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Majority bonus system

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all parties would get their full proportional number of seats, and one party would get the (nominal) bonus on top of that, the total number of seats would increase. While this means the size of the effective bonus (without other factors giving an effective bonus) if always smaller than the nominal one in terms of percentages, this naturally means all the parties who don't receive a bonus have a naturally less seats than they would proportionally.
54: 17: 894: 906: 1072:, a tenth of the assembly seats are granted to the winning coalition on top of those allocated proportionally. The size of majority bonuses may vary greatly, from as low as a few seats to up to 50%. In case of a bonus of 50%, the party also received their proportional share of the other 50% seats, which make a 1672:
As the table shows, especially with a high bonus/jackpot, the two methods lead to different result, with the bonus always providing a higher seat share. For this reason the two are not usually directly compared in this, majority bonuses tend to be smaller than jackpots. The effect of a 55% jackpot
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favoring large parties would give an even larger bonus to the largest party. The reason why the difference of the seats share and vote share (the effective bonus) is lower than the bonus is that the number of non-bonus seats to be allocated proportionally is less than the total number of seats. If
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and an effectively flexible "bonus"), while the bonus system gives the bonus and a proportional share of the rest of the seats. The jackpot only modifies the seat share when the largest party's proportional seats count based on its vote share is below the size of the jackpot.
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The current system as of September 2024 gives no bonus to the first party if it gets less than 25% of the vote. If it gets more than that, then it gets a bonus of 20 seats plus one seat for every 0.5% of the vote above 25% capping off at 50 seats which is reached at
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while its goal in a political science sense is to provide for stable majorities (a bonus lower than 50%) does not ensure it and applies also when a stable majority can already be formed. This is the main difference between a majority bonus and a majority jackpot.
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on the number of votes received by parties. A relatively small majority bonus (such as in the reinforced proportionality system of Greece) may not always guarantee that a single party can form a government. A the same time, as the majority bonus is allocated in a
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is an effective bonus for certain parties. Some properties of other mixed systems such as so called the "winner compensation" element of Hungarian electoral system have been criticized for being effectively just a majority bonus disguised as compensation.
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to some parties (most commonly the largest party), with the aim of providing government stability, particularly in parliamentary systems. The size of the majority bonus can vary significantly and usually it is a fixed number of seats, but it may be
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A simple bonus system (left) is also called a fusion type of mixed system. It mixes the FPTP and PR formulas in the same district and tier. A majority jackpot (right) is a supermixed system with a conditional and compensatory element as
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manner, therefore if the majority bonus if as high as 50% and the largest party which has 50% of the popular vote receives it, this party may win as many as 75% of all seats. This differentiated it from the similar
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The following table shows how small (10%), medium (25%) and large (50%) majority bonuses would work without any additional distortions of proportional systems. Using an
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If the leading party gets 50% of the vote, they get half the seats and the other half are distributed proportionally (leading party gets at least 75% in total).
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The difference between the majority bonus and a majority jackpot is shown in the following table, where the largest party receives a majority bonus/jackpot.
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If no party gets 50% there is a second round (with all parties above 10% contesting) and the winner of the second round gets the bonus 50%.
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electoral system have been described as providing a bonus to certain parties. Systems using single-member districts, particularly
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government (albeit with a slight modification of the original system), so the majority bonus was restored as of the
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was the first politician to enact a law to give automatic seats to the winning party and ensured his victory in the
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The jackpot system essentially gives the size of the jackpot or the vote share (whichever is higher, making it a
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Electoral incentives and the equal value of ballots in vote transfer systems with positive winner compensation
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The bonus system adds a certain fixed number of additional seats to the winning party or alliance. In the
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Used in multi-member districts, but the majority bonus in all districts is given to the same party.
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up to a sixth of the assembly seats are reserved as extra seats for the winning party. In the
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Massicotte & Blais (1999). "Mixed electoral systems: a conceptual and empirical survey".
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method of electing multiple representatives. The majority bonus is typically classified as a
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The majority bonus system was adopted by other European countries, especially
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Caciagli, Mario; Alan S. Zuckerman; Istituto Carlo Cattaneo (2001).
