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| Social choice and electoral systems |
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Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. [1] Score voting includes the well-known approval voting (used to calculate approval ratings), but also lets voters give partial (in-between) approval ratings to candidates. [2]
A crude form of score voting was used in some elections in ancient Sparta, by measuring how loudly the crowd shouted for different candidates. [3] [4] [5] This has a modern-day analog of using clapometers in some television shows and the judging processes of some athletic competitions.
Beginning in the 13th century, the Republic of Venice elected the Doge of Venice using a multi-stage process with multiple rounds of score voting. This may have contributed to the Republic's longevity, being partly responsible for its status as the longest-lived democracy in world history. [6] [7] Score voting was used in Greek legislative elections beginning in 1864, during which time it had a many-party system; it was replaced with party-list proportional representation in 1923. [8]
According to Steven J. Brams, approval was used for some elections in 19th century England. [9]
Score voting is used to elect candidates who represent parties in Latvia's Saeima (parliament) in an open list system. [10]
The selection process for the Secretary-General of the United Nations uses a variant on a three-point scale ("Encourage", "Discourage", and "No Opinion"), with permanent members of the United Nations Security Council holding a veto over any candidate. [11] [12]
Proportional score voting was used in Swedish elections in the early 20th century, prior to being replaced by party-list proportional representation. It is still used for local elections.
| Governor Candidates | Score each candidate by filling in a number (0 is worst; 9 is best) | |
|---|---|---|
| 1: Candidate A | → | ⓿①②③④⑤⑥⑦⑧⑨ |
| 2: Candidate B | → | ⓪①②③④⑤⑥⑦⑧❾ |
| 3: Candidate C | → | ⓪①②③④⑤⑥❼⑧⑨ |
In 2018, Fargo, North Dakota, passed a local ballot initiative adopting approval voting for the city's local elections, becoming the first US city to adopt the method. [13] [14] [15]
Score voting is used by the Green Party of Utah to elect officers, on a 0–9 scale. [16]
Members of Wikipedia's Arbitration Committee are elected based on a three-point scale ("Support", "Neutral", "Oppose"). [17]
Non-governmental uses of score voting are common, such as in Likert scales for customer satisfaction surveys and mechanism involving users rating a product or service in terms of "stars" (such as rating movies on IMDb, products at Amazon, apps in the iOS or Google Play stores, etc.). Judged sports such as gymnastics generally rate competitors on a numeric scale.
A multi-winner proportional variant called Thiele's method or reweighted range voting is used to select five nominees for the Academy Award for Best Visual Effects rated on a 0–10 scale. [18]
Suppose that Tennessee is holding an election on the location of its capital. The population is concentrated around four major cities. All voters want the capital to be as close to them as possible. The options are:
The preferences of each region's voters are:
| 42% of voters Far-West | 26% of voters Center | 15% of voters Center-East | 17% of voters Far-East |
|---|---|---|---|
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|
|
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Suppose that 100 voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance.
| Voter from/ City Choice | Memphis | Nashville | Chattanooga | Knoxville | Total |
|---|---|---|---|---|---|
| Memphis | 420 (42 × 10) | 0 (26 × 0) | 0 (15 × 0) | 0 (17 × 0) | 420 |
| Nashville | 168 (42 × 4) | 260 (26 × 10) | 90 (15 × 6) | 85 (17 × 5) |  603 |
| Chattanooga | 84 (42 × 2) | 104 (26 × 4) | 150 (15 × 10) | 119 (17 × 7) | 457 |
| Knoxville | 0 (42 × 0) | 52 (26 × 2) | 90 (15 × 6) | 170 (17 × 10) | 312 |
Nashville, the capital in real life, likewise wins in the example.
For comparison, note that traditional first-past-the-post would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city. Instant-runoff voting would elect the 2nd-worst choice (Knoxville), because the central candidates would be eliminated early (and Chattanooga voters preferring Knoxville above Nashville). In approval voting, with each voter selecting their top two cities, Nashville would win because of the significant boost from Memphis residents.
Score voting allows voters to express preferences of varying strengths, making it a rated voting system.
Score voting is not vulnerable to the less-is-more paradox, i.e. raising a candidate's rating can never hurt their chances of winning. Score also satisfies the participation criterion, i.e. a candidate can never lose as a result of voters turning out to support them. Score voting satisfies independence of irrelevant alternatives, and does not tend to exhibit spoiler effects.
It does not satisfy the Condorcet criterion, i.e. the method does not always agree with the majority rule. However, when voters all vote strategically, basing their votes on polling or past election results, the majority-preferred candidate will win. [19]
Ideal score voting strategy for well-informed voters is generally identical to their optimal approval voting strategy; voters will want to give their least and most favorite candidates a minimum and a maximum score, respectively. The game-theoretical analysis shows that this claim is not fully general, but holds in most cases. [20] Another strategic voting tactic is given by the weighted mean utility theorem, maximum score for all candidates preferred compared to the expected winners weighted with winning probability and minimum score for all others. [21]
Papers have found that "experimental results support the concept of bias toward unselfish outcomes in large elections." The authors observed what they termed ethical considerations dominating voter behavior as pivot probability decreased. This would imply that larger elections, or those perceived as having a wider margin of victory, would result in fewer tactical voters. [22]
How voters precisely grade candidates is a topic that is not fully settled, although experiments show that their behavior depends on the grade scale, its length, and the possibility to give negative grades. [23]
STAR voting (Score Then Automatic Runoff) is a variant proposed to address some concerns about strategic exaggeration in score voting. Under this system, each voter may assign a score (from 0 to the maximum) to any number of candidates. Of the two highest-scoring candidates, the winner is the one most voters ranked higher. [24] The runoff step was introduced to mitigate the incentive to exaggerate ratings in ordinary score voting. [25] [26]
Albert Heckscher was one of the earliest proponents, advocating for a form of score voting he called the "immanent method" in his 1892 dissertation, in which voters assign any number between -1 and +1 to each alternative, simulating their individual deliberation. [27] [28] [29]
Currently, score voting is advocated by The Center for Election Science.[ citation needed ] Since 2014, the Equal Vote Coalition advocates a variant method (STAR) with an extra second evaluation step to address some of the criticisms of traditional score voting. [30] [31]
Simplified forms of score voting automatically give skipped candidates the lowest possible score for the ballot they were skipped. Other forms have those ballots not affect the candidate's rating at all. Those forms not affecting the candidates rating frequently make use of quotas. Quotas demand a minimum proportion of voters rate that candidate in some way before that candidate is eligible to win.
