913:
48:
888:
900:
1063:
in the number of seats it hands out, and so is more proportional than the Droop quota (which tends to be biased towards larger parties); however, the Droop quota guarantees that a party that wins a majority of votes in a district will win a majority of the seats in the district.
1042:
1138:
The Hare quota gives no advantage to larger or smaller parties. However, in small legislatures with no threshold, the Hare quota can be manipulated by running candidates on many small lists, allowing each list to pick up a single remainder seat.
1207:
1125:
979:
941:
1590:
1486:
2040:
1551:
1808:
632:
1936:
1788:
664:
526:
521:
2035:
1813:
934:
627:
1798:
1583:
1166:
1091:
309:
1515:
1462:
1391:
1327:
833:
2162:
974:
is a quota that is guaranteed to apportion only as many seats as are available in the legislature. Such a quota can be any number between:
84:
1175:
1845:
1511:
1235:
in favor of larger parties; in fact, the Droop quota is the most-biased possible quota that can still be considered to be proportional.
1103:
927:
1576:
1425:
1135:
in the number of seats it hands out. This makes it more proportional than the Droop quota (which is biased towards larger parties).
2180:
828:
2200:
2030:
1976:
1217:
1095:
818:
568:
539:
479:
1828:
1487:"Notes on the Political Consequences of Electoral Laws by Lijphart, Arend, American Political Science Review Vol. 84, No 2 1990"
2157:
1514:
where the DAB ran as two lists and gained twice as many seats as the single-list Civic despite receiving fewer votes in total:
550:
75:
1956:
613:
255:
240:
225:
1999:
1984:
1803:
1221:
1037:{\displaystyle {\frac {\text{votes}}{{\text{seats}}+1}}\leq {\text{quota}}\leq {\frac {\text{votes}}{{\text{seats}}-1}}}
871:
491:
414:
335:
2050:
1773:
1763:
1624:
1277:
955:
303:
285:
126:
856:
2015:
1706:
1490:
747:
730:
697:
677:
461:
449:
419:
220:
178:
111:
555:
2065:
2020:
1966:
1878:
1282:
603:
596:
80:
2055:
1941:
1899:
1818:
1743:
1679:
1637:
1272:
1162:
1158:
1087:
657:
585:
574:
437:
424:
407:
384:
362:
325:
315:
1674:
2080:
2070:
2045:
1861:
1738:
783:
637:
320:
2121:
2060:
1923:
1866:
812:
692:
622:
429:
2025:
1946:
1711:
720:
560:
444:
250:
229:
161:
139:
912:
778:
2095:
1664:
1213:
1083:
851:
838:
806:
70:
2075:
1669:
1243:
757:
591:
244:
2116:
1726:
917:
788:
399:
183:
1684:
866:
2085:
1994:
1951:
1871:
1793:
1716:
1701:
1659:
1458:
1421:
1387:
1323:
823:
793:
715:
652:
486:
213:
188:
171:
39:
2126:
1758:
1614:
1599:
1450:
1379:
1315:
1247:
904:
861:
752:
740:
454:
330:
156:
150:
132:
121:
116:
104:
65:
27:
1216:(1831–1884), who identified it as the minimum amount of support needed to secure a seat in
2174:
2090:
1931:
1909:
1721:
1642:
1632:
1610:
892:
725:
580:
545:
466:
280:
203:
145:
23:
1352:
47:
1989:
1694:
1654:
1558:
762:
702:
687:
498:
367:
342:
193:
887:
2194:
1733:
1414:
771:
471:
259:
97:
60:
35:
1546:
1748:
1689:
1357:
Electoral
Systems and Party Systems: A Study of Twenty-Seven Democracies, 1945-1990
511:
275:
268:
198:
1454:
2131:
1894:
1833:
1753:
1649:
1383:
1319:
1154:
1148:
1056:
389:
347:
290:
235:
1528:
1442:
1904:
1840:
1371:
1307:
1267:
1238:
Today the Droop quota is used in almost all STV elections, including those in
1225:
1073:
1052:
2141:
2136:
1255:
1232:
1130:
1060:
357:
352:
1161:(STV) elections today and is occasionally used in elections held under the
899:
1961:
1447:
Proportional
Representation: Apportionment Methods and Their Applications
1376:
Proportional
Representation: Apportionment Methods and Their Applications
1312:
Proportional
Representation: Apportionment Methods and Their Applications
608:
1823:
394:
1212:
It was first proposed in 1868 by the
English lawyer and mathematician
2111:
1568:
1202:{\displaystyle {\frac {\text{total votes}}{{\text{total seats}}+1}}}
962:
is the number of votes a candidate needs to be guaranteed election.