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The goal of the majority bonus system is to give extra seats in a
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principle are also effectively bonus seats for certain parties.
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for example is better compared to a bonus of around 10% to 30%.
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Italian Politics: Emerging Themes and Institutional Responses
52: 1003:. A majority bonus may also be one of the properties of a 2077:"Italy - Politics, Regions, Constitution | Britannica" 1934:. This change was undone in 2020 by the incumbent 1922:A bill abolishing the majority bonus in favor of 1867:is allowed, second ballot (one used for bonus) 991:. An academic term for such a hybrid system is 1827:municipal elections (above 3500 inhabitants) 1040:and on a local level in Italy and France. In 941: 8: 1906:, a precursor to the majority bonus system. 2002:https://doi.org/10.13140/RG.2.2.15129.34407 1365:Appr. seat share of the largest party (%) 948: 934: 24: 2015:"Parliament votes to change election law" 1728: 1341: 1090: 989:mixed-member majoritarian representation 15: 1964: 1915: 40: 1871:for electing the regional presidency. 1726:for regional and municipal elections. 7: 2025:from the original on 25 January 2020 1970: 1968: 2116:Semi-proportional electoral systems 979:system, as it integrates both the 14: 2102:. Berghahn Books. pp. 87–89. 1819:1-4 seats per district (23%-29%) 917: 904: 892: 840:McKelvey–Schofield chaos theorem 486:Semi-proportional representation 118:First preference plurality (FPP) 1046:Chamber of Deputies of Santa Fe 964:, sometimes referred to as the 878:Harsanyi's utilitarian theorem 835:Moulin's impossibility theorem 800:Conflicting majorities paradox 1: 1989:10.1016/S0261-3794(98)00063-8 1900:1924 Italian general election 1855:plurality bonus (supermixed) 1120:of the 2nd largest party (%) 1108:of the 2nd largest party (%) 704:Frustrated majorities paradox 873:Condorcet dominance theorems 813:Social and collective choice 1924:proportional representation 1830:majority bonus (two-round) 1814:majority bonus (two-round) 962:majority bonus system (MBS) 539:By mechanism of combination 310:Proportional representation 2147: 1687:first-preference plurality 1677:Effective majority bonuses 1332: 1070:Sicilian Regional Assembly 966:reinforced proportionality 737:Multiple districts paradox 468:Fractional approval voting 456:Interactive representation 1846: 1805: 1704:mixed-member proportional 1691:mixed-member majoritarian 1367: 1364: 1358: 1352: 1346: 1114:of the largest party (%) 1102:of the largest party (%) 684:Paradoxes and pathologies 533:Mixed-member proportional 528:Mixed-member majoritarian 523:By results of combination 414:Approval-based committees 1032:It is currently used in 863:Condorcet's jury theorem 664:Double simultaneous vote 639:Rural–urban proportional 634:Dual-member proportional 596: 585: 552:Parallel (superposition) 444:Fractional