3003:, the official threshold is 5% for parties and coalitions. However, since the country is divided into 10 voting districts with 14 elected representatives each, sometimes the threshold can be higher, depending on the number of votes of "fallen lists" (lists that do not receive at least 5%). If many votes are lost in this manner, a list that gets 5% will still get a seat, whereas if there is a small number votes for parties that do not pass the threshold, the actual ("natural") threshold is close to 7.15%. Some systems allow parties to associate their lists together into a single "cartel" in order to overcome the threshold, while some systems set a separate threshold for such cartels. Smaller parties often form pre-election coalitions to make sure they get past the election threshold creating a
1026:
divisions produce fractional numbers of seats. As a result, several methods, of which the D'Hondt method is one, have been devised which ensure that the parties' seat allocations, which are of whole numbers, are as proportional as possible. Although all of these methods approximate proportionality, they do so by minimizing different kinds of disproportionality. The D'Hondt method minimizes the largest seats-to-votes ratio. Empirical studies based on other, more popular concepts of disproportionality show that the D'Hondt method is one of the least proportional among the proportional representation methods. The D'Hondt favours large
2980:, candidates receiving the simple quota in their electoral districts are considered elected, but in the second (district level) and third round of counting (nationwide, modified D'Hondt method) mandates are awarded only to candidate lists receiving more than the threshold of 5% of the votes nationally. The vote threshold simplifies the process of seat allocation and discourages fringe parties (those that are likely to gain very few votes) from competing in the elections. Obviously, the higher the vote threshold, the fewer the parties that will be represented in parliament.
926:
2870:, sum to the required total; in other words, pick a number so that there is no need to examine the remainders. Any number in one range of quotas will accomplish this, with the highest number in the range always being the same as the lowest number used by the D'Hondt method to award a seat (if it is used rather than the Jefferson method), and the lowest number in the range being the smallest number larger than the next number which would award a seat in the D'Hondt calculations.
61:
901:
3139:
region). The votes for parties that have not gained a seat at the regional level are thus discarded, so they do not aggregate at a national level. This means that parties which would have gained seats in a national distribution of seats may still end up with no seats as they did not gain enough votes in any region. This may also lead to skewed seat allocation at a national level, such as in Spain in 2011 where the
3019:), and only the remainder of the seats are distributed proportionally (including to the list which has already received the majority bonus). In Italian local elections a similar system is used, where the party or coalition of parties linked to the elected mayor automatically receives 60% of seats; unlike the French model though the remainder of the seats are not distributed again to the largest party.
913:
2850:
The system can be used both for distributing seats in a legislature among states pursuant to populations or among parties pursuant to an election result. The tasks are mathematically equivalent, putting states in the place of parties and population in place of votes. In some countries, the
Jefferson
3014:
In French municipal and regional elections, the D'Hondt method is used to attribute a number of council seats; however, a fixed proportion of them (50% for municipal elections, 25% for regional elections) is automatically given to the list with the greatest number of votes, to ensure that it has a
2824:
Washington had exercised his first veto power on a bill that introduced a new plan for dividing seats in the House of
Representatives that would have increased the number of seats for northern states. Ten days after the veto, Congress passed a new method of apportionment, now known as Jefferson's
1025:
Proportional representation systems aim to allocate seats to parties approximately in proportion to the number of votes received. For example, if a party wins one-third of the votes then it should gain about one-third of the seats. In general, exact proportionality is not possible because these
3138:
In most countries, seats for the national assembly are divided on a regional or even a provincial level. This means that seats are first divided between individual regions (or provinces) and are then allocated to the parties in each region separately (based on only the votes cast in the given
1628:
For comparison, the "True proportion" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received. (For example, 100,000/230,000 × 8 = 3.48) The slight favouring of the largest party over the smallest is apparent.
1183:
In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Since 8 seats are to be allocated, each party's total votes are divided by 1, then by 2, 3, and 4 (and then, if necessary, by 5, 6, 7, and so on). The 8 highest entries (in bold text) range from
3027:
The D'Hondt method can also be used in conjunction with a quota formula to allocate most seats, applying the D'Hondt method to allocate any remaining seats to get a result identical to that achieved by the standard D'Hondt formula. This variation is known as the
3086:, D'Hondt is applied for the allocation of list seats, taking into account for each party the number of constituency seats it has won (that is, if a party has won 3 constituency seats, the divisor for that party in the first round will be 4, rather than 1).
1624:
The chart below shows an easy way to perform the calculation. Each party's vote is divided by 1, 2, 3, or 4 in consecutive columns, then the 8 highest values resulting are selected. The quantity of highest values in each row is the number of seats won.
2991:, there is no official threshold, but the effective threshold is gaining one seat. The country is divided into districts with different numbers of representatives, so there is a natural threshold, different in each district. The largest district,
2819:
For representatives there can be no such common ratio, or divisor which ... will divide them exactly without a remainder or fraction. I answer then ... that representatives as nearly as the nearest ratio will admit; and the fractions must be
2900:, where any list which does not achieve that threshold will not have any seats allocated to it, even if it received enough votes to have otherwise been rewarded with a seat. Examples of countries using the D'Hondt method with a threshold are
3011:) (until 2017, when they were abolished) could not be used to overcome the threshold, but they do influence the distribution of remainder seats; thus, smaller parties can use them to get a chance which is more like that of the big parties.
3106:
has described the modified d'Hondt system used in the ACT as a "monster ... that few understood, even electoral officials who had to wrestle with its intricacies while spending several weeks counting the votes". It was replaced with the
2638:
1053:
by encouraging coalitions. A method is consistent if it treats parties that received tied votes equally. Monotonicity means that the number of seats provided to any state or party will not decrease if the house size increases.
2332:
4023:
3147:
with only 44% of the national vote. It may also skew results for small parties with broad appeal at a national level compared to small parties with a local appeal (e.g. nationalist parties). For instance, in the
3101:
system of proportional representation, and various methods for preferential voting for candidates and parties, both within and across party lines. The process involves 8 stages of scrutiny. ABC elections analyst
1066:
are calculated for each party. The party with the largest quotient wins one seat, and its quotient is recalculated. This is repeated until the required number of seats is filled. The formula for the quotient is
2846:
To allocate discrete entities proportionally among several numbers, it is necessary to divide these numbers by a common divisor, producing quotients whose sum is equal to the number of entities to be allocated.
2976:, a party must win enough votes for one strictly proportional full seat (note that this is not necessary in plain D'Hondt), which with 150 seats in the lower chamber gives an effective threshold of 0.67%. In
1174:
Alternatively, the procedure can be reversed by starting with a house apportionment that assigns "too many seats" to every party, then removing legislators one at a time from the most-overrepresented party.
2642:
For illustration, continue with the above example of four parties. The advantage ratios of the four parties are 1.2 for A, 1.1 for B, 1 for C, and 0 for D. The reciprocal of the largest advantage ratio is
3408:. The system is also used in practice for the allocation between political groups of numerous posts (vice presidents, committee chairmen and vice-chairmen, delegation chairmen and vice-chairmen) in the
1131:
The total votes cast for each party in the electoral district is divided, first by 1, then by 2, then 3, up to the total number of seats to be allocated for the district/constituency. Say there are
2476:
2394:
1459:
While in this example, parties B, C, and D formed a coalition against Party A. You can see that Party A received 3 seats instead of 4 due to the coalition having 30,000 more votes than Party A.
3039:, the first divisor (when the party has no seats so far, which is normally 1) was raised to favour larger parties and eliminate small ones. In the Czech case, it is set to 1.42 (approximately
2420:. Thanks to this, as shown by Juraj Medzihorsky, the D'Hondt method splits the votes into exactly proportionally represented ones and residual ones. The overall fraction of residual votes is
1192:. For each, the corresponding party gets a seat. Note that in Round 1, the quotient shown in the table, as derived from the formula, is precisely the number of votes returned in the ballot.
1110:
1947:
2198:
2074:
2250:
3118:
in order to overcome the threshold, while some systems set a separate threshold for cartels. In a system of proportional representation in which the country is divided in multiple
1868:
4031:
3130:
to obtain one seat can be very high (5% of votes since 2003), which also favors larger parties. Therefore, some parties pool their voters in order to gain more (or any) seats.
954:
2418:
4421:
3061:
2489:
3090:
2262:
4144:
2103:
1979:
3651:
4223:
2123:
1999:
1888:
2893:
sizes; for legislatures with many members, elected in a single national list, the effects of using one proportional method rather than another are negligible.
4871:
4639:
645:
3739:
2796:
The
Jefferson and the D'Hondt methods are equivalent. They always give the same results, but the methods of presenting the calculation are different.
