Knowledge (XXG)

Later-no-help criterion

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Later-No-Help can be considered not applicable to Dodgson if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Dodgson if the method is assumed to apportion possible rankings among unlisted candidates equally, as shown
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Later-No-Help can be considered not applicable to Coombs if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Coombs if the method is assumed to apportion the last place vote among unlisted candidates equally, as shown
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Checking for failures of the Later-no-help criterion requires ascertaining the probability of a voter's preferred candidate being elected before and after adding a later preference to the ballot, to determine any increase in probability. Later-no-help presumes that later preferences are added to the
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Later-No-Help can be considered not applicable to Anti-Plurality if the method is assumed to not accept truncated preference listings from the voter. On the other hand, Later-No-Help can be applied to Anti-Plurality if the method is assumed to apportion the last place vote among unlisted candidates
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The ten voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Dodgson's method fails the Later-no-help criterion when truncated ballots are considered to apportion the possible rankings amongst unlisted
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Woodall writes about Later-no-help, "... under STV the later preferences on a ballot are not even considered until the fates of all candidates of earlier preference have been decided. Thus a voter can be certain that adding extra preferences to his or her preference listing can neither help nor
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The four voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Coombs' method fails the Later-no-help criterion when truncated ballots are considered to apportion the last place vote amongst unlisted
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The four voters supporting A increase the probability of A winning by adding later preference C to their ballot, changing A from a loser to the winner. Thus, Anti-plurality fails the Later-no-help criterion when truncated ballots are considered to apportion the last place vote amongst unlisted
98:. The criterion is satisfied if, in any election, a voter giving an additional ranking or positive rating to a less-preferred candidate can not cause a more-preferred candidate to win. Voting systems that fail the later-no-help criterion are vulnerable to the 416:
Coombs' method repeatedly eliminates the candidate listed last on most ballots, until a winner is reached. If at any time a candidate wins an absolute majority of first place votes among candidates not eliminated, that candidate is elected.
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By expressing later preferences, the two voters supporting A promote their first preference A from a tie to becoming the outright winner (increasing the probability that A wins). Thus, Copeland's method fails the Later-no-help criterion.
559:: A is listed last on 4 ballots; B is listed last on 4 ballots; C is listed last on 6 ballots. C is listed last on the most ballots. C is eliminated, and B defeats A pairwise 8 to 6. B wins. A loses. 1089:
Dodgson's' method elects a Condorcet winner if there is one, and otherwise elects the candidate who can become the Condorcet winner after the fewest ordinal preference swaps on voters' ballots.
621:: A is listed last on 4 ballots; B is listed last on 6 ballots; C is listed last on 4 ballots. B is listed last on the most ballots. B is eliminated, and A defeats C pairwise 8 to 6. A wins. 1411:: There is no Condorcet winner. A is the Dodgson winner, because A becomes the Condorcet Winner with only two ordinal preference swaps (changing B > A to A > B). A wins. 1161: 1132: 489: 460: 277: 248: 1624: 1541:
any candidate already listed. Supporters of STV usually regard this as a very important property, although not everyone agrees; the property has been described (by
853:: Both A and B have two pairwise wins and one pairwise tie, so A and B are tied for the Copeland winner. Depending on the tie resolution method used, A can lose. 2074: 1842: 339:: A is listed last on 3 ballots; B is listed last on 2 ballots; C is listed last on 6 ballots. B is listed last on the least ballots. B wins. A loses. 1970: 1822: 2069: 1847: 1832: 1617: 1521:
By giving a second preference to candidate C the 28 A voters have caused their first choice to win. Note that, should the C voters decide to
393:: A is listed last on 3 ballots; B is listed last on 4 ballots; C is listed last on 4 ballots. A is listed last on the least ballots. A wins. 2196: 43: 1879: 2234: 1528:
Similar examples can be constructed for any Condorcet-compliant method, as the Condorcet and later-no-help criteria are incompatible.