social choice 431:Expanding approvals rule 260: 245: 230: 161: 150: 126: 2131:Mixed electoral systems 1904:majority jackpot system 1335:Majority jackpot system 1027:majority jackpot system 790:Tyranny of the majority 567:Fusion (majority bonus) 384:Quota-remainder methods 1926:was introduced by the 1094:Nominal size of bonus 987:principles to provide 924:Mathematics portal 830:Majority impossibility 819:Impossibility theorems 615:Negative vote transfer 436:Method of equal shares 57: 22: 1702:in systems using the 1333:Further information: 727:Best-is-worst paradox 716:Pathological response 451:Direct representation 104:Single-winner methods 56: 19: 2019:www.ekathimerini.com 1876:municipal elections 1316:The bonus system is 1085:apportionment method 1044:, it is used in the 999:(superposition) and 911:Economics portal 858:Median voter theorem 77:Comparative politics 2021:. 24 January 2020. 1863:2 ballots (votes), 1852:regional elections 1797:but restored as of 1730: 1693:implementations of 1343: 1081:electoral threshold 899:Politics portal 610:Vote linkage system 581:Seat linkage system 168:Ranked-choice (RCV) 2081:www.britannica.com 1940:June 2023 election 1780:national elections 1729: 1666:conditional system 1361:largest party (%) 1359:Vote share of the 1342: 795:Discursive dilemma 754:Lesser evil voting 629:Supermixed systems 332:Largest remainders 190:Round-robin voting 58: 23: 2121:Electoral systems 1977:Electoral Studies 1888: 1887: 1811:French Polynesia 1737:Type of election 1662: 1661: 1329:Bonus and jackpot 1322:non-compensatory, 1314: 1313: 1118:Appr. seat share 1112:Appr. seat share 1005:supermixed system 973:semi-proportional 958: 957: 845:Gibbard's theorem 785:Dominance paradox 722:Perverse response 426:Phragmen's method 292:Majority judgment 220:Positional voting 178:Condorcet methods 46:electoral systems 2138: 2103: 2092: 2091: 2089: 2088: 2073: 2067: 2066: 2064: 2063: 2041: 2035: 2034: 2032: 2030: 2011: 2005: 1999: 1993: 1992: 1972: 1953: 1949: 1943: 1920: 1896:Benito Mussolini 1865:ticket splitting 1785:plurality bonus 1762:plurality bonus 1759:local elections 1731: 1368:Effective bonus 1344: 1091: 1076:almost certain. 1066:Greek Parliament 1038:French Polynesia 969:electoral system 950: 943: 936: 922: 921: 909: 908: 897: 896: 852:Positive results 747:Strategic voting 644:Majority jackpot 601: 590: 461:Liquid democracy 337:National remnant 327:Highest averages 264: 249: 234: 166: 157:Alternative vote 155: 139:Partisan primary 131: 72:Mechanism design 25: 2146: 2145: 2141: 2140: 2139: 2137: 2136: 2135: 2106: 2105: 2097: 2095: 2086: 2084: 2075: 2074: 2070: 2061: 2059: 2043: 2042: 2038: 2028: 2026: 2013: 2012: 2008: 2000: 1996: 1974: 1973: 1966: 1962: 1957: 1956: 1950: 1946: 1921: 1917: 1912: 1893: 1740:Type of system 1712: 1695:parallel voting 1683:winner-take-all 1679: 1376:Jackpot system 1337: 1331: 1062: 997:parallel voting 985:winner-take-all 981:proportionality 977:mixed electoral 954: 916: 915: 903: 891: 883: 882: 849: 825:Arrow's theorem 815: 805: 804: 773: 743: 732:No-show paradox 713: 699:Cloning paradox 689:Spoiler effects 686: 676: 675: 650: 537: 520: 510: 509: 482: 473:Maximal lottery 440: 421:Thiele's method 410: 380: 312: 302: 301: 287:Approval voting 275:Cardinal voting 271: 216: 210:Maximal lottery 174: 106: 96: 12: 11: 5: 2144: 2142: 2134: 2133: 2128: 2123: 2118: 2108: 2107: 2094: 2093: 2068: 2036: 2006: 1994: 1983:(3): 341–366. 