1049:
The axiomatic properties of the D'Hondt method were studied and they proved that the D'Hondt method is a consistent and monotone method that reduces
4767:
4619:
677:
539:
534:
4866:
4644:
947:
640:
4629:
4414:
2826:
2808:
322:
3597:
846:
4993:
97:
2425:
4676:
4294:
1822:
among all parties. This ratio is also known as the advantage ratio. In contrast, the average seats-to-votes ratio is optimized by the
940:
4407:
4163:
3907:
3468:
1072:
5011:
1895:
841:
4342:
4861:
4807:
1003:
831:
581:
552:
492:
4659:
2647:. The residuals as shares of the total vote are 0% for A, 2.2% for B, 2.2% for C, and 8.7% for party D. Their sum is 13%, i.e.,
4988:
4057:
3094:
3036:
563:
88:
5031:
4787:
2209:
1007:
995:. Compared to ideal proportional representation, the D'Hondt method reduces somewhat the political fragmentation for smaller
626:
1823:
3898:(2003), "Degrees of proportionality of proportional representation formulas", in Grofman, Bernard; Lijphart, Arend (eds.),
3868:
3401:
3149:
268:
253:
238:
4169:
2339:
1795:
A worked-through example for non-experts relating to the 2019 elections in the UK for the
European Parliament written by
4830:
4815:
4634:
3768:
3144:
1807:
884:
504:
427:
348:
3674:
4881:
4604:
4594:
4455:
4121:
3265:
3115:
2851:
system is known by the names of local politicians or experts who introduced them locally. For example, it is known in
988:
316:
298:
139:
869:
4394:
4122:
Comparative report on thresholds and other features of electoral systems which bar parties from access to parliament
4846:
4537:
760:
743:
710:
690:
474:
462:
432:
233:
191:
124:
2128:
2004:
568:
4896:
4851:
4797:
4709:
3413:
3389:
3140:
3075:
3029:
2812:
616:
609:
93:
4886:
4772:
4730:
4649:
4574:
4510:
4468:
3067:
2863:
980:
670:
598:
587:
450:
437:
420:
397:
375:
338:
328:
4505:
1171:
highest numbers in the whole grid; each party is given as many seats as there are winning entries in its row.
3750:
2999:
with 6 representatives, has a natural threshold of 14%. This favors large parties in the small districts. In
4911:
4901:
4876:
4692:
4569:
4155:
2886:
1800:
1050:
992:
796:
650:
333:
3927:
3032:, and is the formula frequently used when a country's electoral system is referred to simply as 'D'Hondt'.
4952:
4891:
4754:
4697:
4073:
3381:
3281:
1039:
825:
705:
635:
442:
3097:
using the "modified d'Hondt" electoral system. The electoral system consisted of the d'Hondt system, the
1829:
4856:
4777:
4542:
3157:
733:
573:
457:
263:
242:
174:
152:
925:
791:
4926:
4495:
3004:
2988:
1819:
1043:
864:
851:
819:
83:
2399:
4906:
4500:
4315:
3409:
3397:
3385:
3153:
3083:
3071:
2904:(3% for single parties, 5% for coalitions of two or more parties, 1% for independent individuals);
2897:
1031:
770:
604:
257:
4053:
4024:"Apportioning Representatives in the United States Congress – Jefferson's Method of Apportionment"
3620:
2877:
from 20,001 to 25,000. More precisely, any number n for which 20,000 < n ≤ 25,000 can be used.
2866:. The divisor is chosen as necessary so that the resulting quotients, disregarding any fractional
4947:
4557:
3841:
3833:
3575:
3233:
3127:
3119:
3042:
2968:(5% for single party, 10% for two-party coalitions, 15% for coalitions of 3 or more parties) and
2890:
2651:. The decomposition of the votes into represented and residual ones is shown in the table below.
996:
930:
801:
412:
196:
4515:
4389:
4008:
879:
4250:
4916:
4825:
4782:
4624:
4547:
4532:
4490:
4159:
4077:
3914:
3903:
3098:
2833:
2804:
1014:
836:
806:
728:
665:
499:
226:
201:
184:
52:
4290:
4095:
4957:
4589:
4445:
4430:
3877:
3825:
3783:
3715:
3666:
3612:
3567:
3439:
2800:
1035:
1010:
917:
874:
765:
753:
467:
343:
169:
163:
145:
134:
129:
117:
78:
40:
3983:
2081:
1957:
1806:
A more mathematically detailed example has been written by
British mathematician Professor
5005:
4921:
4762:
4740:
4552:
4473:
4463:
4441:
4298:
4198:
3490:
3393:
3317:
3079:
1796:
1027:
905:
738:
593:
558:
479:
390:
293:
216:
158:
36:
2257:
The D'Hondt method assigns seats so that this ratio attains its smallest possible value,
1127:
is the number of seats that party has been allocated so far, initially 0 for all parties.
1042:
reduces the disproportional bias towards large parties and it generally has a more equal
3066:
The term "modified D'Hondt" has also been given to the use of the D'Hondt method in the
60:
4820:
4525:
4485:
3895:
3787:
3502:. Notably, it is customary in the Netherlands to write such surnames with a lower-case
3481:
3380:
and the disproportionality of the D'Hondt method is corrected with leveling seats with
2108:
1984:
1873:
984:
775:
715:
700:
511:
380:
355:
206:
17:
3902:, Agathon series on representation, vol. 1, Algora Publishing, pp. 170–179,
3616:
900:
5025:
4564:
3845:
3670:
3579:
3417:
2995:
with 33 representatives, has a natural threshold of 3%, while the smallest district,
784:
484:
272:
110:
73:
48:
4384:
3596:
Schuster, Karsten; Pukelsheim, Friedrich; Drton, Mathias; Draper, Norman R. (2003).
2633:{\displaystyle r_{p}=v_{p}-(1-\pi ^{*})s_{p},\;r_{p}\in ,\sum _{p}\,r_{p}=\pi ^{*}.}
4579:
4520:
4276:
3103:
2987:. It depends on the number of seats that are allocated with the D'Hondt method. In
524:
288:
281:
211:
3720:
3703:
4390:
SciencesPo, R package for performing seats allocation based on the D'Hondt system
3816:
Lijphart, Arend (1990). "The
Political Consequences of Electoral Laws, 1945-85".
3791:
2327:{\displaystyle \delta ^{*}=\min _{\mathbf {s} \in {\mathcal {S}}}\max _{p}a_{p},}
4962:
4725:
4664:
4584:
4480:
3769:"Which Electoral Formula Is the Most Proportional? A New Look with New Evidence"
3357:
3309:
2973:
402:
360:
303:
248:
2889:
by allocating more seats to larger parties. This effect is strongest for small
2832:
It was also invented independently in 1878 in Europe, by
Belgian mathematician
4735:
4671:
3860:
3552:
3341:
3305:
3301:
3289:
3237:
3217:
3108:
2996:
2921:
2909:
4081:
2825:
Method. It was used to achieve the proportional distribution of seats in the
4972:
4967:
4186:
3954:
3377:
3369:
3313:
3257:
3253:
3181:
2964:(5%, or 8% for coalitions; but does not apply for ethnic-minority parties),
2867:
2799:
The method was first described in 1792 by
Statesman and future US President
370:
365:
3114:
Some systems allow parties to associate their lists together into a single
3063:, termed the Koudelka coefficient after the politician who introduced it).
4370:
Simulator
Election calculus simulator based on the modified D'Hondt system
1818:
The D'Hondt method approximates proportionality by minimizing the largest
912:
4792:
3881:
3405:
3349:
3333:
3321:
3225:
3213:
3169:
2953:
2933:
2929:
1063:
621:
4654:
4374:
4291:
Quo Vadis
Thailand? Thai Politics after the 2005 Parliamentary Election
4060:[The Main Variables of Systems of Proportional Representation]
4009:"Founders Online: Proportional Representation, [22 March] 1792"
3837:
3373:
3365:
3337:
3293:
3269:
3261:
3249:
3241:
3229:
3209:
3201:
3197:
3193:
3185:
3173:
3123:
3000:
2992:
2977:
2969:
2965:
2945:
2937:
2905:
2901:
2874:
407:
3598:"Seat biases of apportionment methods for proportional representation"
3082:, in which after constituency seats have been allocated to parties by
4942:
3984:"La représentation Proportionnelle et la méthode des moindres carrés"
3361:
3345:
3329:
3297:
3273:
3205:
3177:
2961:
2957:
2949:
2925:
2917:
2852:
4399:
3829:
3571:
1013:. It was re-invented independently in 1878 by Belgian mathematician
999:
sizes, where it favors larger political parties over small parties.
2873:
Applied to the above example of party lists, this range extends as
2396:
is a seat allocation from the set of all allowed seat allocations
4379:
3416:. It is also used to calculate the results in German and Austrian
3353:
3285:
3277:
3221:
3189:
2913:
2254:
captures how over-represented is the most over-represented party.
