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1194:. Each party is first allocated a number of seats equal to their integer. This will generally leave some remainder seats unallocated. To apportion these seats, the parties are then ranked on the basis of their fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all seats have been allocated. This gives the method its name.
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By the same token, the results of an apportionment for all parties can depend on the exact order of calculations. If the number of independents who win a seat is calculated first, and an apportionment is then computed excluding their seats, the results may be different from those reached by treating
1182:
The largest remainder methods require the numbers of votes for each party to be divided by a quota representing the number of votes required to win a seat. Usually, this is given by the total number of votes cast, divided by the number of seats. The result for each party will consist of an
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to the Union, the House was expanded by 5 seats, equal to
Oklahoma's apportionment, to ensure it would not affect the seats for any exiting state. apportionment. However, when the full apportionment was recalculated, the House was stunned to learn that New York had lost a seat to
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in the number of seats allocated to a certain party. In the example below, when the number of seats to be allocated is increased from 25 to 26 (with the number of votes held constant), parties D and E counterintuitively end up with fewer seats.
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However, a greater concern for social choice theorists, and the primary cause behind their abandonment in most countries, is the tendency of such rules to produce bizarre or irrational behaviors called
1609:(each party's seats are equal to its ideal share of seats, either rounded up or rounded down) and was designed to satisfy that criterion. However, this comes at the cost of greater inequalities in the
1231:. Smaller quotas leave behind fewer seats for small parties (with less than a full quota) to pick up, while larger quotas leave behind more seats. A somewhat counterintuitive result of this is that a
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1078:, i.e. algorithms for distributing the seats in a legislative body among a number of administrative divisions. The quota methods are based on calculating a
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1209:, both of which behave like the largest-remainders method when voters all behave like strict partisans (i.e. only rank candidates of their own party).
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It is easy for a voter to understand how the largest remainder method allocates seats. Moreover, the largest remainder method satisfies the
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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).
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The Hare quota is more generous to less popular parties and the Droop quota to more popular parties. Specifically, the Hare quota is
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1250:. The use of a particular quota with one of the largest remainder methods is often abbreviated as "LR-", such as "LR-Droop".
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avoid all the paradoxes discussed above, with the exception of quota violations. However, quota violations in low-
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1227:. The choice of quota affects the properties of the corresponding largest remainder method, and particularly the
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2391:"Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities"
2360:"Comparing Proportional Representation Electoral Systems: Quotas, Thresholds, Paradoxes and Majorities"
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population relative to another, e.g. go from having 5Ă— as many people to 6Ă— as many people, yet
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How Math
Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics
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of this entitlement, and any seats left over are distributed according to a specified rule.
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2482:"Apportioning Representatives in the United States Congress – Paradoxes of Apportionment"
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1104:, i.e. the most leftover votes). They are typically contrasted with the more popular
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These examples take an election to allocate 10 seats where there are 100,000 votes.
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Proportional
Representation: Apportionment Methods and Their Applications
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Proportional
Representation: Apportionment Methods and Their Applications
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1330:{\displaystyle {\frac {\text{total votes}}{{\text{total seats}}+1}}}
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Largest remainder methods can also be used to apportion votes among
1119:; it is the second-most common apportionment rule worldwide, after
1276:{\displaystyle {\frac {\text{total votes}}{\text{total seats}}}}
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each independent as if they were in their own political party.
29:
2292:, Cham: Springer International Publishing, pp. 159–183,
2245:, Cham: Springer International Publishing, pp. 95–105,
159:
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2284:
Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.),
2237:
Pukelsheim, Friedrich (2017), Pukelsheim, Friedrich (ed.),
1286:
LR-Hare is sometimes called
Hamilton's method, named after
1150:
seats, by increasing the size of the electoral quota. Such
1138:. In particular, the largest remainder methods exhibit the
1636:
a particular party's apportionment, a problem called the
1643:
Adding more parties to the can cause a bizarre kind of
2286:"Securing System Consistency: Coherence and Paradoxes"
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3154:
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3012:
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1096:By far the most common kind of quota method is the
60:. Unsourced material may be challenged and removed.
