Vertimas:Balsavimo sistema

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Balsavimo būdai
Vieno nugalėtojo sistemos
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Balsavimo sistema (kitaip vadinama rinkimine sistema) ar balsavimo teorija leidžia balsuotojams pasirinkti iš galimybių, dažniausiai rinkimuose, kuriuose sprendžiama, kurie kandidatai užims viešas pareigas. Balsavimas naudojamas sprendžiant, kas turi gauti apdovanojimus, pasirenkant veiksmų planą ar kompiuteriniuose skaičiavimuose ieškant problemos sprendimo. Balsavimas gali būti priešinamas su asprendimų priėmimu konsensuso būdu ir hierarchinėmis arba autoritarinėmis sistemomis.

Balsavimo sistemą sudaro balsavimo taisyklės, nustatančios, kada biulenis galioja ir kaip turi būti apdorojami balsai, kad būtų gautas galutinis rezultatas. Mokslo sritis, tirianti formaliai apibrėžtas balsavimo sistemaas, vadinama balsavimo teorija. Jos tyrimų sritis yra tarp politikos mokslų, ekonomikos ir matematikos. Balsavimo teorija formaliai pradėta kurti 18-ame amžiuje, ir nuo to laiko pasiūlyta daugybė balsavimo sistemų.

Balsavimo sistemos atitinka arba absoliučios daugumos, arba proporcingo atstovavimo, arba santykinės daugumos principus su daugybe variacijų ir metodų tokių kaip „pirmasis už [finišo] gairelės“ ar rikiuojamosios sistemos.

Pavyzdžiui, tie, kas nėra pažįstami su balsavimo teorija, dažnai nustemba, kad yra kitokių rinkimų sistemų, arba kad „absoliučios daugumos“ sistemos gali pateikti rezultatus, kurių neremia dauguma. Jeigu visada renkamasi tik iš dviejų galimybių, nugalėtojui nustatyti pakanka vien absoliučios daugumos taisyklės. Tačiau kai yra trys ir daugiau pasirinkimo galimybių, absoliuti dauguma gali neremti nė vienos galimybės. Skirtingos balsavimo sistemos gali duoti labai skirtingus balsavimo rezultatus, ypač tada, kai nėra aišku, kam dauguma teikia pirmenybę.

Daugiau informacijos ieškokite straipsnyje „Skirtingų balsavimo sistemų efektai panašiomis sąlygomis“

Turinys 1 Balsavimo sistemos aspektai 1.1 Biuletenis 1.2 Kandidatų kėlimas 1.3 Nelygiaverčių balsų sistemos 1.4 Esama padėtis (Status quo) 1.5 Rinkimų apygardos 2 Vienintelio nugalėtojo sistemos 2.1 Vieno ar nuosekliojo balso metodai 2.2 Ranked voting methods 2.3 Rated voting methods 2.3.1 Range voting 2.3.2 Approval voting 2.4 Criteria in evaluating single winner voting systems 2.5 Vienmandačių sistemų kriterijų lentelė 3 Multiple-winner methods 3.1 Non-proportional and semi-proportional methods 3.2 Proportional methods 3.3 Semi-proportional methods 4 History 4.1 Early democracy 4.2 Foundations of voting theory 4.3 The single-winner revival 4.4 Influence of game theory 4.5 Post-1980 developments 5 See also 6 References 6.1 General references 6.2 Notes 7 External links

Balsavimo sistemos aspektai

Balsavimo sistema apibrėžia biuletenio formą, turimų balsų skaičių ir skaičiavimo metodą — algoritmą, pagal kurį apskaičuojamas rezultatas. Šis rezultatas gali būti vienas nugalėtojas arba jis gali apimti daugybę nugalėtojų, kaip įstatymų leidybos institucijos rinkimuose. Balsavimo sistema taip pat gali nusakyti, kaip balsavimo galia paskirstoma tarp balsuotojų, ir kaip balsuotojai padalinti į pogrupius (apygardas), kuriuose balsai skaičiuojami nepriklausomai.

Realių rinkimų įgyvendinimas paprastai nelaikomas balsavimo sistemos dalimi. Pavyzdžiui, nors balsavimo sistema abstrakčiai nusako biuletenį, ji neapibrėžia, ar fizinis biultenis turės popieriaus lapo, perforuotos kortelės ar kompiuterio ekrano pavidalą. Balsavimo sistema taip pat nenurodo, ar balsai laikomi slaptais ir kokiu būdu tai užtikrinama, kaip patikrinti, ar balsai suskaičuoti tiksliai, arba kam leidžiama balsuoti. Tai – jau platesnė rinkimų sistemų tema.