4369:
3325:
3245:
2941:
4403:
2896:
An alternative approach to reduce political fragmentation are
2862:
Jefferson's method uses a quota (called a divisor), as in the
2839:
Système pratique et raisonné de représentation proportionnelle
3376:
the D'Hondt method is used to elect part of the seats in the
2405:
2294:
59:
3740:"Seat bias formulas in proportional representation systems"
3652:"Proportionality, disproportionality and electoral systems"
3445:
3384:. The D'Hondt system is used for the "top-up" seats in the
3454:
4145:"Appendix C: Effective threshold and effective magnitude"
1890:
is the overall number of parties, the advantage ratio is
3522:). However, in Belgium it is always capitalized, hence:
3168:
The D'Hondt method is used to elect the legislatures in
3015:
working majority: this is called the "majority bonus" (
4385:
Java D'Hondt, Saint-Lague and Hare-Niemeyer calculator
4316:"D'Hondt system for picking NI ministers in Stormont"
3928:"EU elections voting system explained: D'Hondt worry"
3469:
3457:
3045:
2492:
2428:
2402:
2342:
2265:
2212:
2131:
2111:
2084:
2007:
1987:
1960:
1898:
1876:
1832:
1121:
is the total number of votes that party received, and
1075:
4395:
Downloadable Excel calculator for the D'Hondt method
3460:
3442:
2471:{\displaystyle \pi ^{*}=1-{\frac {1}{\delta ^{*}}}.}
991:
among political parties. It belongs to the class of
4981:
4935:
4839:
4806:
4753:
4718:
4685:
4612:
4603:
4454:
3991:
Annales Scientifiques de l'École Normale Supérieure
3451:
3448:
2655:Allocation of eight seats under the D'Hondt method
2389:{\displaystyle \mathbf {s} =\{s_{1},\dots ,s_{P}\}}
1139:seats. Then a grid of numbers can be created, with
1017:, which is the reason for its two different names.
1002:The method was first described in 1792 by American
3404:era to allocate party-list parliamentary seats in
3055:
2632:
2470:
2412:
2388:
2326:
2244:
2192:
2117:
2097:
2068:
1993:
1973:
1941:
1882:
1862:
1104:
1062:After all the votes have been tallied, successive
4341:Betriebsräten, ifb-Institut zur Fortbildung von.
3697:
3695:
4187:Suhteellisuuden parantaminen eduskuntavaaleissa.
3913:. See in particular the section "Sainte-Lague",
2302:
2280:
2220:
4058:"Hlavní proměnné proporčních volebních systémů"
3900:Electoral Laws and Their Political Consequences
3160:(Catalonia) gained 10 seats for 779,425 votes.
2844:
2817:
1105:{\displaystyle {\text{quot}}={\frac {V}{s+1}}}
4415:
3591:
3589:
1942:{\displaystyle a_{p}={\frac {s_{p}}{v_{p}}},}
948:
8:
4872:Independence of Smith-dominated alternatives
4100:Prof. King’s Teaching and Learning Resources
3514:), while the surname all by itself would be
2837:
2807:regarding the apportionment of seats in the
2383:
2351:
2193:{\displaystyle v_{p}\in ,\;\sum _{p}v_{p}=1}
2069:{\displaystyle s_{p}\in ,\;\sum _{p}s_{p}=1}
1857:
1839:
1155:th column is the number of votes won by the
4289:Aurel Croissant and Daniel J. Pojar, Jr., "
4143:Gallagher, Michael; Mitchell, Paul (2005).
3645:
3643:
3641:
3412:and for the allocation of ministers in the
4609:
4422:
4408:
4400:
4375:Calculations using the pure d'Hondt method
3861:"Criteria for proportional representation"
2554:
2163:
2039:
983:for allocating seats in parliaments among
955:
941:
31:
27:Method for allocating seats in parliaments
3719:
3396:; in some countries for elections to the
3156:gained 1 seat for 969,946 votes, whereas
3046:
3044:
2621:
2608:
2603:
2597:
2581:
2559:
2545:
2532:
2510:
2497:
2491:
2457:
2448:
2433:
2427:
2404:
2403:
2401:
2377:
2358:
2343:
2341:
2315:
2305:
2293:
2292:
2284:
2283:
2270:
2264:
2233:
2223:
2211:
2178:
2168:
2136:
2130:
2110:
2089:
2083:
2054:
2044:
2012:
2006:
1986:
1965:
1959:
1928:
1918:
1912:
1903:
1897:
1875:
1831:
1814:Approximate proportionality under D'Hondt
1084:
1076:
1074:
2653:
1631:
1461:
1194:
4867:Independence of irrelevant alternatives
4645:Sequential proportional approval voting
3553:"The Jefferson method of Apportionment"
3538:
3429:
2245:{\displaystyle \delta =\max _{p}a_{p},}
47:
3859:Balinski, M. L.; Young, H. P. (1979).
3733:
3731:
3551:Balinski, M. L.; Young, H. P. (1978).
2809:United States House of Representatives
4257:. Australian Broadcasting Corporation
3818:The American Political Science Review
3489:
3480:
7:
4380:PHP Implementation of D'Hondt system
4343:"D'Hondtsches Höchstzahlenverfahren"
4199:"Counting the votes | London Elects"
3546:
3544:
3542:
3506:when preceded by the forename: thus
4677:Indirect single transferable voting
4277:"Danish Parliamentary Election Law"
4224:"Modified d'Hondt Electoral System"
4028:Mathematical Association of America
3143:gained an absolute majority in the
1863:{\displaystyle p\in \{1,\dots ,P\}}
4347:D'Hondtsches Höchstzahlenverfahren
3788:10.1093/oxfordjournals.pan.a029822
25:
4152:The Politics of Electoral Systems
2989:Finland's parliamentary elections
2842:, published in Brussels in 1882:
4305:, Volume IV, Issue 6 (June 2005)
3438:
3093:elections were conducted by the
2972:(5%, on regional basis). In the
2344:
2285:
1147:columns, where the entry in the
924:
911:
899:
847:McKelvey–Schofield chaos theorem
493:Semi-proportional representation
125:First preference plurality (FPP)
3704:"Rethinking the D'Hondt method"
3095:Australian Electoral Commission
3007:. In the Netherlands, cartels (
2836:, who wrote in his publication
4788:Mixed ballot transferable vote
3955:"The D'Hondt Method Explained"
3738:Pukelsheim, Friedrich (2007).
2587:
2568:
2538:
2519:
2413:{\displaystyle {\mathcal {S}}}
2157:
2145:
2033:
2021:
1008:President of the United States
885:Harsanyi's utilitarian theorem
842:Moulin's impossibility theorem
807:Conflicting majorities paradox
1:
3997:. l'École Normale Supérieure.
3721:10.1080/2474736X.2019.1625712
3617:10.1016/S0261-3794(02)00027-6
3150:2008 Spanish general election
2829:among the states until 1842.
2204:The largest advantage ratio,
1046:for different sized parties.
711:Frustrated majorities paradox
4989:Comparison of voting systems
4831:Satisfaction approval voting
4816:Single non-transferable vote
4635:Proportional approval voting
3671:10.1016/0261-3794(91)90004-C
1783:
1780:
1772:
1767:
1747:
1742:
1720:
1715:
1689:
1684:
880:Condorcet dominance theorems
820:Social and collective choice
4595:Graduated majority judgment
4124:(Report). Council of Europe
3982:André Sainte-Laguë (1910).
3747:4th ECPR General Conference
3708:Political Research Exchange
3650:Gallagher, Michael (1991).
3056:{\displaystyle {\sqrt {2}}}
2885:The D'Hondt method reduces
2695:
2692:
2645:1/1.15 = 0.87 = 1 − π
1824:Webster/Sainte-Laguë method
989:proportional representation
546:By mechanism of combination
317:Proportional representation
5048:
4847:Condorcet winner criterion
4538:First-past-the-post voting
4120:Venice Commission (2008).
3702:Juraj Medzihorsky (2019).
3400:; and was used during the
3035:In some cases such as the
2813:First United States Census
2105:– the vote share of party
1981:– the seat share of party
1034:over small parties due to
744:Multiple districts paradox
475:Fractional approval voting
463:Interactive representation
5002:
4994:Voting systems by country
4897:Mutual majority criterion
4852:Condorcet loser criterion
4798:Vote linkage mixed system
4710:Largest remainders method
4437:
3414:Northern Ireland Assembly
3390:Senedd (Welsh Parliament)
3111:system from 1995 onward.
