920:
55:
895:
907:
1316:, also known as the Jefferson method sometimes violates the quota rule by allocating more seats than the upper frame allowed. Since Jefferson was the first method used for Congressional apportionment in the United States, this violation led to a substantial problem where larger states often received more representatives than smaller states, which was not corrected until
1300:
Different methods for allocating seats may or may not satisfy the quota rule. While many methods do violate the quota rule, it is sometimes preferable to violate the rule very rarely than to violate some other apportionment paradox; some sophisticated methods violate the rule so rarely that it has
1087:
while the upper frame is the entitlement rounded up. The frame rule states that the only two allocations that a party can receive should be either the lower or upper frame. If at any time an allocation gives a party a greater or lesser number of seats than the upper or lower frame, that allocation
1308:
does satisfy the quota rule. The method works by assigning each party its seat quota, rounded down. Then, the surplus seats are given to the party with the largest fractional part, until there are no more surplus seats. Because it is impossible to give more than one surplus seat to a party, every
1078:
1241:, which means its allocated seats should be either 0 or 1. In all cases, the method for actually allocating the seats determines whether an allocation violates the quota rule, which in this case would mean giving party
995:. For example, if a party receives 10.56% of the vote, and there are 100 seats in a parliament, the quota rule says that when all seats are allotted, the party may get either 10 or 11 seats. The most common
1367:
1239:
1196:
1141:
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1336:
The entitlement for a party is sometimes called their seat quota, leading to the term "quota rule"; such seat quotas should not be confused with the unrelated concept of an
1029:
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is 1, because 1.8 rounded down equal 1. The upper frame, 1.8 rounded up, is 2. Therefore, the quota rule states that the only two allocations allowed for party
1364:
991:, is calculated by multiplying each party's share of the vote by the total number of seats. Equivalently, it is equal to the number of votes divided by the
639:
1301:
not ever happened in a real apportionment, while some methods that never violate the quota rule violate other paradoxes in much more serious fashions.
671:
533:
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1400:
941:
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1445:
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1524:
1496:
934:
1519:
1425:
835:
825:
575:
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486:
557:
82:
1320:
was implemented in 1842. Although
Webster's method can in theory violate the quota rule, such occurrences are extremely rare.
620:
1205:
1162:
1107:
262:
247:
232:
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498:
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984:
977:
310:
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133:
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185:
118:
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332:
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327:
1281:. The theorem itself is broken up into several different proofs that cover a wide number of circumstances.
1317:
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proved in 1980 that if an apportionment method satisfies the quota rule, it must fail to satisfy some
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251:
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Any method that is free of the population paradox must fail the quota rule for some circumstances.
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1088:(and by extension, the method used to allocate it) is said to be in violation of the quota rule.
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190:
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1073:{\displaystyle {\frac {{\text{Votes}}_{\text{party}}}{\#{\text{Votes}}}}\cdot \#{\text{Seats}}}
1313:
966:
830:
800:
722:
659:
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220:
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178:
46:
911:
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759:
747:
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34:
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methods. It says that the number of seats allocated to a party should be equal to their
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If there are 5 available seats in the council of a club with 300 members, and party
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The entitlement for a party (the number of seats the party would ideally get) is:
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1365:"Apportioning Representatives in the United States Congress - The Quota Rule"
1008:
364:
359:
1284:
Specifically, there are two main statements that apply to the quota rule:
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615:
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Any method that follows the quota rule must fail the population paradox.
1003:) violate the quota rule in situations where upholding it would cause a
1084:
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plus or minus one. The ideal number of seats for a party, called their
401:
1083:
The lower frame is then the entitlement rounded down to the nearest
1198:, rounded up and down equals either 2 or 3 seats. Finally, a party
1202:
with the remaining 57 members of the club has a entitlement of
1155:, that has 137 members, then the quota rule states that party
1151:
are 1 or 2 seats on the council. If there is a second party,
53:
1309:
party will always be equal to its lower or upper frame.
1208:
1165:
1110:
1032:
1234:{\displaystyle {\frac {57}{300}}\cdot 5\approx 0.95}
1191:{\displaystyle {\frac {137}{300}}\cdot 5\approx 2.3}
1136:{\displaystyle {\frac {106}{300}}\cdot 5\approx 1.8}
1233:
1190:
1135:
1072:
1100:has 106 members, then the entitlement for party
1374:. MAA Publications. Retrieved October 22, 2018
942:
8:
1417:
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1273:satisfies the quota rule, it violates the
1245:any seats other than 1 or 2, giving party
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1249:any other than 2 or 3, or giving party
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1421:M.L. Balinski and H.P. Young. (1980).
1359:
1357:
7:
1257:Relation to apportionment paradoxes
1062:
1048:
16:Rule in math and political science
14:
1398:Impossibilities of Apportionment
976:describes a desired property of
918:
905:
893:
841:McKelvey–Schofield chaos theorem
487:Semi-proportional representation
119:First preference plurality (FPP)
879:Harsanyi's utilitarian theorem
836:Moulin's impossibility theorem
801:Conflicting majorities paradox
1:
1423:"The Theory of Apportionment"
1396:Beth-Allyn Osikiewicz, Ph.D.
705:Frustrated majorities paradox
1296:Use in apportionment methods
1253:any other than 0 or 1 seat.