Biuletenis

Skirtingos balsavimo sistemos parūpina skirtingus būdus išreikšti savo valią. Tokiose rikiuojamojo biultenio ar „preferencinės“ balsavimo sistemose, kaip Alternatyvinio balsavimo sistema, Borda skaičiavimas arba Condorcet metodas, balsuotojai išrikiuoja rinkčių sąrašą nuo labiausiai iki mažiausiai priimtinos. Vertinamojo balsavimo sistemoje balsuotojai vertina kiekvieną rinktį atskirai. Santykinės daugumos sistemoje (anglakalbėse šalyse žinomoje kaip „first-pass-the-post“ - „pirmas už [finišo] gairelės“), balsuotojai pažymi tik vieną rinktį, o Tvirtinamajame balsavime jie gali žymėti tiek rinkčių, kiek nori. Balsavimo sistemose, kurios leidžia „plumpinimą“, kaip kaupiamasis balsavimas, balsuotojai tam pačiam kandidatui gali atiduoti daugybę balsų.

Kai kurios balsavimo sistemos leidžia papildyti biuletenį papildomomis rinktimis, tokiomis kaip naujų kandidatų įrašymas, balsavimo „prieš visus“ galimybė, arba galimybe išreikšti nepasitikėjimą kandidatu.

Kandidatų kėlimas

Kai kurie metodai šaukia pirminius rinkimus, kuriuose nusprendžiama, kurie kandidatai atsidurs galutiniame biuletenyje.

Nelygiaverčių balsų sistemos

Pagrindinis straipsnis Wikipedijoje: „Nelygiavertis balsavimas“

Daugelis balsavimo sistemų laikosi principo „vienas asmuo, vienas balsas“, reiškiančio, kad visų balsuotojų balsai turi būti vertinami lygiai. Tačiau tai nėra taikoma visiems balsavimams. Korporacijų rinkimuose, pavyzdžiui, kiekvieno balsuotojo balso vertė paprastai atitinka turimą kompanijos akcijų kiekį pagal principą „viena akcija, vienas balsas“. Balsų vertė gali būti tyčia nustatyta nelygi, tarkim, siekiant padidinti geriausiai vertinamų organizacijos narių balsų vertę.

Balso vertė nėra tas pats, kas balsavimo galia. Situacijose kai balsuotojų grupės balsuoja vieningai (pavyzdžiui, politinės partijos parlamente), balsavimo galia nurodo grupės galią pakeisti balsavimo rezultatą. Siekdamos padidinti savo balsavimo galią, grupės gali burtis į koalicijas.

Kai kuriose vokiečių valstybėse, ypač Prusijoje ir Sakonijoje iki 1918 buvo nelygios vertės balsų sistema, žinoma kaip Prūsiškoji luominė balsavimo teisė, kurioje rinkėjai buvo padalinti į tris kategorijas pagal sumokėtą pajamų mokestį. Kiekviena kategorija turėjo vienodą balsavimo galią renkant rinkikus.

Esama padėtis (Status quo)

Kai kurios balsavimo sistemose keliami didesnės daugumos reikalavimai, pvz., jeigu superdaugumos reikalaujama, kad būtų pakeista esama padėtis. Kraštutias atvejis - vieningo pritarimo reikalavimas, kai esamai padėčiai pakeisti reikia kiekvieno balsuojančio asmens pritarimo. Jeigu tai sprendimas, ar priimti naują narį į organizaciją, neigiamas sprendimas taikant šią procedūrą vadinamas blackballing'u.

Kitas būdas, padedantis išsaugoti esamą padėtį, - tai kvorumo reikalavimas, kuris užtikrina, kad esam padėtis išliks, jeigu balsavime nedalyvaus pakankamai daug narių. Kvorumo reikalavimas dažniausiai keliamas tik bendram balsų skaičiui, o ne balsų, atiduotų už laimėtoją, skaičiui; tačiau kartais skatina priešingai nusiteikusius balsuotojus apskritai susilaikyti nuo balsavimo, kad būtų sugriautas kvorumas.

Rinkimų apygardos

Pagrindinis straipsnis Wikipedijoje: „Rinkimų apygarda“

Dažnas balsavimo tikslas - išrinkti įstaymų leidybos instituciją, sudarytą uš daugelio nugalėtojų. Tai galima atlikti, surengus vienerius rinkimus ir išrinkus visus nugalėtojus pagal tą patį balsų rinkinį arba padalinus rinkėjus į apygardas, kuriose iš skirtingų rinkčių renkami skirtingi nugalėtojai.