1963: 1961: 1958: 1955: 1954: 1944: 1914: 1913: 1911: 1908: 1892: 1889: 1886: 1885: 1883: 1881: 1879: 1877: 1873: 1872: 1861: 1858: 1856: 1853: 1850: 1844: 1843: 1837: 1834: 1831: 1828: 1824: 1823: 1820: 1817: 1815: 1812: 1809: 1803: 1802: 1791: 1788: 1786: 1783: 1782:(legislative) 1777: 1771: 1770: 1768: 1765: 1763: 1760: 1757: 1751: 1750: 1747: 1746:Size of bonus 1744: 1741: 1738: 1735: 1711: 1708: 1700:Overhang seats 1678: 1675: 1660: 1659: 1654: 1649: 1647: 1644: 1639: 1636: 1635: 1632: 1629: 1627: 1622: 1617: 1614: 1613: 1610: 1607: 1605: 1600: 1597: 1594: 1593: 1588: 1586: 1581: 1578: 1576: 1570: 1569: 1564: 1562: 1557: 1554: 1552: 1546: 1545: 1540: 1538: 1533: 1530: 1528: 1522: 1521: 1516: 1511: 1509: 1506: 1501: 1498: 1497: 1492: 1487: 1485: 1482: 1477: 1474: 1473: 1468: 1463: 1461: 1458: 1453: 1450: 1449: 1444: 1442: 1437: 1434: 1432: 1426: 1425: 1420: 1418: 1413: 1410: 1408: 1402: 1401: 1396: 1394: 1389: 1386: 1384: 1378: 1377: 1374: 1370: 1369: 1366: 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This was a 1901: 1897: 1890: 1884: 1882: 1880: 1878: 1875: 1874: 1870: 1866: 1862: 1859: 1857: 1854: 1851: 1849: 1845: 1841: 1838: 1835: 1832: 1829: 1826: 1825: 1821: 1818: 1816: 1813: 1810: 1808: 1804: 1800: 1796: 1792: 1789: 1787: 1784: 1781: 1778: 1776: 1773: 1772: 1769: 1766: 1764: 1761: 1758: 1756: 1753: 1752: 1748: 1745: 1742: 1739: 1736: 1733: 1732: 1727: 1725: 1721: 1718:in 2004, and 1717: 1709: 1707: 1705: 1701: 1696: 1692: 1688: 1684: 1676: 1674: 1670: 1667: 1658: 1655: 1653: 1650: 1648: 1645: 1643: 1640: 1638: 1637: 1633: 1630: 1628: 1626: 1623: 1621: 1618: 1616: 1615: 1611: 1608: 1606: 1604: 1601: 1598: 1596: 1595: 1592: 1589: 1587: 1585: 1582: 1579: 1577: 1575: 1572: 1571: 1568: 1565: 1563: 1561: 1558: 1555: 1553: 1551: 1548: 1547: 1544: 1541: 1539: 1537: 1534: 1531: 1529: 1527: 1524: 1523: 1520: 1517: 1515: 1512: 1510: 1507: 1505: 1502: 1500: 1499: 1496: 1493: 1491: 1488: 1486: 1483: 1481: 1478: 1476: 1475: 1472: 1469: 1467: 1464: 1462: 1459: 1457: 1454: 1452: 1451: 1448: 1445: 1443: 1441: 1438: 1435: 1433: 1431: 1428: 1427: 1424: 1421: 1419: 1417: 1414: 1411: 1409: 1407: 1404: 1403: 1400: 1397: 1395: 1393: 1390: 1387: 1385: 1383: 1380: 1379: 1375: 1373:Bonus system 1372: 1371: 1362: 1356: 1350: 1345: 1340: 1336: 1328: 1326: 1323: 1319: 1318:unconditional 1309: 1307: 1304: 1301: 1299: 1296: 1293: 1292: 1288: 1286: 1283: 1280: 1278: 1275: 1272: 1271: 1267: 1265: 1262: 1259: 1257: 1254: 1251: 1250: 1246: 1244: 1241: 1238: 1236: 1233: 1230: 1229: 1225: 1223: 1220: 1217: 1215: 1212: 1209: 1208: 1204: 1202: 1199: 1196: 1194: 1191: 1188: 