1818:. In particular if every voter knows that "A or B are the two most-likely to win" and places their "approval threshold" between the two, then the Condorcet winner, if one exists and is in the set {A,B}, will always win. These systems also satisfy the majority criterion in the weaker sense that any majority can force their candidate to win, if it so desires. (However, as the Condorcet criterion is incompatible with the participation criterion and the consistency criterion, these systems cannot satisfy these criteria in this Nash-equilibrium sense. Laslier, J.-F. (2006)
1949:
meets reversal symmetry; but if the lower one is taken, it does not, because a candidate with would beat a candidate with with or without reversal. However, for rounding methods which do not meet reversal symmetry, the chances of breaking it are on the order of the inverse of the number of voters; this is comparable with the probability of an exact tie in a two-candidate race, and when there's a tie, any method can break reversal symmetry.
21:
45:
1989:
such that it votes at least one candidate each at the top and bottom possible ratings. In this case, Range would not be independent of irrelevant alternatives. Balinski M. and R. Laraki (2007) «A theory of measuring, electing and ranking». Proceedings of the
National Academy of Sciences USA, vol. 104, no. 21, 8720-8725.
2109:
Random ballot: Uniformly random-chosen ballot determines winner. This and closely related systems are of mathematical interest because they are the only possible systems which are truly strategy-free, that is, your best vote will never depend on anything about the other voters. They also satisfy both
2045:
For up to 4 candidates, SODA is monotonic. For more than 4 candidates, it is monotonic for adding an approval, for changing from an approval to a delegation ballot, and for changes in a candidate's preferences. However, if changes in a voter's preferences are executed as changes from a delegation to
1858:
Approval and
Plurality do not allow later preferences. Technically speaking, this means that they pass the technical definition of the LNH criteria - if later preferences or ratings are impossible, then such preferences can not help or harm. However, from the perspective of a voter, these systems do
2060:
For up to 4 candidates, SODA meets the
Participation, IIA, and Cloneproof criteria. It can fail these criteria in certain rare cases with more than 4 candidates. This is considered here as a qualified success for the Consistency and Participation criteria, which do not intrinsically have to do with
1845:
Vol. 4, No. 3 (1987), pp. 185–206.) There is some disagreement about how to extend it to unranked methods, and this disagreement affects whether approval and range voting are considered independent of clones. If the definition of "clones" is that "every voter scores them within ±ε in the
35:
My first language is
English, I speak Spanish fluently (though not perfectly), and I have some understanding of French, Kaqchikel, and Tzotzil. I live in Guatemala. I feel qualified to contribute to Knowledge (XXG) (though not a true expert) in high-energy physics (standard model), neurolinguistics
2070:
SODA voting passes reversal symmetry for all scenarios that are reversible under SODA; that is, if each delegated ballot has a unique last choice. In other situations, it is not clear what it would mean to reverse the ballots, but there is always some possible interpretation under which SODA would
1988:
Range satisfies the mathematical definition of IIA, that is, if each voter scores each candidate independently of which other candidates are in the race. However, since a given range score has no agreed-upon meaning, it is thought that most voters would either "normalize" or exaggerate their vote
1948:
Majority judgment can actually pass or fail reversal symmetry depending on the rounding method used to find the median when there are even numbers of voters. For instance, in a two-candidate, two-voter race, if the ratings are converted to numbers and the two central ratings are averaged, then MJ
1938:
Balinski and Laraki, Majority
Judgment's inventors, point out that it meets a weaker criterion they call "grade consistency": if two electorates give the same rating for a candidate, then so will the combined electorate. Majority Judgment explicitly requires that ratings be expressed in a "common
1898:
Bucklin voting, with skipped and equal-rankings allowed, meets the same criteria as
Majority Judgment; in fact, Majority Judgment may be considered a form of Bucklin voting. Without allowing equal rankings, Bucklin's criteria compliance is worse; in particular, it fails Independence of Irrelevant
1939:
language", that is, that each rating have an absolute meaning. They claim that this is what makes "grade consistency" significant. MJ. Balinski M. and R. Laraki (2007) «A theory of measuring, electing and ranking». Proceedings of the
National Academy of Sciences USA, vol. 104, no. 21, 8720-8725.