Tokios šalys kaip Israelis išrenka visą parlamentą vienoje daugiamandatėje (rinkimų apygardoje), o tokios kaip Airijos Respublika arba Belgija, suskaido nacionalinius rinkimus į mažesnes daugiamandates apygardas, o dar kitos - tokios kaip Jungtinės valstijos ar Jungtinė Karalystė - rengia rinkimus tik vienmndatėse apygardose. Tuo tarpu Australijos dviejų rūmųl parlamentas turi vienmnadates apygardas įstatymų leidybos institucijos (žemesniesiems rūmams) ir daugiamandates apygardas Senatui - (aukšteniesiems rūmams). Kai kurios sistemos kaip Papildomų narių sistema, mažesnes (apygardas) įtraukia į didesnes.

Būdas, kuriuo kuriamos apygardos ir skirstomi mandatai gali ryškiai įtakoti rezultatus. Paskirstymas - tai procesas, kuriuo valstijos, regionai ar didesnės sritys gauna vietas, paprastai pagal gyventojų skaičiaus pokyčius pagal valstybinį surašymą. Apygardų perkūrimas - tai procesas, pagal kurį apygardų ribos yra perbraižomos, perskaičiavus mandatus. Abi procedūros gali tapti smarkių politinių ginčų priežastimi tiek dėl neteisingo paskirstymo, kai nustatomas nevienodas atstovų skaičiaus santykis su gyventojų skaičiumi skirtingose apygardose, tiek dėl sukčiavimo su apygardų ribomis (angl. gerrymandering), kai rinkimų apygardų ribomis yra manipuliuojama dėl politinės naudos. Tokio sukčiavimo pavyzdys buvo Jungtinės Karalystės supuvę ir kišeniniai miesteliai - parlamento rinkimų apygardos, turinčios labai menką elektoratą - t.y. apleisti miestai - ir naudotos politikų pernelyg didelei ir nieko neatstovaujančiai įtakai parlamente įgyti. Tai buvo Bendruomenių Rūmų bruožas prieš Didįjį 1832 m. reformų aktą.

Vienintelio nugalėtojo sistemos

Pagrindinis straipsnis Wikipedijoje: „Vieno nugalėtojo sistemos“

Vieno laimėtojo balsavimo sistemos gali būti klasifikuojamos pagal jų biuletenio tipą. Vieno balso sistemose balsuotojas pasirenka tik vieną kandidatą. Rikuojamosiose balsavimo sistemose kiekvienas balsuotojas išrikiuoja kandidatus pagal savo palankumą jiems. Vertinamosiose balsavimo sistemose balsuotojai suteikia taškus kiekvienai kandidatui.

Vieno ar nuosekliojo balso metodai

Labiausiai paplitęs vieno laimėtojo balsavimo metodas, žymiai lenkiantis kitus populiarumu, yra santykinės daugumos metodas (taip pat vadinamas „pirmasis už [finišo] gairelės“ (angl. first-past-the-post) arba „nugalėtojas gauna viską“ (angl. winner-takes-all) metodais). Jame kiekvienas balsuotojas balsuoja už vieną rinktį, ir rinktis, gavusi daugiausiai balsų, laimi netgi tada, kai ji gauna mažiau nei pusę visų balsų.

Atkrintamieji metodai vyksta daugybę santykinio balsavimo turų, kad būtų užtikrinta, jog nugalėtoją išrinko daugiau kaip pusė rinkėjų. Dvituriame atkrintamajame balsavime, antrajame pagal naudojimo dažnumą metode, taikomame rinkimuose, antrasis turas rengiamas su dviem daugiausiai balsų gavusiomis rinktimis, jeigu oirmajame balsavime nė viena rinktis negavo absoliučios daugumos (50% + 1) balsų. Pakaitinio balso rinkimų sistemoje, silpniausi kandidatai šalinami, kol vienas iš kandidatų gauna absoliučią daugumą balsų.

Taip pat naudojamos pirminių rinkimų ir dviturio atkrintomojo balsavimo sistemos. Du kandidatai ar rinktys, gavusios daugiausiai balsų atviruosiuose pirminiuose rinkimuose, patenka į pagrindinį balsavimą. Atkrintamieji ir atvirų pirminių rinkimai skiriasi tuo, kad nugalėtojas niekada neišrenkamas pirminiuose rinkimuose, kai pirmajame atkrintamųjų rinkimų ture nugalėtojas gali būti išrinktas, jeigu vienas kandidatas gautų virš 50% balsų.