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2330:
1329:
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1253:The Hare (or simple) quota is defined as follows:
2420:Gallagher, Michael; Mitchell, Paul (2005-09-15).
2239:"Quota Methods of Apportionment: Divide and Rank"
1130:discourage the use of quota methods, rather than
2329:Balinski, Michel L.; Young, H. Peyton (1982).
1108:(also called divisor methods). When using the
2588:
1134:, because of their greater susceptibility to
1048:
8:
3045:Independence of Smith-dominated alternatives
2453:. Studies in Choice and Welfare. Springer.
1223:There are several possible choices for the
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2595:
2581:
2573:
2532:Balinski, Michel; H. Peyton Young (1982).
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1711:tend to be both mild and extremely rare.
1313:
1307:
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1261:
120:Learn how and when to remove this message
27:Proportional-representation voting system
2211:. New York: Prentice Hall. p. 128.
1964:
1737:
1727:in the total number of seats leads to a
1375:
3040:Independence of irrelevant alternatives
2818:Sequential proportional approval voting
2488:. Mathematical Association of America.
2480:Caulfield, Michael J. (November 2010).
2324:
2322:
2194:
1235:quota will always be more favorable to
147:
3205:Party-list proportional representation
2564:Hamilton method experimentation applet
2447:Eerik Lagerspetz (26 November 2015).
1613:, which can violate the principle of
1126:Despite their intuitive appeal, most
7:
2395:British Journal of Political Science
2364:British Journal of Political Science
2337:. New Haven: Yale University Press.
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58:adding citations to reliable sources
2850:Indirect single transferable voting
2450:Social Choice and Democratic Values
1695:a seat to the slower-growing state.
1242:The two most common quotas are the
1290:, who devised the method in 1792.
25:
2423:The Politics of Electoral Systems
2208:Excursions in Modern Mathematics
1962:With 26 seats, the results are:
1735:With 25 seats, the results are:
1024:
1011:
999:
947:McKelvey–Schofield chaos theorem
593:Semi-proportional representation
225:First preference plurality (FPP)
34:
2511:. New York: Smithsonian Books.
1340:and is applied to elections in
45:needs additional citations for
2961:Mixed ballot transferable vote
1089:. Every party is assigned the
985:Harsanyi's utilitarian theorem
942:Moulin's impossibility theorem
907:Conflicting majorities paradox
1:
1654:When Congress first admitted
811:Frustrated majorities paradox
3162:Comparison of voting systems
3004:Satisfaction approval voting
2989:Single non-transferable vote
2808:Proportional approval voting
1676:seats, a situation called a
980:Condorcet dominance theorems
920:Social and collective choice
2768:Graduated majority judgment
2389:Gallagher, Michael (1992).
2358:Gallagher, Michael (1992).
2298:10.1007/978-3-319-64707-4_9
2251:10.1007/978-3-319-64707-4_5
646:By mechanism of combination
417:Proportional representation
3226:
3020:Condorcet winner criterion
2711:First-past-the-post voting
2205:Tannenbaum, Peter (2010).
1216:
844:Multiple districts paradox
575:Fractional approval voting
563:Interactive representation
3175:
3167:Voting systems by country
3070:Mutual majority criterion
3025:Condorcet loser criterion
2971:Vote linkage mixed system
2883:Largest remainders method
2610:
1098:largest remainders method
791:Paradoxes and pathologies
640:Mixed-member proportional
635:Mixed-member majoritarian
630:By results of combination
521:Approval-based committees
18:Largest remainders method
3060:Majority loser criterion
2946:Additional member system
2904:Hagenbach-Bischoff quota
2823:Single transferable vote
2748:Positional voting system
2684:Minimax Condorcet method
2642:Combined approval voting
2507:Stein, James D. (2008).