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This example shows that Copeland's method violates the Later-no-help criterion. Assume four candidates A, B, C and D with 7 voters:
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Anti-plurality elects the candidate the fewest voters rank last when submitting a complete ranking of the candidates.
2084: 1807: 1797: 1658: 126: 36: 30: 2049: 1740: 141:(as plurality only applies to the top-ranked candidate). Descending Solid Coalitions also satisfies later-no-help. 2099: 2054: 2000: 1912: 47: 2089: 1975: 1933: 1852: 1777: 1713: 1671: 138: 1708: 2114: 2104: 2079: 1895: 1772: 1554: 1538: 87: 1545:, in a letter to Robert Newland) as 'quite unreasonable', and (by an anonymous referee) as 'unpalatable.'" 2155: 2094: 1957: 1900: 2059: 1980: 1745: 200: 122: 652:
Assume that the two voters supporting A (marked bold) do not express later preferences on the ballots:
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Tony Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002.
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ballot sequentially, so that candidates already listed are preferred to a candidate added later.
1718: 1062:: B now has two pairwise defeats. A still has two pairwise wins, one tie, and no defeats. Thus, 861:
Now assume the two voters supporting A (marked bold) express later preferences on their ballot.
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Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
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Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
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Now assume that the ten voters supporting A (marked bold) add later preference C, as follows:
411: 150: 2160: 1792: 1648: 1633: 1511: 1468: 1105:> B = C by apportioning the possible orderings for B and C equally. Each vote is counted 433:> B = C by apportioning the possible orderings for B and C equally. Each vote is counted 221:> B = C by apportioning the possible orderings for B and C equally. Each vote is counted 134: 107: 2208: 2124: 1965: 1943: 1755: 1676: 1666: 1644: 1573: 1542: 118: 103: 99: 95: 2023: 1728: 1688: 158: 2228: 1767: 91: 1782: 1723: 1515: 1472: 1439: 1429: 154: 130: 2165: 1928: 1867: 1787: 1683: 1577: 1938: 1874: 1597: 2175: 2170: 1995: 1857: 429:
Assume four voters (marked bold) submit a truncated preference listing
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Assume four voters (marked bold) submit a truncated preference listing
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Assume ten voters (marked bold) submit a truncated preference listing
2145: 1602: 1606: 1290:: B is the Condorcet winner and the Dodgson winner. A loses. 15: 1525:
A in response, B will beat A by 72, restoring B to victory.
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Suppose the 28 A voters specify second choice C (they are
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B is preferred to C by 42 votes to 30 votes. (Locked)
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B is preferred to A by 42 votes to 28 votes. (Cycle)
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C is preferred to B by 58 votes to 42 votes. (Locked)
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A is preferred to C by 70 votes to 30 votes. (Locked)
