1158:, the same principles are followed, with the following differences: only parties that have received more than 3 percent of the vote in the county are able to participate in the distribution of seats. There is no 12 percent clause or other possibility for parties that fall below this threshold to gain seats. Finally, the number of adjustment seats is one tenth of the number of seats in the county council. If one tenth is a fractional number (which it always is, since the number of seats in a county council is required to be odd), the fraction is always adjusted upwards, so a county council with 51 seats would have 45 fixed seats and 6 adjustment seats.
913:
48:
888:
900:
1255:
shows a party with "too many" seats. In 2009, the first ideal distribution showed that the Labour Party should have 63 seats overall, but they had already won 64. Those seats were taken out of consideration, and so another ideal distribution of the remaining 103 seats was made between the
Progress Party, the Conservative Party, the Christian Democrats, the Centre Party and the Socialist Left Party.
1146:
seat. If a party is yet to receive a seat in the district, its quotient simply is the number of votes it received. When the fixed seats were distributed among the parties in the district, this number was divided by 1.4, which made it harder for a party to achieve its first seat. Now, however, no such division takes place. The method used is thus pure and not modified Sainte-Laguë.
1055:(which are not treated as an integral part of the Danish election system). The leveling seats are supplementary to the normal seats which are allocated by proportional votes within each county. All parties which achieve at least 2% of the national votes are granted as many leveling seats as required to achieve proportional representation at the national level.
1126:
have been awarded fixed seats in districts where they have had more than 12 percent of the vote are disregarded, and their seats are subtracted from the calculation. If a party has received 2 seats in this fashion, for example, the calculation will be made with 347 seats. Again the modified Sainte-Laguë method is used.
1254:
If a party already has won more seats than the ideal distribution indicates, the party keeps those seats, but will not win any leveling seats. In that case, another ideal distribution is made between the parties still eligible for leveling seats, this may be repeated if the revised distribution again
1125:
In the second stage, the 349 seats are distributed through a calculation based on the total number of votes summed up across the entire country. In this distribution only parties that have received more than 4 percent of the national vote are included. Parties that fall below 4 percent nationally but
1197:
The remaining 19 representatives are allocated one to each county but are elected based on nationwide results for a party, as long as the popular vote at the national level for that party exceeds the exclusion threshold of 4%. The result is that each representative represents an approximately equal
1250:
for the eligible parties. If a party that did not reach the electoral threshold won seats anyway, the party keeps those seats and the number of seats to distribute is reduced accordingly. In 2009 the
Liberal party failed to reach the threshold but won two seats. Therefore, only 167 seats were taken
1279:
The first leveling seat goes to the county and party corresponding to the highest fraction in the table. The second leveling seat goes to county and party corresponding the next highest fraction in the table, and so on. Each time a leveling seat has been determined, the remaining fractions for the
1271:
For each county and eligible party, determine the first unused quotient when the regular district seats were distributed. If the party has not yet won a seat from that county, the quotient is equal to the number of votes the party received there. If the party already has won one mandate from that
1145:
is the number of seats it has been awarded. The district where the party has the highest quotient is awarded an adjustment seat, and a new quotient is then calculated for that district, before the next adjustment seat is distributed. In theory, a district can thus receive more than one adjustment
1129:
In the third stage, a summary is made of the fixed seats that the parties have achieved, and this is compared to the outcome of the nationwide distribution above. If a party has received more fixed seats than its share of the total 349-seat distribution, district seats allocated to that party are
1042:
In 1915, Denmark became one of the first countries in the world to introduce leveling seats in their parliamentary elections. Since then, all parliamentary elections in
Denmark have allocated these adjustment seats as a substantial fraction of the seats in the parliament. The parliamentary seats
1297:
In the 2009 election, a programming fault in the software calculating the allocation prognosis for one county made their leveling seat go to another party. That changed the outcome in two other counties, and it took over a week and a recount until the distribution of leveling seats was finally
1289:
The method for assigning leveling seats usually results in the first leveling seats being given to candidates that did fairly well in the county. However, the last leveling seats may be awarded to candidates that received few votes in the county that they will represent. (In theory it is even
1280:
county that gave its leveling seat are taken out of consideration. Once a party has received all the leveling seats that it is entitled to, the remaining fractions for that party are also taken out of consideration. This process continues until all 19 leveling seats have been distributed.