1701:highest averages methods
1672:a party can cause it to
1632:the number of seats may
1547:Highest-remainder seats
1203:single transferable vote
1201:, as in the case of the
1154:occur by increasing the
1146:a party can cause it to
1106:highest averages methods
970:Condorcet's jury theorem
771:Double simultaneous vote
746:Rural–urban proportional
741:Dual-member proportional
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692:
659:Parallel (superposition)
551:Fractional social choice
538:Expanding approvals rule
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3085:Resolvability criterion
3075:Participation criterion
3050:Later-no-harm criterion
2866:Highest averages method
1623:apportionment paradoxes
1136:apportionment paradoxes
1128:social choice theorists
1112:, the method is called
897:Tyranny of the majority
674:Fusion (majority bonus)
491:Quota-remainder methods
3126:First-preference votes
3065:Monotonicity criterion
3035:Independence of clones
2738:Simple majoritarianism
1331:
1277:
1031:Mathematics portal
937:Majority impossibility
926:Impossibility theorems
722:Negative vote transfer
543:Method of equal shares
164:
3210:Apportionment methods
3030:Consistency criterion
2951:Alternative vote plus
2716:Instant-runoff voting
1332:
1278:
834:Best-is-worst paradox
823:Pathological response
558:Direct representation
211:Single-winner methods
163:
3100:Seats-to-votes ratio
2871:Webster/Sainte-Laguë
1678:negative vote weight
1611:seats-to-votes ratio
1304:
1260:
1152:population paradoxes
1018:Economics portal
965:Median voter theorem
184:Comparative politics
54:improve this article
3080:Plurality criterion
2679:Kemeny–Young method
1076:apportionment rules
1006:Politics portal
717:Vote linkage system
688:Seat linkage system
275:Ranked-choice (RCV)
3121:Election threshold
3055:Majority criterion
2731:Supplementary vote
2494:10.4169/loci003163
1327:
1288:Alexander Hamilton
1273:
1207:quota Borda system
1168:house monotonicity
1121:Jefferson's method
902:Discursive dilemma
861:Lesser evil voting
736:Supermixed systems
439:Largest remainders
297:Round-robin voting
165:
3192:
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3090:Reversal symmetry
2999:Cumulative voting
2981:Semi-proportional
2956:Mixed single vote
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2798:Mixed single vote
2706:Exhaustive ballot
2669:Copeland's method
2664:Condorcet methods
2604:Electoral systems
2433:978-0-19-153151-4
2307:978-3-319-64707-4
2260:978-3-319-64707-4
2218:978-0-321-56803-8
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952:Gibbard's theorem
892:Dominance paradox
829:Perverse response
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399:Majority judgment
327:Positional voting
285:Condorcet methods
153:electoral systems
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16:(Redirected from
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3131:Liquid democracy
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580:Maximal lottery
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2426:. OUP Oxford.
2412:
2401:(4): 469–496.
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2370:(4): 469–496.