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B is preferred to A by 42 votes to 28 votes. (Locked)
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A is preferred to C by 70 votes to 30 votes. (Locked)
1140: 1111: 468: 439: 256: 227: 2184: 2138: 2042: 2009: 1956: 1921: 1888: 1815: 1806: 1657: 1155: 1126: 483: 454: 271: 242: 1434:For example, in an election conducted using the 1618: 1576:, Properties of Preferential Election Rules, 8: 2075:Independence of Smith-dominated alternatives 1033:Pairwise election results (won-tied-lost): 1032: 941: 912:The results would be tabulated as follows: 824:Pairwise election results (won-tied-lost): 823: 732: 703:The results would be tabulated as follows: 1812: 1625: 1611: 1603: 1141: 1139: 1112: 1110: 469: 467: 440: 438: 257: 255: 228: 226: 133:all satisfy the later-no-help criterion. 66:Learn how and when to remove this message 1348: 1300: 1227: 1165: 914: 863: 705: 654: 569: 493: 349: 281: 209:equally, as shown in the example below. 29:This article includes a list of general 2070:Independence of irrelevant alternatives 1848:Sequential proportional approval voting 1578:Voting matters - Issue 3, December 1994 1566: 106:, which can deny victory to a sincere 920: 711: 7: 177:is incompatible with later-no-help. 1880:Indirect single transferable voting 173:do not satisfy later-no-help. The 35:it lacks sufficient corresponding 14: 20: 1399: 1396: 1388: 1383: 1375: 1372: 1278: 1275: 1267: 1262: 1254: 1251: 1156:{\displaystyle {\tfrac {1}{2}}} 1127:{\displaystyle {\tfrac {1}{2}}} 1050: 1045: 1040: 1035: 1023: 1018: 1013: 1010: 1003: 996: 991: 988: 981: 976: 969: 966: 959: 954: 949: 944: 936: 933: 930: 927: 841: 836: 831: 826: 814: 809: 804: 801: 794: 787: 782: 779: 772: 767: 760: 757: 750: 745: 740: 735: 727: 724: 721: 718: 484:{\displaystyle {\tfrac {1}{2}}} 455:{\displaystyle {\tfrac {1}{2}}} 272:{\displaystyle {\tfrac {1}{2}}} 243:{\displaystyle {\tfrac {1}{2}}} 1991:Mixed ballot transferable vote 1442:the following votes are cast: 1: 2192:Comparison of voting systems 2034:Satisfaction approval voting 2019:Single non-transferable vote 1838:Proportional approval voting 1066:is elected Copeland winner. 1798:Graduated majority judgment 2251: 2050:Condorcet winner criterion 1741:First-past-the-post voting 1427: 1082: 916:Pairwise election results 707:Pairwise election results 637: 409: 198: 86:, not to be confused with 2235:Electoral system criteria 2205: 2197:Voting systems by country 2100:Mutual majority criterion 2055:Condorcet loser criterion 2001:Vote linkage mixed system 1913:Largest remainders method 1640: 857:Express later preferences 2090:Majority loser criterion 1976:Additional member system 1934:Hagenbach-Bischoff quota 1853:Single transferable vote 1778:Positional voting system 1714:Minimax Condorcet method 1672:Combined approval voting 1598:Brown v. Smallwood, 1915 1294:Adding Later Preferences 1097:Truncated Ballot Profile 563:Adding Later Preferences 425:Truncated Ballot Profile 343:Adding Later Preferences 213:Truncated Ballot Profile 94:criterion formulated by 2115:Resolvability criterion 2105:Participation criterion 2080:Later-no-harm criterion 1896:Highest averages method 1555:Later-no-harm criterion 80:later-no-help criterion 50:more precise citations. 