Atsitiktinio biultenio metode kiekvienas balsuotojas balsuoja už vieną rinktį, o po to atitiktinai išrenkamas vienas biultenis, pagal kurį nustatomas nugalėtojas. Tai - dažniausiai naudojamas neapibrėžtumo pašalinimo būdas kituose metoduose.

Ranked voting methods

Pagrindinis straipsnis Wikipedijoje: „Preferential voting“

Also known as preferential voting methods, these methods allow each voter to rank the candidates in order of preference. Often it is not necessary to rank all the candidates: unranked candidates are usually considered to be tied for last place. Some ranked ballot methods also allow voters to give multiple candidates the same ranking.

The most common ranked voting method is instant-runoff voting (IRV), also known as the "alternative vote" or simply preferential voting, which uses voters' preferences to simulate an elimination runoff election without multiple voting events. As the votes are tallied, the option with the fewest first-choice votes is eliminated. In successive rounds of counting, the next preferred choice still available from each eliminated ballot is transferred to candidates not yet eliminated. The least preferred option is eliminated in each round of counting until there is a majority winner, with all ballots being considered in every round of counting.

The Borda count is a simple ranked voting method in which the options receive points based on their position on each ballot. A class of similar methods is called positional voting systems.

Other ranked methods include Coombs' method, Supplementary voting, Bucklin voting, and Condorcet method.

Condorcet methods, or pairwise methods, are a class of ranked voting methods that meet the Condorcet criterion. These methods compare every option pairwise with every other option, one at a time, and an option that defeats every other option is the winner. An option defeats another option if a majority of voters rank it higher on their ballot than the other option.

These methods are often referred to collectively as Condorcet methods because the Condorcet criterion ensures that they all give the same result in most elections, where there exists a Condorcet winner. The differences between Condorcet methods occur in situations where no option is undefeated, implying that there exists a cycle of options that defeat one another, called a Condorcet paradox or Smith set. Considering a generic Condorcet method to be an abstract method that does not resolve these cycles, specific versions of Condorcet that select winners even when no Condorcet winner exists are called Condorcet completion methods.

A simple version of Condorcet is Minimax: if no option is undefeated, the option that is defeated by the fewest votes in its worst defeat wins. Another simple method is Copeland's method, in which the winner is the option that wins the most pairwise contests, as in many round-robin tournaments. The Schulze method (also known as "Schwartz sequential dropping", "cloneproof Schwartz sequential dropping" or the "beatpath method") and Ranked Pairs are two recently designed Condorcet methods that satisfy a large number of voting system criteria.

The Kemeny-Young method is a Condorcet method that fully ranks all the candidates from most popular to least popular.

Rated voting methods

Rated ballots allow even more flexibility than ranked ballots, but few methods are designed to use them. Each voter gives a score to each option; the allowable scores could be numeric (for example, from 0 to 100) or could be "grades" like A/B/C/D/F.

Rated ballots can be used for ranked voting methods, as long as the ranked method allows tied rankings. Some ranked methods assume that all the rankings on a ballot are distinct, but many voters would be likely to give multiple candidates the same rating on a rated ballot.

Range voting

In range voting, voters give numeric ratings to each option, and the option with the highest total score wins.

Approval voting

Approval voting, where voters may vote for as many candidates as they like, can be seen as an instance of range voting where the allowable ratings are 0 and 1.

Criteria in evaluating single winner voting systems

In the real world, attitudes toward voting systems are highly influenced by the systems' impact on groups that one supports or opposes. This can make the objective comparison of voting systems difficult. In order to compare systems fairly and independently of political ideologies, voting theorists use voting system criteria, which define potentially desirable properties of voting systems mathematically.

It is impossible for one voting system to pass all criteria in common use. Economist Kenneth Arrow proved Arrow's impossibility theorem, which demonstrates that several desirable features of voting systems are mutually contradictory. For this reason, someone implementing a voting system has to decide which criteria are important for the election.