1251:
1239:
1120:{\displaystyle {\frac {\text{total votes}}{\text{total seats}}}}
1572:
1098:
in his first proposals for STV. It is given by the expression:
1086:) is the most commonly-used quota for apportionments using the
1449:, Cham: Springer International Publishing, pp. 207–223,
1443:"Tracing Peculiarities: Vote Thresholds and Majority Clauses"
1378:, Cham: Springer International Publishing, pp. 127–147,
1314:, Cham: Springer International Publishing, pp. 95–105,
46:
1441:
Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.),
1416:
1370:
Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.),
1306:
Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.),
1372:"Favoring Some at the Expense of Others: Seat Biases"
1224:, leading him to propose it as an alternative to the
1178:
1106:
982:
2150:
2104:
2008:
1975:
1922:
1887:
1854:
1781:
1772:
1623:
1413:
1353:"Appendix A: Proportional Representation Formulas"
1201:
1119:
1036:
1308:"Quota Methods of Apportionment: Divide and Rank"
1129:Specifically, the Hare quota is unique in being
1412:Balinski, Michel L.; Young, H. Peyton (1982).
1584:
935:
8:
2041:Independence of Smith-dominated alternatives
1552:Journal of the Statistical Society of London
1529:"Properties of Preferential Election Rules"
1231:However, the Droop quota has a substantial
1778:
1591:
1577:
1569:
1169:(list PR). It is given by the expression:
942:
928:
18:
1185:
1179:
1177:
1107:
1105:
1020:
1014:
1006:
989:
983:
981:
1547:"On methods of electing representatives"
1051:There are two commonly-used quotas: the
16:Number of votes a candidate needs to win
2036:Independence of irrelevant alternatives
1814:Sequential proportional approval voting
1293:
34:
1556:(June 1881) pp.141-196 , reprinted in
1167:party-list proportional representation
7:
1481:
1479:
1420:. New Haven: Yale University Press.
1346:
1344:
1301:
1299:
1297:
1846:Indirect single transferable voting
1078:The Hare quota (also known as the
14:
1512:2012 election in Hong Kong Island
911:
898:
886:
834:McKelvey–Schofield chaos theorem
480:Semi-proportional representation
112:First preference plurality (FPP)
1957:Mixed ballot transferable vote
872:Harsanyi's utilitarian theorem
829:Moulin's impossibility theorem
794:Conflicting majorities paradox
1:
698:Frustrated majorities paradox
2158:Comparison of voting systems
2000:Satisfaction approval voting
1985:Single non-transferable vote
1804:Proportional approval voting
1455:10.1007/978-3-319-64707-4_11
867:Condorcet dominance theorems
807:Social and collective choice
1764:Graduated majority judgment
1384:10.1007/978-3-319-64707-4_7
1320:10.1007/978-3-319-64707-4_5
1278:Proportional representation
956:proportional representation
533:By mechanism of combination
304:Proportional representation
2217:
2016:Condorcet winner criterion
1707:First-past-the-post voting
1359:. Oxford University Press.
