22:
1092:
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
420:
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
185:
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
208:
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
1419:
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
1536:
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
629:
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
401:
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.
1074:
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.
1593:
1610:
644:
This example shows that
Copeland's method violates the Later-no-help criterion. Assume four candidates A, B, C and D with 7 voters:
65:
2214:
2064:
2010:
1862:
2191:
1990:
2033:
2018:
1837:
205:
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:
2129:
1698:
1592:
Tony
Anderson Solgard and Paul Landskroener, Bench and Bar of Minnesota, Vol 59, No 9, October 2002.
1137:
1108:
639:
465:
436:
253:
224:
166:
2109:
1703:
1435:
1084:
174:
162:
2150:
1760:
186:
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.
170:
567:
Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
347:
Now assume that the four voters supporting A (marked bold) add later preference C, as follows:
2119:
2028:
1985:
1905:
1827:
1750:
1735:
1693:
1298:
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
217:
Assume four voters (marked bold) submit a truncated preference listing
1101:
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.
1487:
1444:
1478:
Suppose the 28 A voters specify second choice C (they are
922:
713:
1464:
B is preferred to C by 42 votes to 30 votes. (Locked)
1142:
1113:
470:
441:
258:
229:
1507:
B is preferred to A by 42 votes to 28 votes. (Cycle)
1505:
C is preferred to B by 58 votes to 42 votes. (Locked)
1503:
A is preferred to C by 70 votes to 30 votes. (Locked)
1462:
B is preferred to A by 42 votes to 28 votes. (Locked)
1460:
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:
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1023:
1018:
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1003:
996:
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988:
981:
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954:
949:
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927:
841:
836:
831:
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782:
779:
772:
767:
760:
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745:
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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:
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2201:
2180:
2134:
2125:Smith criterion
2038:
2005:
1966:Parallel voting
1948:
1944:Imperiali quota
1917:
1884:
1802:
1756:Contingent vote
1719:Nanson's method
1677:Unified primary
1667:Approval voting
1653:
1636:
1631:
1589:
1587:Further reading
1584:
1583:
1572:
1568:
1563:
1551:
1543:Michael Dummett
1534:
1506:
1504:
1463:
1461:
1432:
1426:
1417:
1318:A > C > B
1296:
1136:
1135:
1107:
1106:
1099:
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1081:
1072:
1025:
1020:
1015:
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993:
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971:
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951:
881:A > C > D
859:
816:
811:
806:
796:
789:
784:
774:
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762:
752:
747:
742:
650:
642:
636:
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587:A > C > B
565:
464:
463:
435:
434:
427:
414:
408:
399:
367:A > C > B
345:
252:
251:
223:
222:
215:
203:
197:
192:
183:
171:Nanson's method
147:
127:highest medians
116:
104:mischief voting
100:tactical voting
96:Douglas Woodall
72:
61:
55:
52:
42:Please help to
41:
25:
21:
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2024:Limited voting
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1751:Coombs' method
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1729:Schulze method
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410:Main article:
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199:Main article:
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159:Schulze method
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123:instant-runoff
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1659:Single-winner
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1514:and A is the
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137:satisfies it
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92:voting system
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27:
18:
17:
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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:
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1317:
1312:
1307:Preferences
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1172:Preferences
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870:Preferences
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661:Preferences
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643:
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576:Preferences
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500:Preferences
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356:Preferences
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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:.
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