Using criteria to compare systems does not make the comparison completely objective. For example, it is relatively easy to devise a criterion that is met by one's preferred voting method, and by very few other methods. Doing this, one can then construct a biased argument for the criterion, instead of arguing directly for the method. There is no ultimate authority on which criteria should be considered, but the following are some criteria that are accepted and considered to be desirable by many voting theorists:

• Majority criterion—If there exists a majority that ranks (or rates) a single candidate higher than all other candidates, does that candidate always win?
• Monotonicity criterion—Is it impossible to cause a winning candidate to lose by ranking him higher, or to cause a losing candidate to win by ranking him lower?
• Consistency criterion—If the electorate is divided in two and a choice wins in both parts, does it always win overall?
• Participation criterion—Is voting honestly always better than not voting at all? (This is grouped with the distinct but similar Consistency Criterion in the table below.^[1])
• Condorcet criterion—If a candidate beats every other candidate in pairwise comparison, does that candidate always win? (This implies the majority criterion, above)
• Condorcet loser criterion—If a candidate loses to every other candidate in pairwise comparison, does that candidate always lose?
• Independence of irrelevant alternatives—Is the outcome the same after adding or removing non-winning candidates?
• Independence of clone candidates—Is the outcome the same if candidates identical to existing candidates are added?
• Later-no-harm criterion If, in any election, a voter gives an additional ranking, vote or positive rating to a less preferred candidate, can that additional ranking, vote or rating cause a more preferred candidate to lose?
• Reversal symmetry—If individual preferences of each voter are inverted, does the original winner never win?
• Polynomial time—Can the winner be calculated in a runtime that is polynomial in the number of candidates and in the number of voters?

Vienmandačių sistemų kriterijų lentelė

The following table shows which of the above criteria are met by several single-winner systems.

	Majority	Monotone	Consistency & Participation	Condorcet	Condorcet loser	IIA	Clone independence	Reversal symmetry	Polynomial time
Daugumos sistemos
Santykinės daugumos	Yes	Yes	Yes	No	No	No	No (vote-splitting)	No	Yes
Dviturė	Yes	No	No	No	Yes	No	No (vote-splitting)	No	Yes
Balsavimas rikiuojant
Borda skaičiavimas	No	Yes	Yes	No	Yes	No	No (teaming)	Yes	Yes
Atsarginių balsų	Yes	No	No	No	Yes	No	Yes[2]	No	Yes
Minimax'o	Yes	Yes	No	Yes	No	No	No (vote-splitting)	No	Yes
Kemeny'o-Young'o	Yes	Yes	No	Yes	Yes	No	No	Yes	No
Gretinamų porų	Yes	Yes	No	Yes	Yes	No (see local IIA note)	Yes	Yes	Yes
Schulze's	Yes	Yes	No	Yes	Yes	No (see local IIA note)	Yes	Yes	Yes
Vertinamieji metodai
Approval[3]	Ambiguous	Yes	Yes[4]	No[4]	No	Ambiguous	Ambiguous[5]	Yes	Yes
Range voting[3]	No[4]	Yes	Yes[4]	No[4]	No	Yes[4]	Ambiguous[5]	Yes	Yes

In addition to the above criteria, voting systems are judged using criteria that are not mathematically precise but are still important, such as simplicity, speed of vote-counting, the potential for fraud or disputed results, the opportunity for tactical voting or strategic nomination, and, for multiple-winner methods, the degree of proportionality produced.

It is also possible to simulate large numbers of virtual elections on a computer and see how various voting systems compare in terms of maximum voter satisfaction, called in this context minimum Bayesian regret. Such simulations are sensitive to their assumptions, particularly with regards to voter strategy, but by varying the assumptions they can give repeatable measures that bracket the best and worst cases for a voting system. To date, the only such simulation to compare a wide variety of voting systems was run by a range-voting advocate and has not been peer-reviewed.^[6]

The New Zealand Royal Commission on the Electoral System listed ten criteria for their evaluation of possible new electoral systems for New Zealand. These included fairness between political parties, effective representation of minority or special interest groups, political integration, effective voter participation and legitimacy.

Multiple-winner methods

A vote with multiple winners, such as the election of a legislature, has different practical effects than a single-winner vote. Often, participants in a multiple winner election are more concerned with the overall composition of the legislature than exactly which candidates get elected. For this reason, many multiple-winner systems aim for proportional representation, which means that if a given party (or any other political grouping) gets X% of the vote, it should also get approximately X% of the seats in the legislature. Not all multiple-winner voting systems are proportional.

Non-proportional and semi-proportional methods

Pagrindinis straipsnis Wikipedijoje: „Election by list“

Many multiple-winner voting methods are simple extensions of single-winner methods, without an explicit goal of producing a proportional result. Bloc voting, or plurality-at-large, has each voter vote for N options and selects the top N as the winners. Because of its propensity for landslide victories won by a single winning slate of candidates, bloc voting is non-proportional. Two similar plurality-based methods with multiple winners are the Single Non-Transferable Vote or SNTV method, where the voter votes for only one option, and cumulative voting, described above. Unlike bloc voting, elections using the Single Nontransferable Vote or cumulative voting may achieve proportionality if voters use tactical voting or strategic nomination.

