393:,
1389:,
1385:,
1381:,
1374:.
1083:.
1025:A
1000:.
603:NZ
592:UK
168:US
157:UK
140:)
133:US
1967:e
1960:t
1953:v
1899:.
1865:.
1838:.
1815:.
1445:e
1438:t
1431:v
954:e
947:t
940:v
605::
594::
273:)
264:(
258:)
249:(
243:)
234:(
170::
159::
135::
130:(
98:)
94:(
27:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