2099:
Random winner: Uniformly randomly chosen candidate is winner. Arbitrary winner: some external entity, not a voter, chooses the winner. These systems are not, properly speaking, voting systems at all, but are included to show that even a horrible system can still pass some of the
1813:
In
Approval, Range, and Majority Judgment, if all voters have perfect information about each other's true preferences and use rational strategy, any Majority Condorcet or Majority winner will be strategically forced – that is, win in the unique
36:(and related), mesoamerica (mayan) history and current events, and voting systems, as well as translating and general editing. You could find out my real name if you wanted to, and I don't mind, but please don't use it here on Knowledge (XXG).
2080:
SODA voting is always polytime computable. There are some cases where the optimal strategy for a candidate assigning delegated votes may not be polytime computable; however, such cases are entirely implausible for a real-world
1967:
Majority judgment meets a related, weaker criterion: ranking an additional candidate below the median grade (rather than your own grade) of your favorite candidate, cannot harm your favorite.
1867:
rating or ranking. Thus, for approval, the practically meaningful criterion would be not "later-no-harm" but "same-no-harm" - something neither approval nor any other system satisfies.
1929:
cannot win. However, if some of the losses are not by a majority (including equal-rankings), the
Condorcet loser can, theoretically, win in MJ, although such scenarios are rare.
1791:
These criteria assume that all voters vote their true preference order. This is problematic for
Approval and Range, where various votes are consistent with the same order. See
1889:
Each prospective Kemeny-Young ordering has score equal to the sum of the pairwise entries that agree with it, and so the best ordering can be found using the pairwise matrix.
2110:
consistency and IIA, which is impossible for a deterministic ranked system. However, this system is not generally considered as a serious proposal for a practical method.
2034:
Since at the time of assigning approvals on delegated votes there is always enough information to find an optimum strategy, candidates are assumed to use such a strategy.
2126:
1426:
1217:
685:
471:
88:
81:
65:
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Ballots only are considered (In other words, voters are assumed not to have preferences that cannot be expressed by a delegated or approval vote.)
160:
75:
1979:
A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
1776:"Yes/No", in a column which covers two related criteria, signifies that the given system passes the first criterion and not the second one.
52:
2090:
Later preferences are only possible through delegation, that is, if they agree with the predeclared preferences of the favorite.
1841:
applied only to ranked voting methods. (T. Nicolaus Tideman, "Independence of clones as a criterion for voting rules",
1877:
1925:
Majority judgment passes the "majority condorcet loser" criterion; that is, a candidate who loses to all others by a
127:
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70:
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is busy and is going to be on Knowledge (XXG) in off-and-on doses, and may not respond swiftly to queries.
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Majority Judgment is summable at order KN, where K, the number of ranking categories, is set beforehand.
534:
141:
1899:
Alternatives, which for a ranked method like this variant is incompatible with the Majority Criterion.
1838:
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98:. Here's a version with SODA, for when I manage to publish in a reliable source about that method.
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Delegated votes are considered to be equivalent to voting the candidate's predeclared preferences.
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Later preferences are only possible between the two candidates who make it to the second round.
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numerous candidates, and as a qualified failure for the IIA and Cloneproof criteria, which do.
859:
748:
152:
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majority criterion (a candidate rated solo-top by a majority must win). It does not pass the
1270:
2046:
an approval ballot, such changes are not necessarily monotonic with more than 4 candidates.
1792:
223:
172:
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majority criterion, which is incompatible with Independence of Irrelevant Alternatives.
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1329:
1023:
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2120:
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95:
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not pass these criteria. Approval, in particular, encourages the voter to give the
1166:
1063:
323:
1579:
20:
1863:
ballot rating to a candidate who, in another voting system, would get a
2016:
That is, second-round votes cannot harm candidates already eliminated.
44:
1876:
The number of piles that can be summed from various precincts is
1846:
limit ε→0+", then range voting is immune to clones.
15:
1825:
No. 405 (Marseille, France: Institut D'Economie Publique).)
1754:
1658:
1558:
1462:
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1253:
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407:
303:
1787:
1785:
1820:"Strategic approval voting in a large electorate,"
1975:
1973:
82:Cast your VOTE to select next week's translation!