1290:
possible for a party to receive a leveling seat in a county where they received no votes, or even in a county where they did not field any candidates, a scenario that the election law has no contingency for.) An illustration of this came in 2005 when
1275:
The quotients for each county and party are divided by the total number of votes for all parties in that county and multiplied by the number of regular non-leveling seats allocated to that county. This leaves a table of fractions for each county and
1182:
In order to be eligible for leveling seats, a party must get at least 4% (the exclusion threshold) of the national popular vote. A party may attain enough votes in a given county to elect a representative but may fail to be eligible for leveling
1122:) with the first divisor adjusted to 1.2 (1.4 in elections before 2018). Only parties that have received at least 4 percent of the vote nationally or 12 percent of the vote within the district can participate in this distribution of seats.
1130:
retracted and given to the party with the second 'highest quotient'. The parties are then awarded a number of adjustment seats sufficient to cover the gap between their number of fixed seats and their share in the nationwide distribution.
1030:. Leveling seats are seats of additional members elected to supplement the members directly elected by each constituency. The purpose of these additional seats is to ensure that each party's share of the total seats is roughly
1193:
Of 169 representatives, 150 are elected by popular vote within the county. This means that a party that achieves 40% of the popular vote in a county will send about 40% of the total number of representatives from that
1258:
Once a final ideal distribution has been settled, the number of leveling seats awarded to each party is equal to that party's ideal number of seats minus the number of seats already won from each county.
991:
1272:
seat, the quotient is the number of votes received in that county divided by 3, if the party has already won two seats from the county, the quotient is the number of votes divided by 5, and so on.
1133:
Finally, the adjustment seats that each party has received are distributed among the districts. The application of the Sainte-Laguë number gives each party a quotient ('comparison number',
871:
1079:, for parties having qualified with a total share of votes above a 4%-limit in parliamentary elections and 3%-limit in county council elections. Sweden did not use leveling seats for
1237:
The allocation of leveling seats is a fairly complex process. First the leveling seats are distributed among the parties. The second part is distributing them among the counties.
555:
1294:
of the
Liberal Party received the last leveling seat, in Finnmark, with 826 votes. Thus, the Liberal party gained 20% of Finnmark's seats with about 2% of the vote there.
574:
1083:
elections prior to 2018. With the new election law (effective from the election 2018), leveling seats are used in municipalities with more than one electoral district.
1314:
which demanded a reform of the electoral law for proportional representation, Germany added a provision to create national leveling seats as needed in a case of
941:
778:
1186:
The number of representatives elected per county is a function of the total population in the county and the area of the county. Hence, the county of
1561:
1372:
632:
1202:
In the 2005 elections, the average number of votes on a national level was largely similar across party lines. The largest party, the
1341:
664:
526:
521:
934:
627:
309:
1171:
1167:
1207:
833:
84:
1090:, 310 are fixed seats and 39 are adjustment seats. The 310 fixed seats are distributed among the 29 electoral districts (
927:
828:
1360:
1319:
818:
568:
539:
479:
1063:
Leveling seats have been a part of the election procedures for all
Icelandic parliamentary elections since 1934.
550:
75:
1229:
The arrangement has gone through several adjustments through the years and is the result of legislative action.
1522:
613:
1115:
677:
1556:
1510:
1223:
255:
240:
225:
1399:"Apportionment of Seats to Althingi, the Icelandic Parliament: Analysis of the Elections 2003 + 2007 + 2009"
1551:
1546:
1336:
1311:
1267:
To determine the county that each party will receive its leveling seats in, the following process is done:
491:
414:
335:
1206:, required the fewest votes per representative with 14,139; the party that needed the most votes was the
1031:
856:
303:
285:
126:
1398:
747:
730:
697:
461:
449:
419:
220:
178:
111:
1155:
1076:
603:
596:
80:
1331:
1114:
In the first stage, the fixed seats are distributed within each district according to the modified
1099:
1080:
657:
585:
437:
424:
407:
384:
362:
325:
315:
866:
1190:
needs fewer votes to elect a representative (7,409 in 2005) than Oslo (18,167 the same election).