3076:Senedd (Welsh Parliament)
3030:Hagenbach-Bischoff System
1777:
691:Paradoxes and pathologies
540:Mixed-member proportional
535:Mixed-member majoritarian
530:By results of combination
421:Approval-based committees
4887:Majority loser criterion
4773:Additional member system
4731:Hagenbach-Bischoff quota
4650:Single transferable vote
4575:Positional voting system
4511:Minimax Condorcet method
4469:Combined approval voting
3767:Benoit, Kenneth (2000).
3091:ACT Legislative Assembly
3068:additional member system
3037:Czech regional elections
2864:largest remainder method
2827:House of Representatives
1167:winning entries are the
993:highest-averages methods
977:greatest divisors method
870:Condorcet's jury theorem
671:Double simultaneous vote
646:Rural–urban proportional
641:Dual-member proportional
603:
592:
559:Parallel (superposition)
451:Fractional social choice
438:Expanding approvals rule
267:
252:
237:
168:
157:
133:
4912:Resolvability criterion
4902:Participation criterion
4877:Later-no-harm criterion
4693:Highest averages method
4297:April 19, 2009, at the
4203:www.londonelects.org.uk
4156:Oxford University Press
3932:UK in a changing Europe
2983:The method can cause a
2887:political fragmentation
2480:The residuals of party
1801:UK in a Changing Europe
1051:political fragmentation
797:Tyranny of the majority
574:Fusion (majority bonus)
391:Quota-remainder methods
18:Jefferson's method
4953:First-preference votes
4892:Monotonicity criterion
4862:Independence of clones
4565:Simple majoritarianism
3498:is sometimes spelt as
3057:
2848:
2838:
2822:
2634:
2472:
2414:
2390:
2328:
2246:
2194:
2119:
2099:
2070:
1995:
1975:
1943:
1884:
1864:
1106:
931:Mathematics portal
837:Majority impossibility
826:Impossibility theorems
622:Negative vote transfer
443:Method of equal shares
64:
5032:Apportionment methods
4857:Consistency criterion
4778:Alternative vote plus
4543:Instant-runoff voting
3158:Convergence and Union
3058:
2792:Jefferson and D'Hondt
2649:1 − 0.87 = 0.13
2635:
2473:
2415:
2391:
2329:
2247:
2195:
2120:
2100:
2098:{\displaystyle v_{p}}
2071:
1996:
1976:
1974:{\displaystyle s_{p}}
1944:
1885:
1865:
1561:quotient seats after
1159:th party, divided by
1107:
1038:. In comparison, the
734:Best-is-worst paradox
723:Pathological response
458:Direct representation
111:Single-winner methods
63:
4927:Seats-to-votes ratio
4698:Webster/Sainte-Laguë
4228:elections.act.gov.au
4074:Sociologický časopis
4066:Sociologický Ćasopis
4022:Caulfield, Michael.
3882:10.1287/opre.27.1.80
3145:Congress of Deputies
3043:
3005:coalition government
2898:electoral thresholds
2490:
2426:
2400:
2340:
2263:
2210:
2129:
2109:
2082:
2005:
1985:
1958:
1896:
1874:
1830:
1820:seats-to-votes ratio
1073:
1044:seats-to-votes ratio
981:apportionment method
918:Economics portal
865:Median voter theorem
84:Comparative politics
4907:Plurality criterion
4506:Kemeny–Young method
4175:on 10 October 2015.
4096:"Electoral Systems"
3869:Operations Research
3756:on 7 February 2009.
3680:on 16 November 2013
3626:on 15 February 2016
3410:European Parliament
3398:European Parliament
3386:Scottish Parliament
3382:Sainte-Laguë method
3154:United Left (Spain)
3133:
3120:electoral districts
3084:first-past-the-post
3072:Scottish Parliament
3017:prime à la majorité
2791:
2656:
1813:
1467:(1 seat per round)
1200:(1 seat per round)
1040:Sainte-Laguë method
906:Politics portal
617:Vote linkage system
588:Seat linkage system
175:Ranked-choice (RCV)
4948:Election threshold
4882:Majority criterion
4558:Supplementary vote
4303:Strategic Insights
4251:"Election Preview"
4185:Oikeusministeriö.
3776:Political Analysis
3234:Dominican Republic
3089:In 1989 and 1992,
3053:
2891:electoral district
2654:
2630:
2602:
2468:
2410:
2386:
2324:
2310:
2300:
2242:
2228:
2190:
2173:
2115:
2095:
2066:
2049:
1991:
1971:
1939:
1880:
1860:
1503:seats after round
1408:seats after round
1354:seats after round
1296:seats after round
1236:seats after round
1102:
1004:Secretary of State
997:electoral district
971:, also called the
802:Discursive dilemma
761:Lesser evil voting
636:Supermixed systems
339:Largest remainders
197:Round-robin voting
65:
5019:
5018:
4917:Reversal symmetry
4826:Cumulative voting
4808:Semi-proportional
4783:Mixed single vote
4749:
4748:
4625:Mixed single vote
4533:Exhaustive ballot
4496:Copeland's method
4491:Condorcet methods
4431:Electoral systems
3953:Helen J. Wilson.
3659:Electoral Studies
3605:Electoral Studies
3402:1997 constitution
3099:Australian Senate
3051:
3009:lijstverbindingen
2985:natural threshold
2857:Bader–Ofer system
2805:George Washington
2803:, in a letter to
2789:
2788:
2593:
2463:
2301:
2279:
2219:
2164:
2118:{\displaystyle p}
2040:
1994:{\displaystyle p}
1934:
1883:{\displaystyle P}
1788:
1787:
1622:
1621:
1501:Party A quotient
1457:
1456:
1406:Party D quotient
1352:Party C quotient
1294:Party B quotient
1234:Party A quotient
1100:
1079:
965:
964:
852:Gibbard's theorem
792:Dominance paradox
729:Perverse response
433:Phragmen's method
299:Majority judgment
227:Positional voting
185:Condorcet methods
53:electoral systems
16:(Redirected from
5039:
4958:Liquid democracy
4610:
4590:Two-round system
4501:Dodgson's method
4424:
4417:
4410:
4401:
4358:
4357:
4355:
4353:
4338:
4332:
4331:
4329:
4327:
4312:
4306:
4287:
4281:
4280:
4273:
4267:
4266:
4264:
4262:
4246:
4240:
4239:
4237:
4235:
4230:. 6 January 2015
4220:
4214:
4213:
4211:
4209:
4195:
4189:
4183:
4177:
4176:
4174:
4168:. Archived from
4149:
4140:
4134:
4133:
4131:
4129:
4117:
4111:
4110:
4108:
4106:
4091:
4085:
4084:
4063:
4050:
4044:
4043:
4041:
4039:
4030:. Archived from
4019:
4013:
4012:
4005:
3999:
3998:
3988:
3979:
3973:
3972:
3970:
3968:
3959:
3950:
3944:
3943:
3941:
3939:
3924:
3918:
3912:
3892:
3886:
3885:
3865:
3856:
3850:
3849:
3813:
3807:
3806:
3804:
3802:
3796:
3790:. Archived from
3773:
3764:
3758:
3757:
3755:
3749:. Archived from
3744:
3735:
3726:
3725:
3723:
3699:
3690:
3689:
3687:
3685:
3679:
3673:. Archived from
3656:
3647:
3636:
3635:
3633:
3631:
3625:
3619:. Archived from
3602:
3593:
3584:
3583:
3557:
3548:
3527:
3518:(with a capital
3493:
3488:
3484:
3479:
3473:
3467:
3466:
3463:
3462:
3459:
3456:
3453:
3450:
3447:
3444:
3434:
3164:Usage by country
3134:Regional D'Hondt
3062:
3060:
3059:
3054:
3052:
3047:
2841:
2811:pursuant to the
2801:Thomas Jefferson
2657:
2650:
2646:
2639:
2637:
2636:
2631:
2626:
2625:
2613:
2612:
2601:
2586:
2585:
2564:
2563:
2550:
2549:
2537:
2536:
2515:
2514:
2502:
2501:
2483:
2477:
2475:
2474:
2469:
2464:
2462:
2461:
2449:
2438:
2437:
2419:
2417:
2416:
2411:
2409:
2408:
2395:
2393:
2392:
2387:
2382:
2381:
2363:
2362:
2347:
2333:
2331:
2330:
2325:
2320:
2319:
2309:
2299:
2298:
2297:
2288:
2275:
2274:
2251:
2249:
2248:
2243:
2238:
2237:
2227:
2199:
2197:
2196:
2191:
2183:
2182:
2172:
2141:
2140:
2124:
2122:
2121:
2116:
2104:
2102:
2101:
2096:
2094:
2093:
2075:
2073:
2072:
2067:
2059:
2058:
2048:
2017:
2016:
2000:
1998:
1997:
1992:
1980:
1978:
1977:
1972:
1970:
1969:
1948:
1946:
1945:
1940:
1935:
1933:
1932:
1923:
1922:
1913:
1908:
1907:
1889:
1887:
1886:
1881:
1869:
1867:
1866:
1861:
1791:Further examples
1632:
1559:Coalition B-C-D
1462:
1195:
1170:
1166:
1162:
1158:
1154:
1150:
1146:
1142:
1138:
1134:
1126:
1120:
1111:
1109:
1108:
1103:
1101:
1099:
1085:
1080:
1077:
1036:strategic voting
1011:Thomas Jefferson
973:Jefferson method
957:
950:
943:
929:
928:
916:
915:
904:
903:
859:Positive results
754:Strategic voting
651:Majority jackpot
608:
597:
468:Liquid democracy
344:National remnant
334:Highest averages
271:
256:
241:
173:
164:Alternative vote
162:
146:Partisan primary
138:
79:Mechanism design
32:
21:
5047:
5046:
5042:
5041:
5040:
5038:
5037:
5036:
5022:
5021:
5020:
5015:
4998:
4977:
4931:
4922:Smith criterion
4835:
4802:
4763:Parallel voting
4745:
4741:Imperiali quota
4714:
4681:
4599:
4553:Contingent vote
4516:Nanson's method
4474:Unified primary
4464:Approval voting
4450:
4433:
4428:
4366:
4361:
4351:
4349:
4340:
4339:
4335:
4325:
4323:
4314:
4313:
4309:
4299:Wayback Machine
4288:
4284:
4275:
4274:
4270:
4260:
4258:
4249:Green, Antony.