2156:First-preference votes 2095:Monotonicity criterion 2065:Independence of clones 1768:Simple majoritarianism 1157: 1128: 1093:in the example below. 1078: 485: 456: 421:in the example below. 273: 244: 2060:Consistency criterion 1981:Alternative vote plus 1746:Instant-runoff voting 1158: 1134:A > B > C, and 1129: 648:Truncated preferences 486: 462:A > B > C, and 457: 405: 274: 250:A > B > C, and 245: 201:Anti-plurality voting 2130:Seats-to-votes ratio 1901:Webster/Sainte-Laguë 1420:candidates equally. 1138: 1109: 630:candidates equally. 466: 437: 402:candidates equally. 254: 225: 145:Noncomplying methods 2110:Plurality criterion 1709:Kemeny–Young method 1485:The votes are now: 1351: 1230: 917: 708: 181:Checking Compliance 175:Condorcet criterion 163:Kemeny-Young method 2151:Election threshold 2085:Majority criterion 1761:Supplementary vote 1471:and therefore the 1350:Pairwise Contests 1349: 1229:Pairwise Contests 1228: 1153: 1151: 1124: 1122: 915: 706: 481: 479: 452: 450: 269: 267: 240: 238: 2222: 2221: 2120:Reversal symmetry 2029:Cumulative voting 2011:Semi-proportional 1986:Mixed single vote 1952: 1951: 1828:Mixed single vote 1736:Exhaustive ballot 1699:Copeland's method 1694:Condorcet methods 1634:Electoral systems 1501: 1500: 1458: 1457: 1438:compliant method 1406: 1405: 1347: 1346: 1285: 1284: 1226: 1225: 1198:( > C > B) 1185:( > B > C) 1163:A > C > B: 1150: 1121: 1057: 1056: 910: 909: 848: 847: 701: 700: 640:Copeland's method 616: 615: 554: 553: 526:( > C > B) 513:( > B > C) 491:A > C > B: 478: 449: 388: 387: 334: 333: 314:( > C > B) 301:( > B > C) 279:A > C > B: 266: 237: 167:Copeland's method 151:Minimax Condorcet 114:Complying methods 76: 75: 68: 2242: 2161:Liquid democracy 1813: 1793:Two-round system 1704:Dodgson's method 1627: 1620: 1613: 1604: 1580: 1574:Woodall, Douglas 1571: 1512:Condorcet winner 1488: 1469:Condorcet winner 1445: 1352: 1343:C > A > B 1335:C > B > A 1327:B > A > C 1301: 1231: 1222:C > A > B 1214:C > B > A 1206:B > A > C 1166: 1162: 1160: 1159: 1154: 1152: 1143: 1133: 1131: 1130: 1125: 1123: 1114: 1085:Dodgson's method 1079:Dodgson's method 918: 898:C > D > A 864: 709: 689:C > D > A 655: 612:C > A > B 604:C > B > A 596:B > A > C 570: 550:C > A > B 542:C > B > A 534:B > A > C 494: 490: 488: 487: 482: 480: 471: 461: 459: 458: 453: 451: 442: 384:C > B > A 376:B > A > C 350: 330:C > B > A 322:B > A > C 282: 278: 276: 275: 270: 268: 259: 249: 247: 246: 241: 239: 230: 135:Plurality voting 108:Condorcet winner 102:strategy called 71: 64: 60: 57: 51: 46:this article by 37:inline citations 24: 23: 16: 2250: 2249: 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292: 291: 287: 284: 283: 280: 263: 260: 234: 231: 220: 212: 210: 206: 202: 194: 189: 187: 180: 178: 176: 172: 168: 164: 160: 156: 152: 144: 142: 140: 137:satisfies it 136: 132: 128: 124: 120: 113: 111: 109: 105: 101: 97: 93: 92:voting system 89: 85: 81: 70: 67: 59: 49: 45: 39: 38: 32: 27: 18: 17: 2213: 2207: 1823:Mixed-member 1808:Proportional 1783:Score voting 1724:Ranked pairs 1643:Part of the 1642: 1569: 1535: 1527: 1522: 1520: 1516:Ranked pairs 1510:There is no 1509: 1502: 1484: 1479: 1477: 1473:Ranked pairs 1466: 1459: 1440:Ranked pairs 1433: 1430:Ranked pairs 1424:Ranked pairs 1418: 1408: 1407: 1317: 1312: 1307:Preferences 1297: 1287: 1286: 1195: 1190: 1182: 1177: 1172:Preferences 1102: 1100: 1091: 1088: 1073: 1063: 1059: 1058: 1051: 1046: 