1146:
1071:
731:Multiple districts paradox
462:Fractional approval voting
450:Interactive representation
2171:
2163:Voting systems by country
2066:Mutual majority criterion
2021:Condorcet loser criterion
1967:Vote linkage mixed system
1879:Largest remainders method
1606:
1283:Largest remainders method
1092:party-list representation
678:Paradoxes and pathologies
527:Mixed-member proportional
522:Mixed-member majoritarian
517:By results of combination
408:Approval-based committees
2056:Majority loser criterion
1942:Additional member system
1900:Hagenbach-Bischoff quota
1819:Single transferable vote
1744:Positional voting system
1680:Minimax Condorcet method
1638:Combined approval voting
1351:Lijphart, Arend (1994).
1273:Single transferable vote
1163:largest remainder method
1159:single transferable vote
1088:largest remainder method
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:
2201:Electoral system quotas
2081:Resolvability criterion
2071:Participation criterion
2046:Later-no-harm criterion
1862:Highest averages method
1563:(October 2007) pp.7–46.
1220:voting systems such as
784:Tyranny of the majority
561:Fusion (majority bonus)
378:Quota-remainder methods
2122:First-preference votes
2061:Monotonicity criterion
2031:Independence of clones
1734:Simple majoritarianism
1545:Henry Richmond Droop,
1203:
1121:
1038:
918:Mathematics portal
824:Majority impossibility
813:Impossibility theorems
609:Negative vote transfer
430:Method of equal shares
51:
2026:Consistency criterion
1947:Alternative vote plus
1712:Instant-runoff voting
1516:New York Times report
1204:
1122:
1039:
721:Best-is-worst paradox
710:Pathological response
445:Direct representation
98:Single-winner methods
50:
2096:Seats-to-votes ratio
1867:Webster/Sainte-Laguë
1510:See for example the
1214:Henry Richmond Droop
1176:
1104:
1059:. The Hare quota is
980:
905:Economics portal
852:Median voter theorem
71:Comparative politics
2076:Plurality criterion
1675:Kemeny–Young method
1527:Woodall, Douglass.
1244:Republic of Ireland
893:Politics portal
604:Vote linkage system
575:Seat linkage system
162:Ranked-choice (RCV)
2117:Election threshold
2051:Majority criterion
1727:Supplementary vote
1199:
1117:
1034:
789:Discursive dilemma
748:Lesser evil voting
623:Supermixed systems
326:Largest remainders
184:Round-robin voting
52:
2188:
2187:
2086:Reversal symmetry
1995:Cumulative voting
1977:Semi-proportional
1952:Mixed single vote
1918:
1917:
1794:Mixed single vote
1702:Exhaustive ballot
1665:Copeland's method
1660:Condorcet methods
1600:Electoral systems
1464:978-3-319-64707-4
1393:978-3-319-64707-4
1329:978-3-319-64707-4
1197:
1188:
1183:
1115:
1114:
1111:
1094:. It was used by
1032:
1023:
1018:
1009:
1001:
992:
987:
966:Admissible quotas
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
2208:
2127:Liquid democracy
1779:
1759:Two-round system
1670:Dodgson's method
1593:
1586:
1579:
1570:
1564:
1543:
1537:
1536:
1524:
1518:
1508:
1502:
1501:
1499:
1498:
1489:. Archived from
1483:
1474:
1473:
1472:
1471:
1438:
1432:
1431:
1419:
1409:
1403:
1402:
1401:
1400:
1367:
1361:
1360:
1348:
1339:
1338:
1337:
1336:
1303:
1248:Northern Ireland
1218:semiproportional
1208:
1206:
1205:
1200:
1198:
1196:
1189:
1186:
1181:
1180:
1157:is used in most
1126:
1124:
1123:
1118:
1116:
1112:
1109:
1108:
1084:Hamilton's quota
1043:
1041:
1040:
1035:
1033:
1031:
1024:
1021:
1016:
1015:
1010:
1007:
1002:
1000:
993:
990:
985:
984:
972:admissible quota