4248:
4247:
4243:
4233:
4231:
4222:
4221:
4217:
4207:
4205:
4197:
4196:
4192:
4184:
4180:
4172:
4166:
4147:
4142:
4141:
4137:
4127:
4125:
4119:
4118:
4114:
4104:
4102:
4094:King, Charles.
4093:
4092:
4088:
4061:
4052:
4051:
4047:
4037:
4035:
4034:on 7 March 2016
4021:
4020:
4016:
4007:
4006:
4002:
3986:
3981:
3980:
3976:
3966:
3964:
3957:
3952:
3951:
3947:
3937:
3935:
3926:
3925:
3921:
3910:
3896:Lijphart, Arend
3894:
3893:
3889:
3863:
3858:
3857:
3853:
3830:10.2307/1963530
3815:
3814:
3810:
3800:
3798:
3797:on 28 July 2018
3794:
3771:
3766:
3765:
3761:
3753:
3742:
3737:
3736:
3729:
3701:
3700:
3693:
3683:
3681:
3677:
3654:
3649:
3648:
3639:
3629:
3627:
3623:
3600:
3595:
3594:
3587:
3572:10.1137/1020040
3555:
3550:
3549:
3540:
3536:
3531:
3530:
3486:
3477:
3471:
3441:
3437:
3435:
3431:
3426:
3394:London Assembly
3318:North Macedonia
3166:
3136:
3080:London Assembly
3041:
3040:
3025:
2883:
2794:
2684:
2679:
2674:
2669:
2664:
2648:
2644:
2617:
2604:
2577:
2555:
2541:
2528:
2506:
2493:
2488:
2487:
2481:
2453:
2429:
2424:
2423:
2398:
2397:
2373:
2354:
2338:
2337:
2311:
2266:
2261:
2260:
2229:
2208:
2207:
2174:
2132:
2127:
2126:
2107:
2106:
2085:
2080:
2079:
2050:
2008:
2003:
2002:
1983:
1982:
1961:
1956:
1955:
1924:
1914:
1899:
1894:
1893:
1872:
1871:
1828:
1827:
1816:
1797:Christina Pagel
1793:
1656:
1651:
1611:
1604:
1598:
1592:
1586:
1580:
1574:
1568:
1562:
1560:
1548:
1543:
1537:
1531:
1525:
1519:
1513:
1507:
1502:
1495:
1466:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1395:
1390:
1384:
1378:
1373:
1368:
1363:
1358:
1353:
1341:
1335:
1329:
1324:
1318:
1312:
1306:
1300:
1295:
1282:
1276:
1271:
1265:
1259:
1253:
1247:
1241:
1235:
1228:
1199:
1181:
1168:
1164:
1160:
1156:
1152:
1148:
1144:
1140:
1136:
1132:
1124:
1118:
1089:
1071:
1070:
1060:
1023:
961:
923:
922:
910:
898:
890:
889:
856:
832:Arrow's theorem
822:
812:
811:
780:
750:
739:No-show paradox
720:
706:Cloning paradox
696:Spoiler effects
693:
683:
682:
657:
544:
527:
517:
516:
489:
480:Maximal lottery
447:
428:Thiele's method
417:
387:
319:
309:
308:
294:Approval voting
282:Cardinal voting
278:
223:
217:Maximal lottery
181:
113:
103:
28:
23:
22:
15:
12:
11:
5:
5045:
5043:
5035:
5034:
5024:
5023:
5017:
5016:
5003:
5000:
4999:
4997:
4996:
4991:
4985:
4983:
4979:
4978:
4976:
4975:
4970:
4965:
4960:
4955:
4950:
4945:
4939:
4937:
4933:
4932:
4930:
4929:
4924:
4919:
4914:
4909:
4904:
4899:
4894:
4889:
4884:
4879:
4874:
4869:
4864:
4859:
4854:
4849:
4843:
4841:
4837:
4836:
4834:
4833:
4828:
4823:
4821:Limited voting
4818:
4812:
4810:
4804:
4803:
4801:
4800:
4795:
4790:
4785:
4780:
4775:
4770:
4765:
4759:
4757:
4751:
4750:
4747:
4746:
4744:
4743:
4738:
4733:
4728:
4722:
4720:
4716:
4715:
4713:
4712:
4707:
4706:
4705:
4700:
4689:
4687:
4683:
4682:
4680:
4679:
4674:
4669:
4668:
4667:
4662:
4657:
4647:
4642:
4637:
4632:
4627:
4622:
4616:
4614:
4607:
4601:
4600:
4598:
4597:
4592:
4587:
4582:
4577:
4572:
4567:
4562:
4561:
4560:
4555:
4550:
4548:Coombs' method
4540:
4535:
4530:
4529:
4528:
4526:Schulze method
4523:
4518:
4513:
4508:
4503:
4498:
4488:
4486:Bucklin voting
4483:
4478:
4477:
4476:
4471:
4460:
4458:
4452:
4451:
4438:
4435:
4434:
4429:
4427:
4426:
4419:
4412:
4404:
4398:
4397:
4392:
4387:
4382:
4377:
4372:
4365:
4364:External links
4362:
4360:
4359:
4333:
4307:
4282:
4268:
4255:ACT Votes 2020
4241:
4215:
4190:
4178:
4164:
4135:
4112:
4086:
4045:
4014:
4000:
3974:
3945:
3919:
3908:
3887:
3851:
3824:(2): 481–496.
3808:
3782:(4): 381–388.
3759:
3727:
3714:(1): 1625712.
3691:
3637:
3611:(4): 651–676.
3585:
3566:(2): 278–284.
3537:
3535:
3532:
3529:
3528:
3524:Victor D'Hondt
3510:(with a small
3508:Victor d'Hondt
3491:[dɔ̃t]
3482:[tɔnt]
3428:
3427:
3425:
3422:
3165:
3162:
3141:People's Party
3135:
3132:
3050:
3024:
3021:
2882:
2879:
2834:Victor D'Hondt
2793:
2790:
2787:
2786:
2783:
2780:
2777:
2774:
2771:
2767:
2766:
2763:
2760:
2757:
2754:
2751:
2747:
2746:
2743:
2740:
2737:
2734:
2731:
2727:
2726:
2723:
2720:
2717:
2714:
2711:
2707:
2706:
2703:
2700:
2697:
2694:
2691:
2687:
2686:
2681:
2676:
2671:
2666:
2661:
2629:
2624:
2620:
2616:
2611:
2607:
2600:
2596:
2592:
2589:
2584:
2580:
2576:
2573:
2570:
2567:
2562:
2558:
2553:
2548:
2544:
2540:
2535:
2531:
2527:
2524:
2521:
2518:
2513:
2509:
2505:
2500:
2496:
2467:
2460:
2456:
2452:
2447:
2444:
2441:
2436:
2432:
2407:
2385:
2380:
2376:
2372:
2369:
2366:
2361:
2357:
2353:
2350:
2346:
2323:
2318:
2314:
2308:
2304:
2296:
2291:
2287:
2282:
2278:
2273:
2269:
2241:
2236:
2232:
2226:
2222:
2218:
2215:
2202:
2201:
2189:
2186:
2181:
2177:
2171:
2167:
2162:
2159:
2156:
2153:
2150:
2147:
2144:
2139:
2135:
2114:
2092:
2088:
2077:
2065:
2062:
2057:
2053:
2047:
2043:
2038:
2035:
2032:
2029:
2026:
2023:
2020:
2015:
2011:
1990:
1968:
1964:
1938:
1931:
1927:
1921:
1917:
1911:
1906:
1902:
1879:
1859:
1856:
1853:
1850:
1847:
1844:
1841:
1838:
1835:
1815:
1812:
1803:is available.