1187: 1183: 1181: 1178: 1175: 1173: 1170: 1167: 1166: 1162: 1160: 1157: 1154: 1152: 1149: 1146: 1145: 1141: 1139: 1136: 1133: 1131: 1128: 1125: 1124: 1121: 1117: 1115: 1111: 1109: 1105: 1103: 1099: 1097: 1093: 1092: 1089: 1086: 1082: 1077: 1075: 1074:supermajority 1071: 1067: 1059: 1057: 1055: 1051: 1047: 1043: 1039: 1035: 1030: 1028: 1023: 1018: 1013: 1008: 1006: 1002: 998: 994: 990: 986: 982: 978: 974: 970: 967: 963: 951: 946: 944: 939: 937: 932: 931: 929: 928: 925: 920: 912: 907: 902: 900: 895: 890: 889: 887: 886: 879: 876: 874: 871: 869: 868:May's theorem 866: 864: 861: 859: 856: 855: 854: 853: 846: 843: 841: 838: 836: 833: 831: 828: 826: 823: 822: 821: 820: 814: 809: 808: 801: 798: 796: 793: 791: 788: 786: 783: 782: 781: 780: 779: 778:majority rule 776:Paradoxes of 770: 767: 765: 762: 760: 757: 755: 752: 751: 750: 749: 748: 738: 735: 734: 733: 730: 728: 725: 723: 720: 719: 718: 717: 710: 707: 705: 702: 700: 697: 695: 692: 691: 690: 685: 680: 679: 672: 669: 665: 662: 661: 660: 657: 656: 655: 654: 645: 642: 640: 637: 635: 632: 631: 630: 627: 621: 618: 616: 613: 612: 611: 608: 604: 599: 595: 593: 588: 584: 583: 582: 579: 578: 577: 576: 572: 568: 565: 563: 560: 558: 555: 553: 550: 549: 548: 547: 542: 541: 540: 534: 531: 529: 526: 525: 524: 519: 518:Mixed systems 514: 513: 506: 503: 499: 496: 495: 494: 491: 490: 489: 488: 487: 479: 478:Random ballot 476: 474: 471: 469: 466: 462: 459: 457: 454: 453: 452: 449: 448: 447: 446: 445: 437: 434: 432: 429: 427: 424: 422: 419: 418: 417: 416: 415: 407: 404: 402: 399: 397: 394: 392: 389: 388: 387: 386: 385: 375: 372: 370: 367: 365: 362: 360: 357: 355: 352: 351: 350: 347: 343: 340: 338: 335: 333: 330: 328: 325: 324: 323: 322:Apportionment 320: 319: 318: 317: 311: 306: 305: 298: 295: 293: 290: 288: 285: 283: 280: 279: 278: 277: 276: 267: 263: 258: 257:Antiplurality 255: 252: 248: 243: 240: 237: 233: 228: 225: 224: 223: 222: 221: 211: 208: 206: 203: 201: 198: 196: 193: 192: 191: 188: 186: 185:Condorcet-IRV 183: 182: 181: 180: 179: 169: 164: 160: 158: 153: 149: 148: 147: 144: 140: 137: 136: 134: 129: 124: 121: 119: 116: 115: 114: 112: 105: 100: 99: 92: 88: 85: 83: 80: 78: 75: 73: 70: 68: 67:Social choice 65: 64: 62: 61: 55: 51: 50: 47: 43: 42:Social choice 39: 35: 31: 27: 26: 18: 2099: 2096: 2085:. 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Retrieved 2018: 2009: 1997: 1980: 1976: 1947: 1918: 1894: 1869:is also used 1847: 1840: 1806: 1793:Not used in 1774: 1754: 1713: 1680: 1671: 1663: 1656: 1651: 1641: 1624: 1619: 1602: 1590: 1583: 1573: 1566: 1559: 1549: 1542: 1535: 1525: 1518: 1513: 1503: 1494: 1489: 1479: 1470: 1465: 1455: 1446: 1439: 1429: 1422: 1415: 1405: 1398: 1391: 1381: 1360: 1355:jackpot (%) 1354: 1348: 1338: 1321: 1317: 1315: 1305: 1297: 1284: 1276: 1263: 1255: 1242: 1234: 1221: 1213: 1200: 1192: 1179: 1171: 1158: 1150: 1137: 1129: 1119: 1113: 1107: 1101: 1095: 1078: 1063: 1031: 1022:compensatory 1009: 992: 965: 961: 959: 851: 850: 817: 775: 774: 759:Exaggeration 745: 744: 715: 714: 688: 652: 651: 620:Mixed