Because they encourage proportional results without guaranteeing them, the Single Nontransferable Vote and cumulative voting methods are classified as semi-proportional. Other methods that can be seen as semi-proportional are mixed methods, which combine the results of a plurality election and a party-list election (described below). Parallel voting is an example of a mixed method because it is only proportional for a subset of the winners.

Proportional methods

Pagrindinis straipsnis Wikipedijoje: „Proportional representation“

Truly proportional methods make some guarantee of proportionality by making each winning option represent approximately the same number of voters. This number is called a quota. For example, if the quota is 1000 voters, then each elected candidate reflects the opinions of 1000 voters, within a margin of error. This can be measured using the Gallagher Index.

Most proportional systems in use are based on party-list proportional representation, in which voters vote for parties instead of for individual candidates. For each quota of votes a party receives, one of their candidates wins a seat on the legislature. The methods differ in how the quota is determined or, equivalently, how the proportions of votes are rounded off to match the number of seats.

The methods of seat allocation can be grouped overall into highest averages methods and largest remainder methods. Largest remainder methods set a particular quota based on the number of voters, while highest averages methods, such as the Sainte-Laguë method and the d'Hondt method, determine the quota indirectly by dividing the number of votes the parties receive by a sequence of numbers.

Independently of the method used to assign seats, party-list systems can be open list or closed list. In an open list system, voters decide which candidates within a party win the seats. In a closed list system, the seats are assigned to candidates in a fixed order that the party chooses. The Mixed Member Proportional system is a mixed method that only uses a party list for a subset of the winners, filling other seats with the winners of regional elections, thus having features of open list and closed list systems.

In contrast to party-list systems, the Single Transferable Vote is a proportional representation system in which voters rank individual candidates in order of preference. Unlike party-list systems, STV does not depend on the candidates being grouped into political parties. Votes are transferred between candidates in a manner similar to instant runoff voting, but in addition to transferring votes from candidates who are eliminated, excess votes are also transferred from candidates who already have a quota.

Semi-proportional methods

An alternative method called Cumulative voting (CV) is a semi-proportional voting system in which each voter has n votes, where n is the number of seats to be elected. Voters can distribute portions of their vote between a set of candidates, fully upon one candidate, or a mixture. It is considered a proportional system in allowing a united coalition representing a m/(n+1) fraction of the voters to be guaranteed to elect m seats of an n-seat election. For example in a 3-seat election, 3/4 of the voters (if united on 3 candidates) can guarantee control over all three seats. (In contrast, plurality at large, which allows a united coalition (majority) (50%+1) to control all the seats.)

Cumulative voting is a common way of holding elections in which the voters have unequal voting power, such as in corporate governance under the "one share, one vote" rule. Cumulative voting is also used as a multiple-winner method, such as in elections for a corporate board.

Cumulative voting is not fully proportional because it suffers from the same spoiler effect of the plurality voting system without a run-off process. A group of like-minded voters divided among "too many" candidates may fail to elect any winners, or elect fewer than they deserve by their size. The level of proportionality depends on how well-coordinated the voters are.

Limited voting is a multi-winner system that gives voters fewer votes than the number of seats to be decided. The simplest and most common form of limited voting is Single Non-Transferable Vote (SNTV). It can be considered a special variation of cumulative voting where a full vote cannot be divided among more than one candidate. It depends on a statistical distributions of voters to smooth out preferences that CV can do by individual voters.

For example, in a 4-seat election a candidate needs 20% to guarantee election. A coalition of 40% can guarantee 2-seats in CV by perfectly splitting their votes as individuals between 2 candidates. In comparison, SNTV tends towards collectively dividing 20% between each candidate by assuming every coalition voter flipped a coin to decide which candidate to support with their single vote. This limitation simplifies voting and counting, at the cost of more uncertainty of results.