1792:
1789:
1786:
1785:
1782:
1779:
1775:
1774:
1771:
1766:
1763:
1760:
1757:
1754:
1750:
1749:
1746:
1741:
1738:
1735:
1732:
1727:
1723:
1722:
1719:
1714:
1711:
1706:
1701:
1696:
1692:
1691:
1688:
1683:
1678:
1673:
1668:
1663:
1659:
1658:
1653:
1648:
1645:
1642:
1639:
1636:
1620:
1619:
1614:
1607:
1600:
1595:
1588:
1583:
1576:
1571:
1564:
1556:
1555:
1550:
1545:
1540:
1533:
1528:
1521:
1516:
1509:
1504:
1498:
1497:
1492:
1489:
1486:
1483:
1480:
1477:
1474:
1471:
1468:
1455:
1454:
1449:
1444:
1439:
1434:
1429:
1424:
1419:
1414:
1409:
1403:
1402:
1397:
1392:
1387:
1380:
1375:
1370:
1365:
1360:
1355:
1349:
1348:
1343:
1338:
1331:
1326:
1321:
1314:
1309:
1302:
1297:
1291:
1290:
1285:
1278:
1273:
1268:
1261:
1256:
1249:
1244:
1237:
1231:
1230:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1180:
1177:
1129:
1128:
1122:
1098:
1095:
1092:
1088:
1083:
1059:
1056:
1022:
1019:
1015:Victor D'Hondt
985:federal states
969:D'Hondt method
963:
962:
960:
959:
952:
945:
937:
934:
933:
921:
920:
908:
895:
892:
891:
888:
887:
882:
877:
872:
867:
855:
854:
849:
844:
839:
834:
823:
818:
817:
814:
813:
810:
809:
804:
799:
794:
779:
778:
776:Turkey-raising
773:
768:
763:
749:
748:
747:
746:
736:
731:
719:
718:
716:Center squeeze
713:
708:
703:
701:Spoiler effect
694:
689:
688:
685:
684:
681:
680:
675:
674:
673:
660:By ballot type
656:
655:
654:
653:
648:
643:
633:
632:
631:
630:
629:
624:
614:
613:
612:
601:
578:
577:
576:
571:
566:
561:
543:
542:
537:
528:
523:
522:
519:
518:
515:
514:
512:Limited voting
509:
508:
507:
488:
487:
482:
477:
472:
471:
470:
465:
446:
445:
440:
435:
430:
416:
415:
410:
405:
400:
386:
385:
384:
383:
381:Localized list
378:
373:
368:
363:
353:
352:
351:
349:Biproportional
346:
341:
336:
320:
315:
314:
311:
310:
307:
306:
301:
296:
291:
277:
276:
261:
246:
222:
221:
220:
219:
214:
209:
204:
194:
180:
179:
178:
177:
166:
153:Instant-runoff
150:
149:
148:
140:Jungle primary
127:
116:Single vote -
114:
109:
108:
105:
104:
102:
101:
91:
86:
81:
76:
70:
67:
66:
56:
55:
45:
44:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5044:
5033:
5030:
5029:
5027:
5014:
5013:
5008:
5007:
5001:
4995:
4992:
4990:
4987:
4986:
4984:
4980:
4974:
4971:
4969:
4966:
4964:
4961:
4959:
4956:
4954:
4951:
4949:
4946:
4944:
4941:
4940:
4938:
4934:
4928:
4925:
4923:
4920:
4918:
4915:
4913:
4910:
4908:
4905:
4903:
4900:
4898:
4895:
4893:
4890:
4888:
4885:
4883:
4880:
4878:
4875:
4873:
4870:
4868:
4865:
4863:
4860:
4858:
4855:
4853:
4850:
4848:
4845:
4844:
4842:
4838:
4832:
4829:
4827:
4824:
4822:
4819:
4817:
4814:
4813:
4811:
4809:
4805:
4799:
4796:
4794:
4791:
4789:
4786:
4784:
4781:
4779:
4776:
4774:
4771:
4769:
4766:
4764:
4761:
4760:
4758:
4756:
4752:
4742:
4739:
4737:
4734:
4732:
4729:
4727:
4724:
4723:
4721:
4717:
4711:
4708:
4704:
4701:
4699:
4696:
4695:
4694:
4691:
4690:
4688:
4684:
4678:
4675:
4673:
4670:
4666:
4663:
4661:
4658:
4656:
4653:
4652:
4651:
4648:
4646:
4643:
4641:
4638:
4636:
4633:
4631:
4628:
4626:
4623:
4621:
4618:
4617:
4615:
4611:
4608:
4606:
4602:
4596:
4593:
4591:
4588:
4586:
4583:
4581:
4578:
4576:
4573:
4571:
4568:
4566:
4563:
4559:
4556:
4554:
4551:
4549:
4546:
4545:
4544:
4541:
4539:
4536:
4534:
4531:
4527:
4524:
4522:
4519:
4517:
4514:
4512:
4509:
4507:
4504:
4502:
4499:
4497:
4494:
4493:
4492:
4489:
4487:
4484:
4482:
4479:
4475:
4472:
4470:
4467:
4466:
4465:
4462:
4461:
4459:
4457:
4456:Single-winner
4453:
4449:
4447:
4443:
4436:
4432:
4425:
4420:
4418:
4413:
4411:
4406:
4405:
4402:
4396:
4393:
4391:
4388:
4386:
4383:
4381:
4378:
4376:
4373:
4371:
4368:
4367:
4363:
4348:
4344:
4337:
4334:
4322:. 11 May 2011
4321:
4317:
4311:
4308:
4304:
4300:
4296:
4292:
4286:
4283:
4278:
4272:
4269:
4256:
4252:
4245:
4242:
4229:
4225:
4219:
4216:
4204:
4200:
4194:
4191:
4188:
4182:
4179:
4171:
4167:
4165:9780199257560
4161:
4157:
4153:
4146:
4139:
4136:
4123:
4116:
4113:
4101:
4097:
4090:
4087:
4083:
4079:
4075:
4071:
4067:
4059:
4055:
4054:Lebeda, Tomáš
4049:
4046:
4033:
4029:
4025:
4018:
4015:
4010:
4004:
4001:
3996:
3992:
3985:
3978:
3975:
3963:
3956:
3949:
3946:
3934:. 20 May 2019
3933:
3929:
3923:
3920:
3916:
3911:
3909:9780875862675
3905:
3901:
3897:
3891:
3888:
3883:
3879:
3875:
3871:
3870:
3862:
3855:
3852:
3847:
3843:
3839:
3835:
3831:
3827:
3823:
3819:
3812:
3809:
3793:
3789:
3785:
3781:
3777:
3770:
3763:
3760:
3752:
3748:
3741:
3734:
3732:
3728:
3722:
3717:
3713:
3709:
3705:
3698:
3696:
3692:
3676:
3672:
3668:
3664:
3660:
3653:
3646:
3644:
3642:
3638:
3622:
3618:
3614:
3610:
3606:
3599:
3592:
3590:
3586:
3581:
3577:
3573:
3569:
3565:
3561:
3554:
3547:
3545:
3543:
3539:
3533:
3525:
3521:
3517:
3513:
3509:
3505:
3501:
3497:
3492:
3483:
3475:
3474:
3465:
3433:
3430:
3423:
3421:
3419:
3418:works council
3415:
3411:
3407:
3403:
3399:
3395:
3391:
3387:
3383:
3379:
3375:
3371:
3367:
3363:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3327:
3323:
3319:
3315:
3311:
3307:
3303:
3299:
3295:
3291:
3287:
3283:
3279:
3275:
3271:
3267:
3263:
3259:
3255:
3251:
3247:
3243:
3239:
3235:
3231:
3227:
3223:
3219:
3215:
3211:
3207:
3203:
3199:
3195:
3191:
3187:
3183:
3179:
3175:
3171:
3163:
3161:
3159:
3155:
3151:
3146:
3142:
3131:
3129:
3125:
3121:
3117:
3112:
3110:
3105:
3100:
3096:
3092:
3087:
3085:
3081:
3077:
3073:
3070:used for the
3069:
3064:
3048:
3038:
3033:
3031:
3022:
3020:
3018:
3012:
3010:
3006:
3002:
2998:
2994:
2990:
2986:
2981:
2979:
2975:
2971:
2967:
2963:
2959:
2955:
2951:
2947:
2943:
2939:
2935:
2931:
2927:
2923:
2919:
2915:
2911:
2907:
2903:
2899:
2894:
2892:
2888:
2880:
2878:
2876:
2871:
2869:
2865:
2860:
2858:
2854:
2847:
2843:
2840:
2835:
2830:
2828:
2821:
2816:
2814:
2810:
2806:
2802:
2797:
2784:
2781:
2778:
2775:
2772:
2769:
2768:
2764:
2761:
2758:
2755:
2752:
2749:
2748:
2744:
2741:
2738:
2735:
2732:
2729:
2728:
2724:
2721:
2718:
2715:
2712:
2709:
2708:
2704:
2701:
2698:
2689:
2688:
2682:
2677:
2672:
2667:
2662:
2659:
2658:
2652:
2640:
2627:
2622:
2618:
2614:
2609:
2605:
2598:
2594:
2590:
2582:
2578:
2574:
2571:
2565:
2560:
2556:
2551:
2546:
2542:
2533:
2529:
2525:
2522:
2516:
2511:
2507:
2503:
2498:
2494:
2485:
2478:
2465:
2458:
2454:
2450:
2445:
2442:
2439:
2434:
2430:
2421:
2378:
2374:
2370:
2367:
2364:
2359:
2355:
2348:
2334:
2321:
2316:
2312:
2306:
2289:
2276:
2271:
2267:
2258:
2255:
2252:
2239:
2234:
2230:
2224:
2216:
2213:
2205:
2187:
2184:
2179:
2175:
2169:
2165:
2160:
2154:
2151:
2148:
2142:
2137:
2133:
2112:
2090:
2086:
2078:
2063:
2060:
2055:
2051:
2045:
2041:
2036:
2030:
2027:
2024:
2018:
2013:
2009:
1988:
1966:
1962:
1954:
1953:
1952:
1949:
1936:
1929:
1925:
1919:
1915:
1909:
1904:
1900:
1891:
1877:
1854:
1851:
1848:
1845:
1842:
1836:
1833:
1825:
1821:
1811:
1809:
1804:
1802:
1798:
1790:
1776:
1770:
1764:
1761:
1758:
1755:
1752:
1751:
1745:
1739:
1736:
1733:
1731:
1728:
1725:
1724:
1718:
1712:
1710:
1707:
1705:
1702:
1700:
1697:
1694:
1693:
1687:
1682:
1679:
1677:
1674:
1672:
1669:
1667:
1664:
1661:
1660:
1654:
1649:
1646:
1643:
1640:
1637:
1634:
1633:
1630:
1626:
1618:
1615:
1613:
1608:
1606:
1601:
1596:
1594:
1589:
1584:
1582:
1577:
1572:
1570:
1565:
1558:
1557:
1554:
1551:
1546:
1541:
1539:
1534:
1529:
1527:
1522:
1517:
1515:
1510:
1505:
1500:
1499:
1493:
1490:
1487:
1484:
1481:
1478:
1475:
1472:
1469:
1464:
1463:
1460:
1453:
1450:
1445:
1440:
1435:
1430:
1425:
1420:
1415:
1410:
1405:
1404:
1401:
1398:
1393:
1388:
1386:
1381:
1376:
1371:
1366:
1361:
1356:
1351:
1350:
1347:
1344:
1339:
1337:
1332:
1327:
1322:
1320:
1315:
1310:
1308:
1303:
1298:
1293:
1292:
1289:
1286:
1284:
1279:
1274:
1269:
1267:
1262:
1257:
1255:
1250:
1245:
1243:
1238:
1233:
1232:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1202:
1197:
1196:
1193:
1191:
1187:
1178:
1176:
1172:
1123:
1117:
1116:
1115:
1112:
1096:
1093:
1090:
1086:
1081:
1068:
1065:
1057:
1055:
1052:
1047:
1045:
1041:
1037:
1033:
1029:
1020:
1018:
1016:
1012:
1009:
1005:
1000:
998:
994:
990:
986:
982:
978:
974:
970:
958:
953:
951:
946:
944:
939:
938:
936:
935:
932:
927:
919:
914:
909:
907:
902:
897:
896:
894:
893:
886:
883:
881:
878:
876:
875:May's theorem
873:
871:
868:
866:
863:
862:
861:
860:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
829:
828:
827:
821:
816:
815:
808:
805:
803:
800:
798:
795:
793:
790:
789:
788:
787:
786:
785:majority rule
783:Paradoxes of
777:
774:
772:
769:
767:
764:
762:
759:
758:
757:
756:
755:
745:
742:
741:
740:
737:
735:
732:
730:
727:
726:
725:
724:
717:
714:
712:
709:
707:
704:
702:
699:
698:
697:
692:
687:
686:
679:
676:
672:
669:
668:
667:
664:
663:
662:
661:
652:
649:
647:
644:
642:
639:
638:
637:
634:
628:
625:
623:
620:
619:
618:
615:
611:
606:
602:
600:
595:
591:
590:
589:
586:
585:
584:
583:
579:
575:
572:
570:
567:
565:
562:
560:
557:
556:
555:
554:
549:
548:
547:
541:
538:
536:
533:
532:
531:
526:
525:Mixed systems
521:
520:
513:
510:
506:
503:
502:
501:
498:
497:
496:
495:
494:
486:
485:Random ballot
483:
481:
478:
476:
473:
469:
466:
464:
461:
460:
459:
456:
455:
454:
453:
452:
444:
441:
439:
436:
434:
431:
429:
426:
425:
424:
423:
422:
414:
411:
409:
406:
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392:
382:
379:
377:
374:
372:
369:
367:
364:
362:
359:
358:
357:
354:
350:
347:
345:
342:
340:
337:
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332:
331:
330:
329:Apportionment
327:
326:
325:
324:
318:
313:
312:
305:
302:
300:
297:
295:
292:
290:
287:
286:
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284:
283:
274:
270:
265:
264:Antiplurality
262:
259:
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247:
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235:
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230:
229:
228:
218:
215:
213:
210:
208:
205:
203:
200:
199:
198:
195:
193:
192:Condorcet-IRV
190:
189:
188:
187:
186:
176:
171:
167:
165:
160:
156:
155:
154:
151:
147:
144:
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119:
112:
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106:
99:
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92:
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87:
85:
82:
80:
77:
75:
74:Social choice
72:
71:
69:
68:
62:
58:
57:
54:
50:
49:Social choice
46:
42:
38:
34:
33:
30:
19:
5010:
5004:
4702:
4620:Mixed-member
4605:Proportional
4580:Score voting
4521:Ranked pairs
4440:Part of the
4439:
4350:. Retrieved
4346:
4336:
4324:. Retrieved
4319:
4310:
4302:
4285:
4271:
4259:. Retrieved
4254:
4244:
4232:. Retrieved
4227:
4218:
4206:. Retrieved
4202:
4193:
4181:
4170:the original
4151:
4138:
4126:. Retrieved
4115:
4103:. Retrieved
4099:
4089:
4069:
4065:
4048:
4036:. Retrieved
4032:the original
4027:
4017:
4003:
3994:
3990:
3977:
3965:. Retrieved
3961:
3948:
3936:. Retrieved
3931:
3922:
3899:
3890:
3873:
3867:
3854:
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3817:
3811:
3799:. Retrieved
3792:the original
3779:
3775:
3762:
3751:the original
3746:
3711:
3707:
3682:. Retrieved
3675:the original
3665:(1): 33–51.
3662:
3658:
3628:. Retrieved
3621:the original
3608:
3604:
3563:
3559:
3523:
3519:
3515:
3511:
3507:
3503:
3499:
3495:
3432:
3282:mixed system
3266:mixed system
3167:
3137:
3113:
3104:Antony Green
3088:
3065:
3034:
3026:
3016:
3013:
3008:
2984:
2982:
2895:
2884:
2872:
2861:
2856:
2849:
2845:
2831:
2823:
2818:
2798:
2795:
2641:
2486:
2479:
2422:
2335:
2259:
2256:
2253:
2206:
2203:
1950:
1892:
1826:. For party
1817:
1808:Helen Wilson
1805:
1794:
1768:
1743:
1729:
1716:
1708:
1703:
1698:
1685:
1680:
1675:
1670:
1665:
1627:
1623:
1616:
1609:
1602:
1590:
1578:
1566:
1552:
1535:
1523:
1511:
1458:
1451:
1399:
1382:
1345:
1333:
1316:
1304:
1287:
1280:
1263:
1251:
1239:
1189:
1185:
1182:
1173:
1135:parties and
1130:
1113:
1069:
1061:
1048:
1024:
1001:
976:
972:
968:
966:
858:
857:
824:
782:
781:
766:Exaggeration
752:
751:
722:
721:
695:
659:
658:
627:Mixed ballot
582:Compensatory
580:
553:compensatory
550:
545:
529:
491:
490:
449:
448:
419:
418:
389:
388:
376:List-free PR
321:
289:Score voting
280:
279:
225:
224:
212:Ranked pairs
183:
182:
115:
29:
4963:Spoilt vote
4726:Droop quota
4665:Schulze STV
4640:Rural–urban
4585:STAR voting
4481:Borda count
4128:14 February
3915:pp. 174–175
3801:11 February
3494:. The name
3420:elections.