1041: 1036: 911: 880: 875: 870:Preferences 860: 850: 849: 842: 837: 832: 827: 702: 671: 666: 661:Preferences 651: 643: 628: 618: 617: 586: 581: 576:Preferences 566: 556: 555: 523: 518: 510: 505: 500:Preferences 430: 428: 419: 415: 400: 390: 389: 366: 361: 356:Preferences 346: 336: 335: 311: 306: 298: 293: 288:Preferences 218: 216: 207: 204: 184: 155:Ranked Pairs 148: 117: 83: 79: 77: 62: 56:October 2011 53: 34: 2166:Spoilt vote 1929:Droop quota 1868:Schulze STV 1843:Rural–urban 1788:STAR voting 1684:Borda count 1494:42: B>A 1491:28: A>C 1451:42: B>A 1304:# of voters 1169:# of voters 867:# of voters 658:# of voters 573:# of voters 497:# of voters 353:# of voters 285:# of voters 48:introducing 2185:Comparison 1939:Hare quota 1889:Allocation 1875:Spare vote 1863:Hare-Clark 1833:Party-list 1561:References 1532:Commentary 1415:Conclusion 1363:Against C 1242:Against C 1070:Conclusion 625:Conclusion 397:Conclusion 31:references 2176:Unseating 2171:Sortition 1773:Plurality 1649:Economics 1467:B is the 1436:Condorcet 1360:Against B 1357:Against A 1239:Against B 1236:Against A 906:D > C 890:B > A 697:D > C 681:B > A 153:methods, 139:trivially 2229:Category 2043:Criteria 1996:Scorporo 1645:politics 1549:See also 1518:winner. 1475:winner. 634:Copeland 190:Examples 119:Approval 2215:Project 1906:D'Hondt 1858:CPO-STV 1816:Systems 1480:burying 90:) is a 44:improve 2209:Portal 2146:Ballot 1922:Quotas 1651:series 1497:30: C 1454:30: C 1448:28: A 1409:Result 1394:For C 1381:For B 1368:For A 1288:Result 1273:For C 1260:For B 1247:For A 1060:Result 851:Result 619:Result 557:Result 391:Result 337:Result 169:, and 129:, and 33:, but 2139:Other 1958:Mixed 1052:1-0-2 1047:2-0-1 1042:0-1-2 1037:2-1-0 843:0-1-2 838:0-1-2 833:2-1-0 828:2-1-0 131:score 1647:and 1539:harm 1523:bury 1482:B). 149:All 84:LNHe 82:(or 78:The 1971:MMP 1389:10 1376:20 1268:15 1255:20 88:LNH 2231:: 2212:— 1400:13 1384:12 1373:11 1324:10 1313:10 1263:12 1252:11 1203:10 1026:1 1024:3 1021:4 1019:3 1016:2 1014:5 1011:D 1006:3 1004:1 999:4 997:3 994:2 992:5 989:C 984:3 982:4 979:3 977:4 972:3 970:3 967:B 962:5 960:2 957:5 955:2 952:3 950:3 945:A 942:Y 937:D 934:C 931:B 928:A 923:X 817:1 815:1 812:2 810:3 807:2 805:5 802:D 797:1 795:1 790:2 788:3 785:2 783:5 780:C 775:3 773:2 770:3 768:2 763:3 761:3 758:B 753:5 751:2 748:5 746:2 743:3 741:3 736:A 733:Y 728:D 725:C 722:B 719:A 714:X 165:, 161:, 157:, 125:, 121:, 110:. 1626:e 1619:t 1612:v 1397:3 1340:1 1332:2 1279:8 1276:3 1219:1 1211:2 1196:A 1191:5 1183:A 1178:5 1148:2 1145:1 1119:2 1116:1 1103:A 1064:A 903:1 895:1 887:3 876:2 694:1 686:1 678:3 672:A 667:2 609:2 601:4 593:4 582:4 547:2 539:4 531:4 524:A 519:2 511:A 506:2 476:2 473:1 447:2 444:1 431:A 381:3 373:4 362:4 327:3 319:4 312:A 307:2 299:A 294:2 264:2 261:1 235:2 232:1 219:A 69:) 63:( 58:) 54:( 40:.

Index

references
inline citations
improve
introducing
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LNH
voting system
Douglas Woodall
tactical voting
mischief voting
Condorcet winner
Approval
instant-runoff
highest medians
score
Plurality voting
trivially
Minimax Condorcet
Ranked Pairs
Schulze method
Kemeny-Young method
Copeland's method
Nanson's method
Condorcet criterion
Anti-plurality voting
Coombs' method
Copeland's method
Dodgson's method
Ranked pairs
Condorcet

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