History

Early democracy

Voting has been used as a feature of democracy since the 6th century BC, when democracy was introduced by the Athenian democracy. However, in Athenian democracy, voting was seen as the least democratic among methods used for selecting public officials, and was little used, because elections were believed to inherently favor the wealthy and well-known over average citizens. Viewed as more democratic were assemblies open to all citizens, and selection by lot (known as sortition), as well as rotation of office. One of the earliest recorded elections in Athens was a plurality vote that it was undesirable to "win": in the process called ostracism, voters chose the citizen they most wanted to exile for ten years. Most elections in the early history of democracy were held using plurality voting or some variant, but as an exception, the state of Venice in the 13th century adopted the system we now know as approval voting to elect their Great Council.^[7]

The Venetians' system for electing the Doge was a particularly convoluted process, consisting of five rounds of drawing lots (sortition) and five rounds of approval voting. By drawing lots, a body of 30 electors was chosen, which was further reduced to nine electors by drawing lots again. An electoral college of nine members elected 40 people by approval voting; those 40 were reduced to form a second electoral college of 12 members by drawing lots again. The second electoral college elected 25 people by approval voting, which were reduced to form a third electoral college of nine members by drawing lots. The third electoral college elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. They in turn elected a final electoral body of 41 members, who ultimately elected the Doge. Despite its complexity, the system had certain desirable properties such as being hard to game and ensuring that the winner reflected the opinions of both majority and minority factions.^[8] This process was used with little modification from 1268 until the end of the Republic of Venice in 1797, and was one of the factors contributing to the durability of the republic.

Foundations of voting theory

Voting theory became an object of academic study around the time of the French Revolution.^[7] Jean-Charles de Borda proposed the Borda count in 1770 as a method for electing members to the French Academy of Sciences. His system was opposed by the Marquis de Condorcet, who proposed instead the method of pairwise comparison that he had devised. Implementations of this method are known as Condorcet methods. He also wrote about the Condorcet paradox, which he called the intransitivity of majority preferences.^[9]

While Condorcet and Borda are usually credited as the founders of voting theory, recent research has shown that the philosopher Ramon Llull discovered both the Borda count and a pairwise method that satisfied the Condorcet criterion in the 13th century. The manuscripts in which he described these methods had been lost to history until they were rediscovered in 2001.^[10]

Later in the 18th century, the related topic of apportionment began to be studied. The impetus for research into fair apportionment methods came, in fact, from the United States Constitution, which mandated that seats in the United States House of Representatives had to be allocated among the states proportionally to their population, but did not specify how to do so.^[11] A variety of methods were proposed by statesmen such as Alexander Hamilton, Thomas Jefferson, and Daniel Webster. Some of the apportionment methods discovered in the United States were in a sense rediscovered in Europe in the 19th century, as seat allocation methods for the newly proposed system of party-list proportional representation. The result is that many apportionment methods have two names: for instance, Jefferson's method is equivalent to the d'Hondt method, as is Webster's method to the Sainte-Lagu? method, while Hamilton's method is identical to the Hare largest remainder method.^[12]

The Single Transferable Vote system was devised by Carl Andrae in Denmark in 1855, and also in England by Thomas Hare in 1857. Their discoveries may or may not have been independent. STV elections were first held in Denmark in 1856, and in Tasmania in 1896 after its use was promoted by Andrew Inglis Clark. Party-list proportional representation was first implemented to elect European legislatures in the early 20th century, with Belgium implementing it first in 1899. Since then, proportional and semi-proportional methods have come to be used in almost all democratic countries, with most exceptions being former British colonies.^[13]

The single-winner revival

Perhaps influenced by the rapid development of multiple-winner voting methods, theorists began to publish new findings about single-winner methods in the late 19th century. This began around 1870, when William Robert Ware proposed applying STV to single-winner elections, yielding instant runoff voting.^[14] Soon, mathematicians began to revisit Condorcet's ideas and invent new methods for Condorcet completion. Edward J. Nanson combined the newly described instant runoff voting with the Borda count to yield a new Condorcet method called Nanson's method. Charles Dodgson, better known as Lewis Carroll, published pamphlets on voting theory, focusing in particular on Condorcet voting. He introduced the use of matrices to analyze Condorcet elections, though this, too, had already been done in some form in the then-lost manuscripts of Ramon Llull. He also proposed the straightforward Condorcet method known as Dodgson's method.

Ranked voting systems eventually gathered enough support to be adopted for use in government elections. In Australia, IRV was first adopted in 1893, and continues to be used along with STV today. In the United States in the early 20th century, various municipalities began to use Bucklin voting. Bucklin is no longer used in any government elections, and has even been declared unconstitutional in Minnesota.^[15]

Influence of game theory

After John von Neumann and others developed the mathematical field of game theory in the 1940s, new mathematical tools were available to analyze voting systems and strategic voting. This led to significant new results that changed the field of voting theory.^[7] The use of mathematical criteria to evaluate voting systems was introduced when Kenneth Arrow showed in Arrow's impossibility theorem that certain intuitively desirable criteria were actually mutually contradictory, demonstrating the inherent limitations of voting theorems. These circumscribe nonetheless to ordinal voting systems, and do not apply to cardinal ones like range voting, as John Harsanyi pointed out. Arrow's theorem is easily the single most cited result in voting theory, and it inspired further significant results such as the Gibbard-Satterthwaite theorem, which showed that strategic voting is unavoidable in certain common circumstances.