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2118:
2115:
2112:
2108:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2086:
2082:
2081:
2079:
2076:
2073:
2070:
2067:
2064:
2061:
2057:
2056:
2053:
2051:
2049:
2047:
2045:
2043:
2041:
2037:
2036:
2033:
2031:
2029:
2027:
2025:
2023:
2021:
2017:
2016:
2013:
2010:
2007:
2004:
2001:
1998:
1995:
1991:
1990:
1987:
1984:
1981:
1978:
1975:
1972:
1969:
1958:
1957:
1954:
1951:
1948:
1945:
1942:
1939:
1936:
1932:
1931:
1928:
1925:
1922:
1919:
1916:
1913:
1910:
1909:Surplus seats
1906:
1905:
1903:
1900:
1897:
1894:
1891:
1888:
1885:
1881:
1880:
1877:
1874:
1871:
1868:
1865:
1862:
1859:
1855:
1854:
1852:
1849:
1846:
1843:
1840:
1837:
1834:
1830:
1829:
1826:
1824:
1822:
1820:
1818:
1816:
1814:
1810:
1809:
1806:
1804:
1802:
1800:
1798:
1796:
1794:
1790:
1789:
1786:
1783:
1780:
1777:
1774:
1771:
1768:
1764:
1763:
1760:
1757:
1754:
1751:
1748:
1745:
1742:
1716:
1713:
1697:
1696:
1687:One state can
1685:
1666:
1665:
1664:
1660:
1645:spoiler effect
1641:
1602:
1599:
1596:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1570:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1544:
1543:
1541:
1538:
1535:
1532:
1529:
1526:
1523:
1519:
1518:
1515:
1512:
1509:
1506:
1503:
1500:
1497:
1493:
1492:
1490:
1487:
1484:
1481:
1478:
1475:
1472:
1468:
1467:
1464:
1462:
1460:
1458:
1456:
1454:
1452:
1448:
1447:
1444:
1442:
1440:
1438:
1436:
1434:
1432:
1428:
1427:
1424:
1421:
1418:
1415:
1412:
1409:
1406:
1402:
1401:
1398:
1395:
1392:
1389:
1386:
1383:
1380:
1373:
1370:
1366:
1363:
1358:
1355:
1338:
1337:
1323:
1320:
1284:
1283:
1217:Main article:
1214:
1211:
1179:
1176:
1142:, i.e. voting
1063:
1062:
1060:
1059:
1052:
1045:
1037:
1034:
1033:
1021:
1020:
1008:
995:
992:
991:
988:
987:
982:
977:
972:
967:
955:
954:
949:
944:
939:
934:
923:
918:
917:
914:
913:
910:
909:
904:
899:
894:
879:
878:
876:Turkey-raising
873:
868:
863:
849:
848:
847:
846:
836:
831:
819:
818:
816:Center squeeze
813:
808:
803:
801:Spoiler effect
794:
789:
788:
785:
784:
781:
780:
775:
774:
773:
760:By ballot type
756:
755:
754:
753:
748:
743:
733:
732:
731:
730:
729:
724:
714:
713:
712:
701:
678:
677:
676:
671:
666:
661:
643:
642:
637:
628:
623:
622:
619:
618:
615:
614:
612:Limited voting
609:
608:
607:
588:
587:
582:
577:
572:
571:
570:
565:
546:
545:
540:
535:
530:
516:
515:
510:
505:
500:
486:
485:
484:
483:
481:Localized list
478:
473:
468:
463:
453:
452:
451:
449:Biproportional
446:
441:
436:
420:
415:
414:
411:
410:
407:
406:
401:
396:
391:
377:
376:
361:
346:
322:
321:
320:
319:
314:
309:
304:
294:
280:
279:
278:
277:
266:
253:Instant-runoff
250:
249:
248:
240:Jungle primary
227:
216:Single vote -
214:
209:
208:
205:
204:
202:
201:
191:
186:
181:
176:
170:
167:
166:
156:
155:
145:
144:
128:
127:
69:"Quota method"
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3222:
3211:
3208:
3206:
3203:
3202:
3200:
3187:
3186:
3181:
3180:
3174:
3168:
3165:
3163:
3160:
3159:
3157:
3153:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3124:
3122:
3119:
3117:
3114:
3113:
3111:
3107:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3021:
3018:
3017:
3015:
3011:
3005:
3002:
3000:
2997:
2995:
2992:
2990:
2987:
2986:
2984:
2982:
2978:
2972:
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2933:
2931:
2929:
2925:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2896:
2894:
2890:
2884:
2881:
2877:
2874:
2872:
2869:
2868:
2867:
2864:
2863:
2861:
2857:
2851:
2848:
2846:
2843:
2839:
2836:
2834:
2831:
2829:
2826:
2825:
2824:
2821:
2819:
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2796:
2794:
2791:
2790:
2788:
2784:
2781:
2779:
2775:
2769:
2766:
2764:
2761:
2759:
2756:
2754:
2751:
2749:
2746:
2744:
2741:
2739:
2736:
2732:
2729:
2727:
2724:
2722:
2719:
2718:
2717:
2714:
2712:
2709:
2707:
2704:
2700:
2697:
2695:
2692:
2690:
2687:
2685:
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2666:
2665:
2662:
2660:
2657:
2655:
2652:
2648:
2645:
2643:
2640:
2639:
2638:
2635:
2634:
2632:
2630:
2629:Single-winner
2626:
2622:
2620:
2616:
2609:
2605:
2598:
2593:
2591:
2586:
2584:
2579:
2578:
2575:
2569:
2565:
2562:
2561:
2557:
2549:
2547:0-300-02724-9
2543:
2538:
2537:
2528:
2525:
2520:
2518:9780061241765
2514:
2510:
2503:
2500:
2495:
2491:
2487:
2483:
2476:
2473:
2462:
2460:9783319232614
2456:
2452:
2451:
2443:
2440:
2435:
2429:
2425:
2424:
2416:
2413:
2408:
2404:
2400:
2396:
2392:
2385:
2382:
2377:
2373:
2369:
2365:
2361:
2354:
2351:
2346:
2344:0-300-02724-9
2340:
2335:
2334:
2325:
2323:
2319:
2309:
2303:
2299:
2295:
2291:
2287:
2280:
2278:
2276:
2272:
2262:
2256:
2252:
2248:
2244:
2240:
2233:
2231:
2229:
2225:
2220:
2214:
2210:
2209:
2201:
2199:
2195:
2189:
2182:
2179:
2176:
2173:
2170:
2167:
2164:
2161:
2160:
2156:
2153:
2150:
2147:
2144:
2141:
2138:
2135:
2134:
2131:
2128:
2125:
2122:
2119:
2116:
2113:
2110:
2109:
2105:
2102:
2099:
2096:
2093:
2090:
2087:
2084:
2083:
2080:
2077:
2074:
2071:
2068:
2065:
2062:
2059:
2058:
2054:
2052:
2050:
2048:
2046:
2044:
2042:
2039:
2038:
2034:
2032:
2030:
2028:
2026:
2024:
2022:
2019:
2018:
2014:
2011:
2008:
2005:
2002:
1999:
1996:
1993:
1992:
1988:
1985:
1982:
1979:
1976:
1973:
1970:
1967:
1966:
1963:
1955:
1952:
1949:
1946:
1943:
1940:
1937:
1934:
1933:
1929:
1926:
1923:
1920:
1917:
1914:
1911:
1908:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1883:
1882:
1878:
1875:
1872:
1869:
1866:
1863:
1860:
1857:
1856:
1853:
1850:
1847:
1844:
1841:
1838:
1835:
1832:
1831:
1827:
1825:
1823:
1821:
1819:
1817:
1815:
1812:
1811:
1807:
1805:
1803:
1801:
1799:
1797:
1795:
1792:
1791:
1787:
1784:
1781:
1778:
1775:
1772:
1769:
1766:
1765:
1761:
1758:
1755:
1752:
1749:
1746:
1743:
1740:
1739:
1736:
1733:
1730:
1726:
1722:
1714:
1712:
1710:
1707:methods like
1706:
1702:
1694:
1690:
1686:
1683:
1679:
1675:
1671:
1667:
1661:
1657:
1653:
1652:
1650:
1646:
1642:
1639:
1635:
1631:
1628:
1627:
1626:
1624:
1618:
1616:
1612:
1608:
1601:Pros and cons
1600:
1593:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1571:
1567:
1564:
1561:
1558:
1555:
1552:
1549:
1546:
1545:
1542:
1539:
1536:
1533:
1530:
1527:
1524:
1521:
1520:
1516:
1513:
1510:
1507:
1504:
1501:
1498:
1495:
1494:
1491:
1488:
1485:
1482:
1479:
1476:
1473:
1470:
1469:
1465:
1463:
1461:
1459:
1457:
1455:
1453:
1450:
1449:
1446:10 (10+1=11)
1445:
1443:
1441:
1439:
1437:
1435:
1433:
1430:
1429:
1425:
1422:
1419:
1416:
1413:
1410:
1407:
1404:
1403:
1399:
1396:
1393:
1390:
1387:
1384:
1381:
1378:
1377:
1371:
1369:
1364:
1362:
1356:
1354:
1352:
1351:
1345:
1343:
1321:
1318:
1300:
1299:
1298:
1297:is given by:
1296:
1291:
1289:
1256:
1255:
1254:
1251:
1249:
1245:
1240:
1238:
1234:
1230:
1226:
1220:
1212:
1210:
1208:
1204:
1200:
1195:
1193:
1190:
1186:
1177:
1175:
1173:
1169:
1165:
1162:and can fail
1161:
1157:
1153:
1149:
1145:
1141:
1137:
1133:
1129:
1124:
1122:
1118:
1116:
1111:
1107:
1103:
1099:
1094:
1092:
1088:
1084:
1081:
1077:
1073:
1071:
1058:
1053:
1051:
1046:
1044:
1039:
1038:
1036:
1035:
1032:
1027:
1019:
1014:
1009:
1007:
1002:
997:
996:
994:
993:
986:
983:
981:
978:
976:
975:May's theorem
973:
971:
968:
966:
963:
962:
961:
960:
953:
950:
948:
945:
943:
940:
938:
935:
933:
930:
929:
928:
927:
921:
916:
915:
908:
905:
903:
900:
898:
895:
893:
890:
889:
888:
887:
886:
885:majority rule
883:Paradoxes of
877:
874:
872:
869:
867:
864:
862:
859:
858:
857:
856:
855:
845:
842:
841:
840:
837:
835:
832:
830:
827:
826:
825:
824:
817:
814:
812:
809:
807:
804:
802:
799:
798:
797:
792:
787:
786:
779:
776:
772:
769:
768:
767:
764:
763:
762:
761:
752:
749:
747:
744:
742:
739:
738:
737:
734:
728:
725:
723:
720:
719:
718:
715:
711:
706:
702:
700:
695:
691:
690:
689:
686:
685:
684:
683:
679:
675:
672:
670:
667:
665:
662:
660:
657:
656:
655:
654:
649:
648:
647:
641:
638:
636:
633:
632:
631:
626:
625:Mixed systems
621:
620:
613:
610:
606:
603:
602:
601:
598:
597:
596:
595:
594:
586:
585:Random ballot
583:
581:
578:
576:
573:
569:
566:
564:
561:
560:
559:
556:
555:
554:
553:
552:
544:
541:
539:
536:
534:
531:
529:
526:
525:
524:
523:
522:
514:
511:
509:
506:
504:
501:
499:
496:
495:
494:
493:
492:
482:
479:
477:
474:
472:
469:
467:
464:
462:
459:
458:
457:
454:
450:
447:
445:
442:
440:
437:
435:
432:
431:
430:
429:Apportionment
427:
426:
425:
424:
418:
413:
412:
405:
402:
400:
397:
395:
392:
390:
387:
386:
385:
384:
383:
374:
370:
365:
364:Antiplurality
362:
359:
355:
350:
347:
344:
340:
335:
332:
331:
330:
329:
328:
318:
315:
313:
310:
308:
305:
303:
300:
299:
298:
295:
293:
292:Condorcet-IRV
290:
289:
288:
287:
286:
276:
271:
267:
265:
260:
256:
255:
254:
251:
247:
244:
243:
241:
236:
231:
228:
226:
223:
222:
221:
219:
212:
207:
206:
199:
195:
192:
190:
187:
185:
182:
180:
177:
175:
174:Social choice
172:
171:
169:
168:
162:
158:
157:
154:
150:
149:Social choice
146:
142:
138:
134:
133:
124:
121:
113:
110:November 2011
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
3183:
3177:
2793:Mixed-member
2778:Proportional
2753:Score voting
2694:Ranked pairs
2613:Part of the
2612:
2568:cut-the-knot
2535:
2527:
2508:
2502:
2485:
2475:
2464:. Retrieved
2449:
2442:
2422:
2415:
2398:
2394:
2384:
2367:
2363:
2353:
2332:
2311:, retrieved
2289:
2264:, retrieved
2242:
2207:
2162:Total seats
1961:
1935:Total seats
1734:
1728:
1724:
1718:
1698:
1692:
1688:
1673:
1669:
1633:
1629:
1619:
1604:
1573:Total seats
1471:Ideal seats
1451:Droop quota
1368:
1360:
1349:
1346:
1342:South Africa
1339:
1292:
1285:
1252:
1241:
1236:
1232:
1222:
1196:
1187:part plus a
1181:
1147:
1143:
1125:
1113:
1097:
1095:
1079:
1068:
1066:
958:
957:
924:
882:
881:
866:Exaggeration
852:
851:
822:
821:
795:
759:
758:
727:Mixed ballot
682:Compensatory
680:
653:compensatory
650:
645:
629:
591:
590:
549:
548:
519:
518:
489:
488:
476:List-free PR
421:
389:Score voting
380:
379:
325:
324:
312:Ranked pairs
283:
282:
215:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
3136:Spoilt vote
2899:Droop quota
2838:Schulze STV
2813:Rural–urban
2758:STAR voting
2654:Borda count
2486:Convergence
2040:Hare quota
1813:Hare quota
1723:is when an
1647:called the
1372:Droop quota
1315:total seats
1310:total votes
1295:Droop quota
1269:total seats
1266:total votes
1248:Droop quota
766:Single vote
669:Conditional
664:Coexistence
513:Quota Borda
503:Schulze STV
461:Closed list
404:STAR voting
349:Borda count
3199:Categories
3155:Comparison
2909:Hare quota
2859:Allocation
2845:Spare vote
2833:Hare-Clark
2803:Party-list
2466:2017-08-17
2313:2024-05-10
2266:2024-05-10
2190:References
2111:Remainder
1884:Remainder
1630:Increasing
1607:quota rule
1522:Remainder
1365:Hare quota
1244:Hare quota
1189:fractional
1110:Hare quota
1102:remainders
871:Truncation
600:Cumulative
423:Party-list
198:By country
189:Comparison
80:newspapers
3146:Unseating
3141:Sortition
2743:Plurality
2619:Economics
2407:0007-1234
2376:0007-1234
1239:parties.
1229:seat bias
1192:remainder
1117:'s method
778:Dual-vote
471:Panachage
466:Open list
456:List type
334:Plurality
230:Two-round
218:plurality
141:Economics
3013:Criteria
2966:Scorporo
2615:politics
1729:decrease
1725:increase
1656:Oklahoma
1634:decrease
1426:100,000
1357:Examples
1350:unbiased
1246:and the
1164:resource
1115:Hamilton
498:Hare STV
137:Politics
135:A joint
3185:Project
2876:D'Hondt
2828:CPO-STV
2786:Systems
1668:Voting
1382:Yellows
1237:smaller
1205:or the
1185:integer
1072:methods
508:CPO-STV
358:Baldwin
307:Schulze
302:Minimax
220:methods
94:scholar
3179:Portal
3116:Ballot
2892:Quotas
2621:series
2544:
2515:
2457:
2430:
2405:
2374:
2341:
2304:
2257:
2215:
2020:Seats
1994:Votes
1989:Total
1793:Seats
1767:Votes
1762:Total
1659:Maine.