3358:Switzerland
3310:Netherlands
2974:Netherlands
2683:Represented
1657:proportion
1635:Denominator
1151:th row and
666:Single vote
569:Conditional
564:Coexistence
413:Quota Borda
403:Schulze STV
361:Closed list
304:STAR voting
249:Borda count
4982:Comparison
4736:Hare quota
4686:Allocation
4672:Spare vote
4660:Hare-Clark
4630:Party-list
4352:28 January
3684:30 January
3630:2 February
3534:References
3342:San Marino
3306:Mozambique
3302:Montenegro
3290:Luxembourg
3238:East Timor
3218:Cape Verde
3122:, such as
3109:Hare-Clark
3023:Variations
2997:South Savo
2922:Montenegro
2910:East Timor
2868:remainders
2820:neglected.
1494:Seats won
1227:Seats won
1032:coalitions
1021:Motivation
1006:and later
771:Truncation
500:Cumulative
323:Party-list
98:By country
89:Comparison
4973:Unseating
4968:Sortition
4570:Plurality
4446:Economics
4082:0038-0288
3962:ucl.ac.uk
3938:6 October
3876:: 80–95.
3846:146438586
3580:122291481
3436:English:
3378:Folketing
3370:Venezuela
3314:Nicaragua
3258:Guatemala
3254:Greenland
3182:Argentina
3128:threshold
2928:(3.25%);
2881:Threshold
2673:Advantage
2623:∗
2619:π
2595:∑
2566:∈
2534:∗
2530:π
2526:−
2517:−
2459:∗
2455:δ
2446:−
2435:∗
2431:π
2368:…
2290:∈
2272:∗
2268:δ
2214:δ
2166:∑
2143:∈
2042:∑
2019:∈
1849:…
1837:∈
1143:rows and
1064:quotients
1058:Procedure
678:Dual-vote
371:Panachage
366:Open list
356:List type
234:Plurality
130:Two-round
118:plurality
41:Economics
5026:Category
4840:Criteria
4793:Scorporo
4442:politics
4320:BBC News
4295:Archived
4261:16 April
4056:(2001),
3560:SIAM Rev
3406:Thailand
3392:and the
3350:Slovenia
3334:Portugal
3322:Paraguay
3226:Colombia
3214:Cambodia
2954:Tanzania
2934:Bulgaria
2930:Slovenia
2875:integers
2678:Residual
1870:, where
1666:100,000*
1188:down to
987:, or in
979:, is an
398:Hare STV
37:Politics
35:A joint
5012:Project
4703:D'Hondt
4655:CPO-STV
4613:Systems
4076:: 442,
4038:25 June
3967:23 June
3838:1963530
3516:D'Hondt
3500:d'Hondt
3496:D'Hondt
3487:French:
3374:Denmark
3366:Uruguay
3338:Romania
3294:Moldova
3270:Iceland
3262:Hungary
3250:Finland
3242:Estonia
3230:Croatia
3210:Burundi
3202:Bolivia
3198:Belgium
3194:Austria
3186:Armenia
3174:Albania
3124:Belgium
3001:Croatia
2993:Uusimaa
2978:Estonia
2970:Belgium
2966:Hungary
2946:Romania
2938:Croatia
2906:Denmark
2902:Albania
2855:as the
1753:Party D
1730:30,000*
1726:Party C
1709:26,667*
1704:40,000*
1699:80,000*
1695:Party B
1681:25,000*
1676:33,333*
1671:50,000*
1662:Party A
1652:won (*)
1567:130,000
1512:100,000
1506:100,000
1496:(bold)
1240:100,000
1229:(bold)
1186:100,000
1179:Example
1114:where:
1028:parties
975:or the
408:CPO-STV
258:Baldwin
207:Schulze
202:Minimax
120:methods
5006:Portal
4943:Ballot
4719:Quotas
4448:series
4326:7 July
4162:
4080:
3906:
3844:
3836:
3578:
3478:Dutch:
3388:, the
3372:. In
3362:Turkey
3346:Serbia
3330:Poland
3298:Monaco
3280:(in a
3274:Israel
3264:(in a
3232:, the
3206:Brazil
3178:Angola
3116:kartel
3078:, and
2962:Poland
2960:(7%);
2958:Turkey
2956:(5%);
2950:Russia
2936:(4%);
2926:Israel
2924:(3%);
2920:, and
2918:Serbia
2908:(2%);
2853:Israel
2745:10.9%
2725:32.6%
2705:43.5%
2685:votes
2680:votes
2675:ratio
2670:share
2665:share
2660:Party
2336:where
1951:where
1778:Total
1759:10,000
1756:20,000
1737:10,000
1734:15,000
1713:20,000
1650:Seats
1610:26,000
1603:32,500
1597:32,500
1591:43,333
1585:43,333
1579:65,000
1573:65,000
1563:round
1547:25,000
1542:25,000
1536:33,333
1530:33,333
1524:50,000
1518:50,000
1465:Round
1446:20,000
1441:20,000
1436:20,000
1431:20,000
1426:20,000
1421:20,000
1416:20,000
1411:20,000
1394:15,000
1389:15,000
1383:30,000
1377:30,000
1372:30,000
1367:30,000
1362:30,000
1357:30,000
1340:20,000
1334:26,667
1328:26,667
1323:26,667
1317:40,000
1311:40,000
1305:80,000
1299:80,000
1281:25,000
1275:25,000
1270:25,000
1264:33,333
1258:33,333
1252:50,000
1246:50,000
1198:Round
1190:25,000
1163:. The
273:Coombs
43:series
4936:Other
4755:Mixed
4234:5 May
4208:4 May
4173:(PDF)
4148:(PDF)
4105:5 May
4072:(4),
4062:(PDF)
3987:(PDF)
3958:(PDF)
3864:(PDF)
3842:S2CID
3834:JSTOR
3795:(PDF)
3772:(PDF)
3754:(PDF)
3743:(PDF)
3678:(PDF)
3655:(PDF)
3624:(PDF)
3601:(PDF)
3576:S2CID
3556:(PDF)
3424:Notes
3354:Spain
3286:Japan
3278:Italy
3222:Chile
3190:Aruba
3170:Åland
2914:Spain
2770:Total
2765:0.0%
2736:12.5%
2733:13.0%
2716:37.5%
2713:34.8%
2696:50.0%
2693:43.5%
1765:5,000
1762:6,667
1740:7,500
1655:True
610:'MMP'
599:'AMS'
4444:and
4354:2022
4328:2013
4263:2021
4236:2018
4210:2024
4160:ISBN
4130:2016
4107:2018
4078:ISSN
4040:2017
3969:2023
3940:2019
3904:ISBN
3803:2016
3686:2016
3632:2016
3472:HONT
3368:and
3326:Peru
3246:Fiji
3126:the
2952:and
2942:Fiji
2932:and
2785:87%
2776:100%
2773:100%
2762:8.7%
2759:0.00
2756:0.0%
2753:8.7%
2742:2.2%
2739:0.96
2722:2.2%
2719:1.08
2702:0.0%
2699:1.15
2668:Seat
2663:Vote
2484:are
1799:for
1773:0.7
1748:1.0
1721:2.8
1690:3.5
1078:quot
1030:and
967:The
551:Non-
505:SNTV
94:List
51:and
39:and
4768:MMP
3878:doi
3826:doi
3784:doi
3716:doi
3667:doi
3613:doi
3568:doi
3470:də-
3284:),
3268:),
2782:13%
2303:max
2281:min
2221:max
269:el.
254:el.
243:IRV
239:el.
5028::
5009:—
4345:.
4318:.
4301:,
4293:"
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4226:.
4201:.
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4098:.
4070:37
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4064:,
4026:.
3995:27
3993:.
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3960:.
3930:.
3874:27
3872:.
3866:.
3840:.
3832:.
3822:84
3820:.
3778:.
3774:.
3745:.
3730:^
3710:.
3706:.
3694:^
3663:10
3661:.
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3609:22
3607:.
3603:.
3588:^
3574:.
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594:UK
170:US
159:UK
142:)
135:US
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3971:.
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2779:—
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