The use of game theory to analyze voting systems also led to discoveries about the emergent strategic effects of certain systems. Duverger's law is a prominent example of such a result, showing that plurality voting often leads to a two-party system. Further research into the game theory aspects of voting led Steven Brams and Peter Fishburn to formally define and promote the use of approval voting in 1977. While approval voting had been used before that, it had not been named or considered as an object of academic study, particularly because it violated the assumption made by most research that single-winner methods were based on preference rankings.

Post-1980 developments

Voting theory has come to focus on voting system criteria almost as much as it does on particular voting systems. Now, any description of a benefit or weakness in a voting system is expected to be backed up by a mathematically defined criterion. Recent research in voting theory has largely involved devising new criteria and new methods devised to meet certain criteria.

Political scientists of the 20th century published many studies on the effects that the voting systems have on voters' choices and political parties,^[16][17][18] and on political stability.^[19][20] A few scholars also studied what effects caused a nation to change for a particular voting system.^{[21][22][23][24][25]} One prominent current voting theorist is Nicolaus Tideman, who formalized concepts such as strategic nomination and the spoiler effect in the independence of clones criterion. Tideman also devised the ranked pairs method, a Condorcet method that is not susceptible to clones. Also, Donald G. Saari has brought renewed interest to the Borda count with the books he has published since 2001. Saari uses geometric models of positional voting systems to promote the Borda count.

The increased availability of computer processing has increased the practicality of using the Kemeny-Young, ranked pairs, and Schulze methods that fully rank all the choices from most popular to least popular.

The advent of the Internet has increased the interest in voting systems. Unlike many other mathematical fields, voting theory is generally accessible enough to non-experts that new results can be discovered by amateurs, and frequently are.

The study of voting systems has influenced a new push for electoral reform that is going on today, with proposals being made to replace plurality voting in governmental elections with other methods. Various municipalities in the United States have begun to adopt instant-runoff voting in the 2000s. New Zealand adopted Mixed Member Proportional for Parliamentary elections in 1993 and Single Transferable Vote for some local elections in 2004 (see Electoral reform in New Zealand). The Canadian province of British Columbia held two unsuccessful referenda (in 2005 and 2009) to adopt an STV system. The Province of Ontario held a Referendum on October 10, 2007, on whether to adopt a Mixed Member Proportional system, which was defeated. An even wider range of voting systems is now seen in non-governmental organizations.

See also

• E-democracy
• Electronic voting
• Opinion poll
• Table of voting systems by nation
• Vote counting system
• Voting machine

References

General references

Notes

External links

• Handbook of Electoral System Choice
• ACE Electoral Knowledge Network Site on electoral systems and management
• A handbook of electoral system Design
• Proportional Representation Society of Australia Electoral reform NGO
• Accurate Democracy: electoral and legislative voting rules
• Electowiki A wiki that focuses on voting theory
• Election methods resource. Concise definitions of various methods.
• National Brainstorming project Canadian site.
• Evaluating Voting Methods by Matt Corks
• OpenSTV Software for computing a variety of voting systems including IRV, STV, and Condorcet.
• Ranked Ballot Voting Methods: tutorial, evaluation, and calculator
• Student's Social Choice by Alex Bogomolny. Illustrates various concepts of choice using Java applets.
• Voting, Arbitration, and Fair Division by Marcus Pivato
• Voting and Election Reform: election calculator and other resources
• Voting Systems by Paul E. Johnson. A textbook-style overview of voting methods and their mathematical properties.
• U.S. Voting System Analysis
• A New Nation Votes: American Elections Returns 1787–1825
• Logicracy On-line referendum engine
• Criteria by Blake Cretney
• Voting Methods: Tutorial and essays by James Green-Armytage
• Electoral systems and the protection and participation of minorities, report by Minority Rights Group, 2006
• Individual Decision Power A new decision making system based on ant society.
• Citizens for Approval Voting
• Center for Range Voting
• Center for Voting and Democracy Advocates using IRV in the United States.
• Analysis of an electronic voting system
• Practical multi-candidate election system
• Designing the Voting System for the Council of the European Union

Category:Public choice theory Category:Psephology Category:Social choice theory Voting system criteria Voting systems