2025:Unless otherwise noted, for SODA's compliances:
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1807:
1805:
1803:
1801:
842:
834:
94:I did a lot of work on the following table on
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8:
1833:
1831:
1795:for compliance under various voter models.
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2127:WikiProject Mesoamerica participants
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76:JoaquĂn Torres GarcĂa/Translation
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1604:
1598:
1592:
1586:
1570:
1564:
1552:
1546:
1540:
1534:
1528:
1522:
1513:
1507:
1501:
1489:
1483:
1470:
1456:
1450:
1444:
1438:
1432:
1419:
1413:
1407:
1401:
1395:
1387:
1379:
1366:
1352:
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1340:
1334:
1324:
1318:
1312:
1306:
1300:
1294:
1286:
1274:
1261:
1247:
1241:
1235:
1229:
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1210:
1204:
1198:
1192:
1186:
1178:
1170:
1157:
1143:
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1125:
1113:
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1101:
1095:
1089:
1075:
1067:
1054:
1052:
1040:
1034:
1028:
1018:
1012:
1006:
1000:
994:
988:
980:
968:
955:
941:
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923:
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895:
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863:
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828:
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89:Nominate a good Spanish article
74:was chosen to be translated to
66:Spanish Translation of the Week
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1:
1908:Majority judgment passes the
1538:Up to 4 cand. (then crowds)
64:You showed support for the
2143:
1843:Social Choice and Welfare
50:This user is a member of
71:es:JoaquĂn Torres GarcĂa
1816:Strong Nash equilibrium
749:Majority Judgment
53:WikiProject Mesoamerica
1998:Once for each round.
1532:Up to 4 candidates
2071:pass the criterion.
1823:IDEP Working Papers
147:Participation
123:Majority Condorcet
1777:
1773:
1772:
1584:arbitrary winner
1511:Ambiguous
1430:
1221:
689:
475:
142:Consistency
60:
59:
33:
32:
2134:
2111:
2107:
2101:
2097:
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2062:
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1021:
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971:
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944:
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772:
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370:
364:
358:
352:
346:
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330:
317:
312:
306:
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294:
288:
282:
277:Ambiguous
276:
270:
264:
258:
252:
247:
243:
238:
230:
178:Resolvable
101:
47:
40:
23:
16:
2142:
2141:
2137:
2136:
2135:
2133:
2132:
2131:
2117:
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2114:
2108:
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2079:
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2044:
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2015:
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1962:
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1943:
1937:
1933:
1924:
1920:
1907:
1903:
1897:
1893:
1888:
1884:
1880:((e-1) N!) - 1.
1875:
1871:
1857:
1850:
1836:
1829:
1812:
1799:
1793:approval voting
1790:
1783:
1766:
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1734:
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1719:
1713:
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1514:
1508:
1502:
1497:
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1484:
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1463:
1457:
1451:
1445:
1439:
1433:
1420:
1414:
1408:
1402:
1396:
1388:
1380:
1367:
1359:
1353:
1347:
1341:
1335:
1325:
1319:
1313:
1307:
1301:
1295:
1287:
1282:
1275:
1262:
1254:
1248:
1242:
1236:
1230:
1224:
1211:
1205:
1199:
1193:
1187:
1179:
1171:
1158:
1150:
1144:
1138:
1132:
1126:
1120:
1114:
1108:
1102:
1096:
1090:
1085:
1079:
1076:
1068:
1055:
1047:
1041:
1035:
1029:
1019:
1013:
1007:
1001:
995:
989:
981:
976:
969:
956:
948:
942:
936:
930:
924:
914:
908:
902:
896:
890:
884:
876:
871:
864:
851:
846:
843:
835:
829:
823:
817:
811:
805:
799:
793:
787:
781:
775:
770:
764:
761:
753:
740:
732:
726:
720:
714:
709:
705:
702:
692:
679:
673:
667:
661:
655:
647:
639:
626:
618:
612:
606:
600:
594:
588:
582:
576:
570:
562:
556:
548:
540:
526:
518:
512:
506:
500:
495:
491:
488:
478:
465:
459:
453:
447:
441:
435:
429:
416:
408:
402:
396:
390:
384:
374:
368:
362:
356:
350:
344:
336:
328:
315:
310:
304:
298:
292:
286:
280:
274:
268:
262:
256:
250:
245:
239:
236:
232:Ambiguous
228:
216:
214:
209:
207:
200:
198:
196:
192:
190:
186:
180:
176:
169:
163:
157:
154:
149:
145:
138:
132:
129:
121:
114:
110:
92:
85:
79:
61:
12:
11:
5:
2140:
2138:
2130:
2129:
2119:
2118:
2113:
2112:
2102:
2092:
2083:
2073:
2063:
2048:
2038:
2036:
2035:
2032:
2029:
2018:
2009:
2000:
1991:
1981:
1969:
1960:
1951:
1941:
1931:
1918:
1901:
1891:
1882:
1869:
1848:
1827:
1797:
1780:
1779:
1771:
1770:
1764:
1759:
1753:
1747:
1741:
1729:
1723:
1717:
1711:
1705:
1699:
1693:
1687:
1681:
1675:
1674:
1668:
1663:
1657:
1651:
1645:
1633:
1627:
1621:
1615:
1609:
1603:
1597:
1591:
1585:
1576:
1575:
1569:
1563:
1557:
1551:
1545:
1539:
1533:
1527:
1521:
1512:
1506:
1500:
1488:
1482:
1476:
1475:
1469:
1461:
1455:
1449:
1443:
1437:
1431:
1418:
1412:
1406:
1400:
1394:
1386:
1378:
1372:
1371:
1365:
1357:
1351:
1345:
1339:
1333:
1323:
1317:
1311:
1305:
1299:
1293:
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1273:
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1246:
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1234:
1228:
1222:
1209:
1203:
1197:
1191:
1185:
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1169:
1163:
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1156:
1148:
1142:
1136:
1130:
1124:
1118:
1112:
1106:
1100:
1094:
1088:
1086:Strategic yes
1074:
1066:
1060:
1059:
1053:
1051:
1045:
1039:
1033:
1027:
1017:
1011:
1005:
999:
993:
987:
979:
967:
961:
960:
954:
946:
940:
939:Some variants
934:
928:
922:
912:
906:
900:
894:
888:
882:
874:
862:
856:
855:
849:
841:
833:
827:
821:
815:
809:
803:
797:
791:
785:
779:
773:
771:Strategic yes
759:
751:
745:
744:
738:
730:
724:
718:
712:
700:
690:
677:
671:
665:
659:
653:
645:
637:
631:
630:
624:
616:
610:
604:
598:
592:
586:
580:
574:
568:
560:
554:
546:
538:
531:
530:
524:
516:
510:
504:
498:
486:
476:
463:
457:
451:
445:
439:
433:
427:
421:
420:
414:
406:
400:
394:
388:
382:
372:
366:
360:
354:
348:
342:
334:
326:
320:
319:
313:
308:
302:
296:
290:
284:
278:
272:
266:
260:
254:
248:
234:
226:
220:
219:
210:
201:
193:
189:Equal rankings
187:
184:Summable
181:
173:Polytime
170:
164:
158:
155:symmetry
153:Reversal
150:
139:
136:Monotone
133:
125:
115:
107:Majority
104:
62:
58:
57:
48:
38:
31:
30:
24:
13:
10:
9:
6:
4:
3:
2:
2139:
2128:
2125:
2124:
2122:
2106:
2103:
2096:
2093:
2087:
2084:
2077:
2074:
2067:
2064:
2057:
2055:
2053:
2049:
2042:
2039:
2033:
2030:
2027:
2026:
2022:
2019:
2013:
2010:
2004:
2001:
1995:
1992:
1985:
1982:
1976:
1974:
1970:
1964:
1961:
1955:
1952:
1945:
1942:
1935:
1932:
1928:
1922:
1919:
1915:
1911:
1905:
1902:
1895:
1892:
1886:
1883:
1879:
1873:
1870:
1866:
1862:
1855:
1853:
1849:
1844:
1840:
1837:The original
1834:
1832:
1828:
1824:
1821:
1817:
1810:
1808:
1806:
1804:
1802:
1798:
1794:
1788:
1786:
1782:
1778:
1680:
1679:Random ballot
1677:
1676:
1581:
1580:Random winner
1578:
1577:
1494:Strategic yes
1481:
1478:
1477:
1468:
1428:
1393:
1385:
1377:
1374:
1373:
1364:
1331:
1292:
1280:
1272:
1271:Runoff voting
1269:
1268:
1259:
1219:
1184:
1176:
1168:
1165:
1164:
1155:
1123:Ambig.