783:
637:
320:
752:
1203:
812:
692:
622:
429:
1322:, in addition to the traditional leveling seats that already existed in many state elections.
1247:
1426:
720:
560:
444:
250:
229:
161:
139:
1489:
1315:
1023:
851:
838:
806:
70:
8:
757:
591:
244:
982:
974:
917:
788:
399:
183:
1210:, with 16,262. On a county by county basis, however, there were greater disparities:
1299:
912:
823:
793:
715:
652:
486:
213:
188:
171:
39:
1443:
1215:
1211:
1091:
1007:
966:
904:
861:
740:
454:
330:
156:
150:
132:
121:
116:
104:
65:
27:
1291:
1106:. The distribution of seats between the parties then takes place in four stages.
995:
958:
892:
725:
580:
545:
466:
377:
280:
203:
145:
23:
1044:
762:
702:
687:
498:
367:
342:
193:
1137:) in each district, which is its number of votes in the district divided by (2
1540:
1048:
1043:
currently comprise 135 county seats and 40 leveling seats, with a further 4 "
771:
471:
259:
97:
60:
35:
1246:
A nationwide "ideal" distribution of all 169 seats is calculated using the
1018:
also introduced national leveling seats for their national parliament, the
511:
275:
268:
198:
47:
1071:
Since 1970, Sweden has used leveling seats in its elections for both the
389:
347:
290:
235:
887:
1103:
1466:
1052:
1019:
357:
352:
1526:
1422:
1219:
1187:
608:
1087:
1072:
1015:
1011:
394:
1047:
seats" elected separately by proportional representation in the
1175:
899:
1034:
to the party's overall shares of votes at the national level.
1214:
needed only 3,503 votes to elect one representative from the
1006:, are an election mechanism employed for many years by all
1404:. The National Electoral Commission of Iceland. April 2010
1178:. Its current form is based on the following principles:
1014:) in elections for their national legislatures. In 2013,
1222:needed 22,555 to elect one representative from the
1026:removed the leveling seats, and replaced them with
1538:
1523:"Bundestag: Deutschland hat ein neues Wahlrecht"
1166:Leveling seats were introduced in Norway in the
16:Tool used to make legislatures more proportional
1361:Germany passes law to shrink its XXL parliament
1232:
1174:, there are 19 leveling mandates, one for each
1310:In February 2013, following a decision of the
935:
1262:
1240:
1109:
942:
928:
1342:Mixed-member proportional representation
1251:into account for the ideal distribution.
1379:(in Danish). Gyldendal. 2 February 2009
1562:Party-list proportional representation
1539:
1464:
1149:
1487:
1170:when there were 8 such seats. Since
1490:"Slik fungerer utjevningsmandatene"
1024:electoral reform in Germany in 2023
13:
46:
14:
1573:
1488:Sved, Børge (9 September 2009).