voting rules in which the voter freely grades each candidate on a pre-defined numerical scale. .. also called utilitarian voting
Using the following Range Voting System, the Green Party of Utah elected a new slate of officers
Five productions shall be selected using reweighted range voting to become the nominations for final voting for the Visual Effects award.
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Approval voting is a single-winner rated voting system in which voters mark all the candidates they support, instead of just choosing one. It is a form of score voting where only two scores are allowed: 0 and 1 (approved). The candidate with the highest approval rating is elected. Approval voting is currently in use for government elections in St. Louis, Missouri, USA, Fargo, North Dakota, USA, and in the United Nations to elect the Secretary General.
Plurality voting refers to electoral systems in which the candidates in an electoral district who poll more than any other are elected.
Proportional representation (PR) refers to any type of electoral system under which subgroups of an electorate are reflected proportionately in the elected body. The concept applies mainly to political divisions among voters. The essence of such systems is that all votes cast – or almost all votes cast – contribute to the result and are effectively used to help elect someone. Under other election systems, a bare plurality or a scant majority are all that are used to elect candidates. PR systems provide balanced representation to different factions, reflecting how votes are cast.
The two-round system, also called ballotage, top-two runoff, or two-round plurality, is a single winner voting method. It is sometimes called plurality-runoff, although this term can also be used for other, closely-related systems such as instant-runoff voting or the exhaustive ballot. It falls under the class of plurality-based voting rules, together with instant-runoff and first-past-the-post (FPP). In a two-round system, if no candidate receives a majority of the vote in the first round, the two candidates with the most votes in the first round proceed to a second round where all other candidates are excluded. Both rounds are held under choose-one voting, where the voter marks a single favored candidate.
The single transferable vote (STV) or proportional-ranked choice voting (P-RCV), is a multi-winner electoral system in which each voter casts a single vote in the form of a ranked ballot. Voters have the option to rank candidates, and their vote may be transferred according to alternative preferences if their preferred candidate is eliminated or elected with surplus votes, so that their vote is used to elect someone they prefer over others in the running. STV aims to approach proportional representation based on votes cast in the district where it is used, so that each vote is worth about the same as another.
Strategic or tactical voting is voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results.
In social choice, a no-show paradox is a surprising behavior in some voting rules, where a candidate loses an election as a result of having too many supporters. More formally, a no-show paradox occurs when adding voters who prefer Alice to Bob causes Alice to lose the election to Bob. Voting systems without the no-show paradox are said to satisfy the participation criterion.
The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Both methods are designed to satisfy the Condorcet criterion, and allow for incomplete ballots and equal rankings.
An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating.
Rated, evaluative, graded, or cardinalvotingrules are a class of voting methods that allow voters to state how strongly they support a candidate, by giving each one a grade on a separate scale.
Ranked voting is any voting system that uses voters' rankings of candidates to choose a single winner or multiple winners. More formally, a ranked system is one that depends only on which of two candidates is preferred by a voter, and as such does not incorporate any information about intensity of preferences. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies and are only applied when all higher-ranked preferences on a ballot have been eliminated or when one of the higher ranked preferences has been elected and surplus votes need to be transferred.
Proportional approval voting (PAV) is a proportional electoral system for multiwinner elections. It is a multiwinner approval method that extends the D'Hondt method of apportionment commonly used to calculate apportionments for party-list proportional representation. However, PAV allows voters to support only the candidates they approve of, rather than being forced to approve or reject all candidates on a given party list.
Sequential proportional approval voting (SPAV) or reweighted approval voting (RAV) is an electoral system that extends the concept of approval voting to a multiple winner election. It is a simplified version of proportional approval voting. It is a special case of Thiele's voting rules, proposed by Danish statistician Thorvald N. Thiele in the early 1900s. It was used in Sweden from 1909 to 1921, when it was replaced by a cruder "party-list" style system as it was easier to calculate, and is still used for some local elections.
This article discusses the methods and results of comparing different electoral systems. There are two broad ways to compare voting systems:
Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate. The winner is the candidate with the highest score, which is determined by subtracting the number of approval votes by the number of disapproval votes.
STAR voting is an electoral system for single-seat elections. The name stands for "Score Then Automatic Runoff", referring to the fact that this system is a combination of score voting, to pick two finalists with the highest total scores, followed by an "automatic runoff" in which the finalist who is preferred on more ballots wins. It is a type of cardinal voting electoral system.
The sincere favorite or no favorite-betrayal criterion is a property of some voting systems that says voters should have no incentive to vote for someone else over their favorite. It protects voters from having to engage in lesser-evil voting or a strategy called "decapitation".
The highest median voting rules are a class of graded voting rules where the candidate with the highest median rating is elected.
Multiwinner approval voting, sometimes also called approval-based committee (ABC) voting, refers to a family of multi-winner electoral systems that use approval ballots. Each voter may select ("approve") any number of candidates, and multiple candidates are elected.