1143:. The lower frame for party
874:Condorcet dominance theorems
814:Social and collective choice
1503:Retrieved October 23, 2018.
1483:Retrieved October 22, 2018.
1464:Retrieved October 22, 2018.
1452:. Retrieved October 22 2018
1432:. Retrieved October 23 2018
1407:Retrieved October 23, 2018.
540:By mechanism of combination
311:Proportional representation
1541:
1387:Retrieved December 9, 2018
738:Multiple districts paradox
469:Fractional approval voting
457:Interactive representation
18:
1525:Electoral system criteria
1494:Apportionment. Lecture 4.
1269:. For instance, although
1011:apportionment rules like
685:Paradoxes and pathologies
534:Mixed-member proportional
529:Mixed-member majoritarian
524:By results of combination
415:Approval-based committees
1520:Apportionment (politics)
1306:largest remainder method
1271:largest remainder method
1001:highest averages methods
864:Condorcet's jury theorem
665:Double simultaneous vote
640:Rural–urban proportional
635:Dual-member proportional
597:
586:
553:Parallel (superposition)
445:Fractional social choice
432:Expanding approvals rule
261:
246:
231:
162:
151:
127:
19:Not to be confused with
1492:Ghidewon Abay Asmerom.
791:Tyranny of the majority
568:Fusion (majority bonus)
385:Quota-remainder methods
1363:Michael J. Caulfield.
1263:Balinski–Young theorem
1235:
1192:
1137:
1074:
925:Mathematics portal
831:Majority impossibility
820:Impossibility theorems
616:Negative vote transfer
437:Method of equal shares
58:
1385:Apportionment Methods
1267:apportionment paradox
1236:
1193:
1138:
1075:
997:apportionment methods
728:Best-is-worst paradox
717:Pathological response
452:Direct representation
105:Single-winner methods
57:
1206:
1163:
1108:
1030:
912:Economics portal
859:Median voter theorem
78:Comparative politics
1015:do so only rarely.
900:Politics portal
611:Vote linkage system
582:Seat linkage system
169:Ranked-choice (RCV)
1499:2020-09-27 at the
1479:2021-01-20 at the
1474:Jefferson’s Method
1448:2018-09-20 at the
1428:2024-07-31 at the
1403:2020-09-29 at the
1370:2019-05-22 at the
1279:population paradox
1231:
1188:
1133:
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1005:population paradox
796:Discursive dilemma
755:Lesser evil voting
630:Supermixed systems
333:Largest remainders
191:Round-robin voting
59:
1462:"Apportionment 2"
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1174:
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967:political science
959:
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846:Gibbard's theorem
786:Dominance paradox
723:Perverse response
427:Phragmen's method
293:Majority judgment
221:Positional voting
179:Condorcet methods
47:electoral systems
1532:
1504:
1490:
1484:
1471:
1465:
1459:
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1441:Hilary Freeman.
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853:Positive results
748:Strategic voting
645:Majority jackpot
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462:Liquid democracy
338:National remnant
328:Highest averages
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158:Alternative vote
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140:Partisan primary
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1501:Wayback Machine
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1443:"Apportionment"
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779:majority rule
777:Paradoxes of
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479:Random ballot
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43:Social choice
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370:List-free PR
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206:Ranked pairs
177:
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109:
1019:Mathematics
1007:, although
985:entitlement
963:mathematics
660:Single vote
563:Conditional
558:Coexistence
407:Quota Borda
397:Schulze STV
355:Closed list
298:STAR voting
243:Borda count
1514:Categories
1348:References
993:Hare quota
765:Truncation
494:Cumulative
317:Party-list
92:By country
83:Comparison
1226:≈
1220:⋅
1183:≈
1177:⋅
1128:≈
1122:⋅
1063:#
1060:⋅
1049:#
672:Dual-vote
365:Panachage
360:Open list
350:List type
228:Plurality
124:Two-round
112:plurality
35:Economics
1497:Archived
1477:Archived
1446:Archived
1426:Archived
1401:Archived
1368:Archived
1277:and the
1009:unbiased
392:Hare STV
31:Politics
29:A joint
1092:Example
1085:integer
402:CPO-STV
252:Baldwin
201:Schulze
196:Minimax
114:methods
969:, the
267:Coombs
37:series
1324:Notes
1159:gets
1067:Seats
1053:Votes
1043:party
1038:Votes
999:(the
971:quota
604:'MMP'
593:'AMS'
1312:The
1304:The
1261:The
1229:0.95
974:rule
965:and
545:Non-
499:SNTV
88:List
45:and
33:and
1215:300
1186:2.3
1172:300
1169:137
1131:1.8
1117:300
1114:106
1104:is
961:In
263:el.
248:el.
237:IRV
233:el.
1516::
1412:^
1356:^
1212:57
599:NZ
588:UK
164:US
153:UK
136:)
129:US
1340:.
1251:C
1247:B
1243:A
1223:5
1200:C
1180:5
1157:B
1153:B
1149:A
1145:A
1125:5
1102:A
1098:A
950:e
943:t
936:v
601::
590::
269:)
260:(
254:)
245:(
239:)
230:(
166::
155::
131::
126:(
94:)
90:(
23:.
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