1320:mixed member proportional system
1284:
911:
898:
886:
834:McKelvey–Schofield chaos theorem
480:Semi-proportional representation
112:First preference plurality (FPP)
1515:
1504:
1481:
1458:
1436:
1416:
1391:
1365:
1354:
872:Harsanyi's utilitarian theorem
829:Moulin's impossibility theorem
794:Conflicting majorities paradox
1:
1511:No counting error in Rogaland
1492:(in Norwegian). Adresseavisen
1347:
698:Frustrated majorities paradox
1377:Den Store Danske Encyklopædi
1337:Biproportional apportionment
1312:Federal Constitutional Court
1233:Allocation of leveling seats
867:Condorcet dominance theorems
807:Social and collective choice
7:
1325:
1168:1989 parliamentary election
533:By mechanism of combination
304:Proportional representation
10:
1578:
1467:"Den norske valgordningen"
1444:"Den norske valgordningen"
1430:, retrieved 13 April 2013
1305:
1058:
1037:
1002:), commonly known also as
731:Multiple districts paradox
462:Fractional approval voting
450:Interactive representation
1263:Allocating among counties
1161:
1066:
678:Paradoxes and pathologies
527:Mixed-member proportional
522:Mixed-member majoritarian
517:By results of combination
408:Approval-based committees
1332:Additional Member System
1241:Allocation among parties
1110:Leveling seat allocation
1100:largest remainder method
1086:Of the 349 seats in the
857:Condorcet's jury theorem
658:Double simultaneous vote
633:Rural–urban proportional
628:Dual-member proportional
590:
579:
546:Parallel (superposition)
438:Fractional social choice
425:Expanding approvals rule
254:
239:
224:
155:
144:
120:
1120:jämkade uddatalsmetoden
784:Tyranny of the majority
561:Fusion (majority bonus)
378:Quota-remainder methods
1204:Norwegian Labour Party
1095:
999:
986:
978:
970:
962:
918:Mathematics portal
824:Majority impossibility
813:Impossibility theorems
609:Negative vote transfer
430:Method of equal shares
51:
1427:Store norske leksikon
721:Best-is-worst paradox
710:Pathological response
445:Direct representation
98:Single-winner methods
50:
1557:Elections in Denmark
1316:negative vote weight
1302:got the final seat.
1224:Socialist Left Party
1154:In elections to the
905:Economics portal
852:Median voter theorem
71:Comparative politics
1552:Elections in Sweden
1547:Elections in Norway
1248:Sainte-Laguë method
1208:Christian Democrats
1116:Sainte-Laguë method
1098:) according to the
1028:Zweitstimmendeckung
893:Politics portal
604:Vote linkage system
575:Seat linkage system
162:Ranked-choice (RCV)
1465:Seierstad, Taral.
1423:utjevningsmandater
1150:In local elections
1010:countries (except
979:utjevningsmandater
789:Discursive dilemma
748:Lesser evil voting
623:Supermixed systems
326:Largest remainders
184:Round-robin voting
52:
1373:"Tillægsmandater"
1318:occurring in its
1300:Mette Hanekamhaug
1198:number of voters.
952:
951:
839:Gibbard's theorem
779:Dominance paradox
716:Perverse response
420:Phragmen's method
286:Majority judgment
214:Positional voting
172:Condorcet methods
40:electoral systems
1569:
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1519:
1513:
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1403:
1395:
1389:
1388:
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1384:
1369:
1363:
1358:
1212:Sogn og Fjordane
1004:adjustment seats
1000:Ausgleichsmandat
994:
971:utjämningsmandat
944:
937:
930:
916:
915:
903:
902:
891:
890:
846:Positive results
741:Strategic voting
638:Majority jackpot
595:
584:
455:Liquid democracy
331:National remnant
321:Highest averages
258:
243:
228:
160:
151:Alternative vote
149:
133:Partisan primary
125:
66:Mechanism design
19:
18:
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1576:
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1366:
1359:
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1328:
1308:
1287:
1265:
1243:
1235:
1164:
1156:county councils
1152:
1112:
1077:county councils
1069:
1061:
1040:
990:
948:
910:
909:
897:
885:
877:
876:
843:
819:Arrow's theorem
809:
799:
798:
767:
737:
726:No-show paradox
707:
693:Cloning paradox
683:Spoiler effects
680:
670:
669:
644:
531:
514:
504:
503:
476:
467:Maximal lottery
434:
415:Thiele's method
404:
374:
306:
296:
295:
281:Approval voting
269:Cardinal voting
265:
210:
204:Maximal lottery
168:
100:
90:
17:
12:
11:
5:
1575:
1565:
1564:
1559:
1554:
1549:
1533:
1532:
1514:
1503:
1480:
1469:(in Norwegian)
1457:
1446:(in Norwegian)
1435:
1432:(in Norwegian)
1415:
1390:
1364:
1352:
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1346:
1345:
1344:
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1242:
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1234:
1231:
1200:
1199:
1195:
1191:
1184:
1163:
1160:
1151:
1148:
1111:
1108:
1068:
1065:
1060:
1057:
1045:North Atlantic
1039:
1036:
955:Leveling seats
950:
949:
947:
946:
939:
932:
924:
921:
920:
908:
907:
895:
882:
879:
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869:
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786:
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766:
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763:Turkey-raising
760:
755:
750:
736:
735:
734:
733:
723:
718:
706:
705:
703:Center squeeze
700:
695:
690:
688:Spoiler effect
681:
676:
675:
672:
671:
668:
667:
662:
661:
660:
647:By ballot type
643:
642:
641:
640:
635:
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620:
619:
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611:
601:
600:
599:
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564:
563:
558:
553:
548:
530:
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510:
509:
506:
505:
502:
501:
499:Limited voting
496:
495:
494:
475:
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469:
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459:
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457:
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433:
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427:
422:
417:
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397:
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373:
372:
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368:Localized list
365:
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336:Biproportional
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167:
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140:Instant-runoff
137:
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135:
127:Jungle primary
114:
103:Single vote -
101:
96:
95:
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91:
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78:
73:
68:
63:
57:
54:
53:
43:
42:
32:
31:
15:
9:
6:
4:
3:
2:
1574:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1544:
1542:
1529:. 2013-02-22.