1119:
1082:
1073:
1065:
1062:
1061:
1025:
986:
974:
966:
963:
962:
953:
920:
881:
869:
861:
858:
857:
840:
767:
758:
750:
747:
746:
737:
698:
687:
652:
644:
636:
633:
632:
623:
567:
553:
545:
536:
533:
532:
523:
484:
473:
426:
423:
422:
413:
380:
341:
333:
325:
322:
321:
283:Ambig.
279:
273:
246:Strategic yes
242:
233:
227:
225:
222:
221:
218:
211:
208:Later-no-help
205:
204:Later-no-harm
194:
188:
185:
182:
179:
174:
171:
168:
165:
162:
159:
156:
151:
148:
143:
140:
137:
134:
131:
126:
124:
119:
116:
113:
108:
105:
103:
102:
99:
97:
96:voting system
91:
90:
86:
84:
83:
77:
73:
72:
67:
55:
54:
49:
46:
42:
41:
37:
28:
25:
22:
18:
17:
2105:
2095:
2086:
2076:
2066:
2041:
2021:
2012:
2003:
1994:
1984:
1963:
1954:
1944:
1934:
1926:
1921:
1913:
1909:
1904:
1894:
1885:
1872:
1864:
1860:
1842:
1822:
1774:
1167:Ranked pairs
1064:Range voting
635:Kemeny-Young
603:O(N!)
212:
122:
93:
87:
80:
69:
68:. This week
63:
51:
34:
26:
1480:SODA voting
1344:O(N)
820:O(N)
717:O(N)
324:Borda count
167:Cloneproof
2100:criteria.
2081:election.
965:Plurality
118:Condorcet
2121:Category
1927:majority
1562:Limited
1330:spoilers
1024:spoilers
919:spoilers
483:crowding
425:Copeland
224:Approval
217:betrayal
215:favorite
1376:Schulze
1084:/
860:Minimax
769:/
697:teaming
379:teaming
244:/
206:/
199:allowed
191:allowed
1914:ranked
213:FBC:No
27:Homunq
1910:rated
1878:floor
1865:later
1746:O(N)
1650:O(1)
1550:O(N)
1544:Yes
1526:Yes
1448:O(N)
1425:(but
1239:O(N)
1216:(but
1135:O(N)
1038:O(N)
933:O(N)
684:(but
537:(AV)
503:O(N)
470:(but
393:O(N)
295:O(N)
197:prefs
195:Later
130:loser
128:Cond.
1861:same
1769:Yes
1728:Yes
1722:Yes
1716:Yes
1710:Yes
1704:Yes
1673:Yes
1626:Yes
1620:Yes
1574:Yes
1568:Yes
1556:Yes
1505:Yes
1487:Yes
1460:Yes
1454:Yes
1442:Yes
1436:Yes
1427:ISDA
1417:Yes
1405:Yes
1399:Yes
1338:Yes
1328:No (
1298:Yes
1251:Yes
1245:Yes
1233:Yes
1227:Yes
1218:ISDA
1208:Yes
1196:Yes
1190:Yes
1161:Yes
1147:Yes
1141:Yes
1129:Yes
1117:Yes
1111:Yes
1105:Yes
1099:Yes
1032:Yes
1022:No (
1004:Yes
998:Yes
945:Yes
927:Yes
917:No (
893:Yes
854:Yes
832:Yes
826:Yes
814:Yes
808:Yes
802:Yes
784:Yes
729:Yes
723:Yes
695:No (
686:ISDA
676:Yes
664:Yes
658:Yes
615:Yes
597:Yes
591:Yes
559:Yes
515:Yes
509:Yes
481:No (
472:ISDA
462:Yes
450:Yes
444:Yes
438:Yes
432:Yes
405:Yes
387:Yes
377:No (
365:Yes
359:Yes
353:Yes
347:Yes
318:Yes
301:Yes
289:Yes
271:Yes
265:Yes
259:Yes
1758:No
1752:No
1735:Yes
1698:No
1692:No