1466:9,091
1417:12,000
1414:15,800
1411:16,000
1408:47,000
1405:Votes
1400:Total
1391:Greens
1385:Whites
1233:larger
1213:Quotas
1178:Method
373:Coombs
143:series
96:
89:
82:
75:
67:
3109:Other
2928:Mixed
2015:5100
1968:Party
1788:5100
1741:Party
1540:0.341
1537:0.671
1534:0.320
1531:0.738
1528:0.760
1525:0.170
1489:0.341
1486:0.671
1483:1.320
1480:1.738
1477:1.760
1474:5.170
1423:3,100
1420:6,100
1397:Pinks
1394:Blues
1379:Party
1080:fixed
1070:quota
710:'MMP'
699:'AMS'
101:JSTOR
87:books
2617:and
2542:ISBN
2513:ISBN
2455:ISBN
2428:ISBN
2403:ISSN
2372:ISSN
2339:ISBN
2302:ISBN
2255:ISBN
2213:ISBN
2129:0.02
2126:0.55
2123:0.55
2120:0.59
2117:0.65
2114:0.65
2078:1.02
2075:2.55
2072:2.55
2069:4.59
2066:7.65
2063:7.65
2055:196
2000:1500
1997:1500
1902:0.98
1899:0.45
1896:0.45
1893:0.41
1890:0.35
1887:0.35
1851:0.98
1848:2.45
1845:2.45
1842:4.41
1839:7.35
1836:7.35
1828:204
1773:1500
1770:1500
1719:The
1705:bias
1699:The
1693:lose
1689:gain
1674:lose
1388:Reds
1293:The
1148:lose
1067:The
651:Non-
605:SNTV
194:List
151:and
139:and
73:news
2941:MMP
2566:at
2490:doi
2294:doi
2247:doi
2183:26
2106:23
2035:26
2012:200
2009:500
2006:500
2003:900
1956:25
1879:22
1808:25
1785:200
1782:500
1779:500
1776:900
1680:or
1670:for
1594:10
1174:).
1166:or
1144:for
369:el.
354:el.
343:IRV
339:el.
56:by
3201::
3182:—
2484:.
2399:22
2397:.
2393:.
2368:22
2366:.
2362:.
2321:^
2300:,
2288:,
2274:^
2253:,
2241:,
2227:^
2197:^
2157:3
1930:3
1651:.
1625::
1617:.
1568:2
1517:8
1344:.
1123:.
705:NZ
694:UK
270:US
259:UK
242:)
235:US
2596:e
2589:t
2582:v
2550:.
2521:.
2496:.
2492::
2469:.
2436:.
2409:.
2378:.
2347:.
2296::
2249::
2221:.
2180:1
2177:2
2174:2
2171:5
2168:8
2165:8
2154:0
2151:0
2148:0
2145:1
2142:1
2139:1
2103:1
2100:2
2097:2
2094:4
2091:7
2088:7
1986:F
1983:E
1980:D
1977:C
1974:B
1971:A
1953:1
1950:3
1947:3
1944:4
1941:7
1938:7
1927:1
1924:1
1921:1
1918:0
1915:0
1912:0
1876:0
1873:2
1870:2
1867:4
1864:7
1861:7
1759:F
1756:E
1753:D
1750:C
1747:B
1744:A
1684:.
1640:.
1591:0
1588:0
1585:1
1582:2
1579:2
1576:5
1565:0
1562:0
1559:0
1556:1
1553:1
1550:0
1514:0
1511:0
1508:1
1505:1
1502:1
1499:5
1322:1
1319:+
1056:e
1049:t
1042:v
707::
696::
375:)
366:(
360:)
351:(
345:)
336:(
272::
261::
237::
232:(
200:)
196:(
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
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