1528:
1525:(in German).
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1292:Vera Lysklætt
1285:Peculiarities
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1268:
1257:
1253:
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1216:Liberal Party
1213:
1209:
1205:
1196:
1192:
1189:
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1179:
1177:
1173:
1169:
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1157:
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1135:jämförelsetal
1131:
1127:
1123:
1121:
1117:
1107:
1105:
1101:
1097:
1093:
1089:
1084:
1082:
1078:
1074:
1064:
1056:
1054:
1050:
1049:Faroe Islands
1046:
1035:
1033:
1029:
1025:
1021:
1017:
1013:
1009:
1005:
1001:
997:
993:
988:
984:
980:
976:
972:
968:
964:
963:tillægsmandat
960:
956:
945:
940:
938:
933:
931:
926:
925:
923:
922:
919:
914:
906:
901:
896:
894:
889:
884:
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881:
880:
873:
870:
868:
865:
863:
862:May's theorem
860:
858:
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849:
848:
847:
840:
837:
835:
832:
830:
827:
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815:
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808:
803:
802:
795:
792:
790:
787:
785:
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774:
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772:majority rule
770:Paradoxes of
764:
761:
759:
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751:
749:
746:
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744:
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742:
732:
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1496:22 September
1494:. Retrieved
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1471:. Retrieved
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1450:9 September
1141:+1), where
653:Single vote
556:Conditional
551:Coexistence
400:Quota Borda
390:Schulze STV
348:Closed list
291:STAR voting
236:Borda count
1541:Categories
1348:References
1104:Hare quota
1096:valkretsar
758:Truncation
487:Cumulative
310:Party-list
85:By country
76:Comparison
1298:decided.
1102:with the
1081:municipal
1053:Greenland
1020:Bundestag
992:‹See Tfd›
983:Icelandic
975:Norwegian
665:Dual-vote
358:Panachage
353:Open list
343:List type
221:Plurality
117:Two-round
105:plurality
28:Economics
1527:Die Zeit
1408:13 April
1383:13 April
1326:See also
1220:Akershus
1218:, while
1188:Finnmark
385:Hare STV
24:Politics
22:A joint
1306:Germany
1194:county.
1092:Swedish
1088:Riksdag
1073:Riksdag
1059:Iceland
1038:Denmark
1016:Germany
1012:Finland
967:Swedish
395:CPO-STV
245:Baldwin
194:Schulze
189:Minimax
107:methods
1276:party.
1183:seats.
1176:county
1162:Norway
1067:Sweden
1022:. The
1008:Nordic
996:German
959:Danish
260:Coombs
30:series
1402:(PDF)
597:'MMP'
586:'AMS'
1498:2013
1475:2013
1452:2013
1410:2013
1385:2013
1172:2005
1075:and
1051:and
538:Non-
492:SNTV
81:List
38:and
26:and
256:el.
241:el.
230:IRV
226:el.
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