ballot 575:Compensatory 573: 566: 546:compensatory 543: 538: 522: 484: 483: 442: 441: 412: 411: 382: 381: 369:List-free PR 314: 282:Score voting 273: 272: 218: 217: 205:Ranked pairs 176: 175: 108: 1743:Used since 1106:Vote share 1100:Vote share 1017:conditional 1012:legislature 1001:coexistence 659:Single vote 562:Conditional 557:Coexistence 406:Quota Borda 396:Schulze STV 354:Closed list 297:STAR voting 242:Borda count 2110:Categories 2087:2024-08-11 2062:2023-06-07 2029:25 January 1960:References 1790:0%-16.66% 1349:bonus (%) 1054:Entre RĂ­os 764:Truncation 493:Cumulative 316:Party-list 91:By country 82:Comparison 2057:0013-0613 1799:June 2023 1060:Mechanism 1042:Argentina 671:Dual-vote 364:Panachage 359:Open list 349:List type 227:Plurality 123:Two-round 111:plurality 34:Economics 2023:Archived 1932:May 2023 1795:May 2023 1734:Country 1353:Size of 1347:Size of 391:Hare STV 30:Politics 28:A joint 2126:Fascism 1891:History 1755:Andorra 401:CPO-STV 251:Baldwin 200:Schulze 195:Minimax 113:methods 2055:  1928:Syriza 1807:France 1775:Greece 1749:Notes 1720:France 1716:Greece 1083:or an 1052:, and 1050:Chubut 1034:Greece 993:fusion 266:Coombs 36:series 1910:Notes 1848:Italy 1833:1982 1724:Italy 1681:Many 971:is a 603:'MMP' 592:'AMS' 21:well. 2053:ISSN 2031:2020 1952:40%. 1860:20% 1836:50% 1767:50% 1722:and 1646:55% 1631:55% 1609:55% 1599:50% 1580:55% 1556:55% 1532:55% 1508:45% 1484:45% 1460:45% 1436:45% 1412:45% 1388:45% 1320:and 1310:11% 1302:25% 1294:55% 1289:19% 1281:25% 1273:25% 1268:23% 1260:25% 1252:10% 1247:11% 1239:25% 1231:55% 1226:19% 1218:25% 1210:25% 1205:23% 1197:25% 1189:10% 1184:13% 1176:25% 1168:50% 1163:19% 1155:25% 1147:25% 1142:23% 1134:25% 1126:10% 1096:(%) 1020:non- 983:and 960:The 544:Non- 498:SNTV 87:List 44:and 32:and 1985:doi 1710:Use 1652:60% 1642:60% 1634:0% 1625:55% 1620:55% 1612:0% 1603:55% 1591:23% 1584:78% 1574:50% 1567:11% 1560:66% 1550:25% 1536:60% 1526:10% 1519:15% 1514:60% 1504:60% 1495:10% 1490:55% 1480:55% 1466:50% 1456:50% 1447:28% 1440:73% 1430:50% 1423:14% 1416:59% 1406:25% 1392:51% 1382:10% 1306:82% 1298:60% 1285:70% 1277:60% 1264:64% 1256:60% 1243:75% 1235:45% 1222:59% 1214:45% 1201:51% 1193:45% 1180:65% 1172:30% 1159:48% 1151:30% 1138:37% 1130:30% 262:el. 247:el. 236:IRV 232:el. 2112:: 2079:. 2051:. 2047:. 2017:. 1981:18 1979:. 1967:^ 1801:. 1657:5% 1543:5% 1471:5% 1399:6% 1056:. 1048:, 1036:, 1029:. 1007:. 598:NZ 587:UK 163:US 152:UK 135:) 128:US 2090:. 2065:. 2033:. 1991:. 1987:: 1942:. 949:e 942:t 935:v 600:: 589:: 268:) 259:( 253:) 244:( 238:) 229:( 165:: 154:: 130:: 125:( 93:) 89:(

Index


Politics
Economics
Social choice
electoral systems

Social choice
Mechanism design
Comparative politics
Comparison
List
By country
Single-winner methods
plurality
First preference plurality (FPP)
Two-round
US
Jungle primary
Partisan primary
Instant-runoff
UK
Alternative vote
US
Ranked-choice (RCV)
Condorcet methods
Condorcet-IRV
Round-robin voting
Minimax
Schulze
Ranked pairs

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