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:
2216:
2215:
2211:
2210:
2209:
2207:
2206:
2205:
2191:
2190:
2189:
2184:
2167:
2146:
2100:
2091:Smith criterion
2004:
1971:
1932:Parallel voting
1914:
1910:Imperiali quota
1883:
1850:
1768:
1722:Contingent vote
1685:Nanson's method
1643:Unified primary
1633:Approval voting
1619:
1602:
1597:
1567:
1544:
1540:
1526:
1525:
1521:
1509:
1505:
1496:
1494:
1485:
1484:
1477:
1469:
1467:
1465:
1440:
1439:
1435:
1428:
1411:
1410:
1406:
1398:
1396:
1394:
1369:
1368:
1364:
1350:
1349:
1342:
1334:
1332:
1330:
1305:
1304:
1295:
1291:
1264:
1184:
1174:
1173:
1151:
1145:
1102:
1101:
1076:
1070:
1049:
1019:
988:
978:
977:
968:
960:electoral quota
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:
2214:
2212:
2204:
2203:
2193:
2192:
2186:
2185:
2172:
2169:
2168:
2166:
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2145:
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2139:
2134:
2129:
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2101:
2099:
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2068:
2063:
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2053:
2048:
2043:
2038:
2033:
2028:
2023:
2018:
2012:
2010:
2006:
2005:
2003:
2002:
1997:
1992:
1990:Limited voting
1987:
1981:
1979:
1973:
1972:
1970:
1969:
1964:
1959:
1954:
1949:
1944:
1939:
1934:
1928:
1926:
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1902:
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1884:
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1869:
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1761:
1756:
1751:
1746:
1741:
1736:
1731:
1730:
1729:
1724:
1719:
1717:Coombs' method
1709:
1704:
1699:
1698:
1697:
1695:Schulze method
1692:
1687:
1682:
1677:
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1667:
1657:
1655:Bucklin voting
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1559:Voting matters
1538:
1533:Voting Matters
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1147:Main article:
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1141:
1072:Main article:
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763:Turkey-raising
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718:
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703:Center squeeze
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688:Spoiler effect
681:
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647:By ballot type
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563:
558:
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529:
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509:
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502:
501:
499:Limited voting
496:
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387:
373:
372:
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368:Localized list
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336:Biproportional
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140:Instant-runoff
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127:Jungle primary
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103:Single vote -
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1737:
1735:
1732:
1728:
1725:
1723:
1720:
1718:
1715:
1714:
1713:
1710:
1708:
1705:
1703:
1700:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1678:
1676:
1673:
1671:
1668:
1666:
1663:
1662:
1661:
1658:
1656:
1653:
1651:
1648:
1644:
1641:
1639:
1636:
1635:
1634:
1631:
1630:
1628:
1626:
1625:Single-winner
1622:
1618:
1616:
1612:
1605:
1601:
1594:
1589:
1587:
1582:
1580:
1575:
1574:
1571:
1562:
1560:
1555:
1554:Vol. 44 No. 2
1553:
1548:
1542:
1539:
1534:
1530:
1523:
1520:
1517:
1513:
1507:
1504:
1493:on 2006-05-16
1492:
1488:
1482:
1480:
1476:
1466:
1460:
1456:
1452:
1448:
1444:
1437:
1434:
1429:
1427:0-300-02724-9
1423:
1418:
1417:
1408:
1405:
1395:
1389:
1385:
1381:
1377:
1373:
1366:
1363:
1358:
1354:
1347:
1345:
1341:
1331:
1325:
1321:
1317:
1313:
1309:
1302:
1300:
1298:
1294:
1288:
1284:
1281:
1279:
1276:
1274:
1271:
1269:
1266:
1265:
1261:
1259:
1257:
1253:
1249:
1245:
1241:
1236:
1234:
1229:
1227:
1223:
1219:
1215:
1193:
1190:
1172:
1171:
1170:
1168:
1164:
1160:
1156:
1150:
1142:
1140:
1136:
1134:
1133:
1127:
1099:
1097:
1093:
1089:
1085:
1081:
1075:
1067:
1065:
1062:
1058:
1054:
1047:Common quotas
1046:
1044:
1028:
1025:
1011:
1003:
997:
994:
975:
973:
965:
963:
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:
2179:
2173:
1789:Mixed-member
1774:Proportional
1749:Score voting
1690:Ranked pairs
1609:Part of the
1608:
1557:
1550:
1541:
1532:
1522:
1506:
1495:. Retrieved
1491:the original
1468:, retrieved
1446:
1436:
1415:
1407:
1397:, retrieved
1375:
1365:
1356:
1333:, retrieved
1311:
1237:
1230:
1211:
1152:
1137:
1131:
1128:
1100:
1079:
1077:
1057:Droop quotas
1050:
976:
971:
969:
959:
958:systems, an
953:
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:
377:
376:
375:
363:List-free PR
308:
276:Score voting
267:
266:
212:
211:
199:Ranked pairs
170:
169:
102:
2132:Spoilt vote
1895:Droop quota
1834:Schulze STV
1809:Rural–urban
1754:STAR voting
1650:Borda count
1187:total seats
1182:total votes
1155:Droop quota
1149:Droop quota
1143:Droop quota
1113:total seats
1110:total votes
1096:Thomas Hare
653:Single vote
556:Conditional
551:Coexistence
400:Quota Borda
390:Schulze STV
348:Closed list
291:STAR voting
236:Borda count
2151:Comparison
1905:Hare quota
1855:Allocation
1841:Spare vote
1829:Hare-Clark
1799:Party-list
1497:2006-05-16
1470:2024-05-10
1399:2024-05-10
1335:2024-05-10
1289:References
1268:Quota rule
1226:Hare quota
1074:Hare quota
1068:Hare quota
758:Truncation
487:Cumulative
310:Party-list
85:By country
76:Comparison
2142:Unseating
2137:Sortition
1739:Plurality
1615:Economics
1256:Australia
1233:seat bias
1082:quota or
1026:−
1012:≤
1004:≤
665:Dual-vote
358:Panachage
353:Open list
343:List type
221:Plurality
117:Two-round
105:plurality
28:Economics
2195:Category
2009:Criteria
1962:Scorporo
1611:politics
1561:Issue 24
1262:See also
1132:unbiased
1061:unbiased
385:Hare STV
24:Politics
22:A joint
2181:Project
1872:D'Hondt
1824:CPO-STV
1782:Systems
1549:in the
395:CPO-STV
245:Baldwin
194:Schulze
189:Minimax
107:methods
2175:Portal
2112:Ballot
1888:Quotas
1617:series
1461:
1424:
1390:
1326:
1254:, and
1242:, the
1080:simple
260:Coombs
30:series
2105:Other
1924:Mixed
1252:Malta
1240:India
1022:seats
1017:votes
1008:quota
991:seats
986:votes
597:'MMP'
586:'AMS'
1613:and
1535:(3).
1459:ISBN
1422:ISBN
1388:ISBN
1324:ISBN
1222:SNTV
1153:The
1055:and
1053:Hare
538:Non-
492:SNTV
81:List
38:and
26:and
1937:MMP
1451:doi
1380:doi
1316:doi
1165:of
1090:of
970:An
954:In
256:el.
241:el.
230:IRV
226:el.
2197::
2178:—
1531:.
1478:^
1457:,
1445:,
1386:,
1374:,
1355:.
1343:^
1322:,
1310:,
1296:^
1258:.
1250:,
1246:,
1228:.
592:NZ
581:UK
157:US
146:UK
129:)
122:US
1592:e
1585:t
1578:v
1500:.
1453::
1430:.
1382::
1318::
1194:1
1191:+
1029:1
998:1
995:+
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.