1686:No
1662:No
1656:No
1639:Yes
1632:NA
1614:No
1608:NA
1602:No
1596:No
1590:No
1518:Yes
1498:yes
1474:No
1423:No
1411:No
1392:Yes
1384:Yes
1370:No
1363:Yes
1356:No
1350:No
1322:No
1316:No
1310:No
1304:No
1279:Yes
1265:No
1214:No
1202:No
1183:Yes
1175:Yes
1093:No
1058:No
1050:No
1044:No
1016:No
1010:No
992:No
973:Yes
959:No
911:No
905:No
899:No
887:No
880:Yes
868:Yes
847:Yes
796:No
790:No
778:No
757:Yes
743:No
710:Yes
682:No
670:No
651:Yes
643:Yes
629:No
622:Yes
609:No
585:No
579:No
573:No
544:Yes
535:IRV
529:No
492:Yes
468:No
456:No
419:No
399:No
371:No
307:No
253:No
161:IIA
112:MMC
2123::
2051:^
1972:^
1851:^
1830:^
1800:^
1784:^
1739:No
1643:No
1467:No
1332:)
1291:No
1283:No
1258:No
1154:No
1081:No
1072:No
1026:)
985:No
977:No
952:No
921:)
872:No
839:No
766:No
736:No
706:No
699:)
566:No
552:No
522:No
496:No
485:)
412:No
381:)
340:No
332:No
241:No
78:.
1767:1
1762:5
1756:5
1750:5
1744:1
1737:/
1732:3
1726:1
1720:1
1714:1
1708:1
1702:1
1696:5
1690:5
1684:5
1671:1
1666:5
1660:5
1654:5
1648:0
1641:/
1636:3
1630:5
1624:1
1618:1
1612:5
1606:5
1600:5
1594:5
1588:5
1582:/
1572:1
1566:3
1560:4
1554:1
1548:1
1542:1
1536:4
1530:4
1524:1
1515:2
1509:2
1503:1
1496:/
1491:2
1485:1
1472:5
1464:5
1458:1
1452:1
1446:2
1440:1
1434:1
1429:)
1421:4
1415:1
1409:5
1403:1
1397:1
1389:1
1381:1
1368:5
1360:2
1354:4
1348:5
1342:2
1336:1
1326:5
1320:5
1314:5
1308:5
1302:5
1296:1
1288:5
1281:/
1276:2
1263:5
1255:5
1249:1
1243:1
1237:2
1231:1
1225:1
1220:)
1212:4
1206:1
1200:5
1194:1
1188:1
1180:1
1172:1
1159:1
1151:5
1145:1
1139:1
1133:1
1127:1
1121:3
1115:2
1109:1
1103:2
1097:1
1091:5
1077:4
1069:5
1056:5
1048:5
1042:5
1036:1
1030:1
1020:5
1014:5
1008:5
1002:1
996:1
990:5
982:5
975:/
970:2
957:5
949:4
943:1
937:3
931:2
925:1
915:5
909:5
903:5
897:5
891:1
885:5
877:2
870:/
865:2
852:1
844:1
836:3
830:1
824:1
818:1
812:1
806:1
800:2
794:4
788:4
782:1
776:4
762:4
754:1
741:5
733:5
727:1
721:1
715:2
708:/
703:3
693:5
688:)
680:4
674:1
668:5
662:1
656:1
648:1
640:1
627:5
619:1
613:1
607:5
601:5
595:1
589:1
583:5
577:5
571:5
563:5
557:1
549:5
541:1
527:5
519:5
513:1
507:1
501:2
494:/
489:3
479:5
474:)
466:4
460:1
454:5
448:1
442:1
436:1
430:1
417:5
409:5
403:1
397:5
391:1
385:1
375:5
369:5
363:1
357:1
351:1
345:1
337:5
329:5
316:1
311:4
305:5
299:1
293:1
287:1
281:3
275:3
269:1
263:2
257:1
251:5
237:4
229:3
175:/
144:/
120:/
109:/
56:.
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