Score voting: Difference between revisions

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in the Olympics to award gold medals to gymnasts.

"Score voting" typically refers to real-world systems in which the voter may give to each candidate any number of points within some specified range, such as 0-5 or 0-10. "Range voting" is the more theoretical mathematical model of Score, in which voters express a real number from 0 to 1.<ref name=":1">{{Cite web|url=https://epub.ub.uni-muenchen.de/653/|title=The Case for Utilitarian Voting|last=Hillinger|first=Claude|date=2005-05-01|website=Open Access LMU|location=Munich|language=en|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1.}}</ref><ref name=":2">{{Cite web|url=https://voteupapp.com/blog/expressive-voting|title=Should you be using a more expressive voting system?|last=|first=|date=|website=VoteUp app|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Score Voting -- it’s just like range voting except the scores are discrete instead of spanning a continuous range.}}</ref><ref>{{Cite web|url=http://rangevoting.org/PreEmProp.html|title=Good criteria support range voting|last=|first=|date=|website=RangeVoting.org|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Definition 1: For us "Range voting" shall mean the following voting method. Each voter provides as her vote, a set of real number scores, each in [0,1], one for each candidate. The candidate with greatest score-sum, is elected.}}</ref><ref>{{Cite web|url=http://scorevoting.net/WarrenSmithPages/homepage/rangevote.pdf|title=Range Voting|last=Smith|first=Warren D.|date=December 2000|website=|archive-url=|archive-date=|dead-url=|access-date=|quote=The “range voting” system is as follows. In a c-candidate election, you select a vector of c real numbers, each of absolute value ≤1, as your vote. E.g. you could vote (+1, −1, +.3, −.9, +1) in a 5-candidate election. The vote-vectors are summed to get a c-vector x and the winner is the i such that xᵢ is maximum.}}</ref>

"Score voting" typically refers to real-world systems in which the voter may give to each candidate any number of points within some specified range, such as 0-5 or 0-10. "Range voting" is the more theoretical mathematical model of Score, in which voters express a real number from 0 to 1<ref name=":1">{{Cite web|url=https://epub.ub.uni-muenchen.de/653/|title=The Case for Utilitarian Voting|last=Hillinger|first=Claude|date=2005-05-01|website=Open Access LMU|location=Munich|language=en|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Specific UV rules that have been proposed are approval voting, allowing the scores 0, 1; range voting, allowing all numbers in an interval as scores; evaluative voting, allowing the scores -1, 0, 1.}}</ref><ref name=":2">{{Cite web|url=https://voteupapp.com/blog/expressive-voting|title=Should you be using a more expressive voting system?|last=|first=|date=|website=VoteUp app|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Score Voting -- it’s just like range voting except the scores are discrete instead of spanning a continuous range.}}</ref><ref>{{Cite web|url=http://rangevoting.org/PreEmProp.html|title=Good criteria support range voting|last=|first=|date=|website=RangeVoting.org|archive-url=|archive-date=|dead-url=|access-date=2018-05-15|quote=Definition 1: For us "Range voting" shall mean the following voting method. Each voter provides as her vote, a set of real number scores, each in [0,1], one for each candidate. The candidate with greatest score-sum, is elected.}}</ref><ref>{{Cite web|url=http://scorevoting.net/WarrenSmithPages/homepage/rangevote.pdf|title=Range Voting|last=Smith|first=Warren D.|date=December 2000|website=|archive-url=|archive-date=|dead-url=|access-date=|quote=The “range voting” system is as follows. In a c-candidate election, you select a vector of c real numbers, each of absolute value ≤1, as your vote. E.g. you could vote (+1, −1, +.3, −.9, +1) in a 5-candidate election. The vote-vectors are summed to get a c-vector x and the winner is the i such that xᵢ is maximum.}}</ref>, though this has often also been used to mean Score voting.

[[Approval voting]] is equivalent to Score voting with only 0 or 1 (approve or abstain) as scores.

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In general, the optimal strategy for range voting is to vote it identically to approval voting, so that all candidates are given either the maximum score or the minimum score. For more detailed strategies, see [[approval voting]].

In both Approval and Score, the best strategy will always involve giving maximal support to your 1st choice(s) and no support to your least favorite(s) (how you score the other candidates will depend more on the situation). This is because this maximizes the chances the candidates you prefer most win and minimizes the chances the candidates you want least win. Because of this, Score and Approval always pass the [[Majority criterion|majority criterion]] in the two-candidate case, and the [[Mutual majority criterion|mutual majority criterion]] (indeed, even the [[Smith criterion]] and [[Condorcet criterion]]) when voters' preferences are dichotomous (i.e. they view all candidates as either good or bad, implying they are all either one of the voter's 1st choices or one of their last choices) for any number of candidates, if all voters are strategic.

In both Approval and Score, the best strategy will always involve [[normalization]], which in itself involves giving maximal support to your 1st choice(s) and no support to your least favorite(s) (how you score the other candidates will depend more on the situation). This is because this maximizes the chances the candidates you prefer most win and minimizes the chances the candidates you want least win. Because of this, Score and Approval always pass the [[Majority criterion|majority criterion]] in the two-candidate case, and the [[Mutual majority criterion|mutual majority criterion]] (indeed, even the [[Smith criterion]] and [[Condorcet criterion]]) when voters' preferences are dichotomous (i.e. they view all candidates as either good or bad, implying they are all either one of the voter's 1st choices or one of their last choices) for any number of candidates, if all voters are strategic.

If half of the voters give every candidate in a set of candidates the maximal score and all other candidates the minimal score, they can guarantee that one of the candidates in that set will tie or win (because every candidate in that set will have at least 50% [[Approval rating|approval]], while all other candidates, receiving support from at most half of the voters, will have at most 50% approval). When a majority of voters do this, they can guarantee one of the candidates in the set will win, rather than only tie or win, therefore Score voting passes a weak form of the [[Mutual majority criterion|mutual majority criterion]].

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== Notes ==

Score voting can be simulated with Approval ballots if every voter votes probabilistically according to their utility value for each candidate i.e. a voter who thinks a candidate is a 6 out of 10 would use a dice or other randomizing device to approve that candidate with only 60% probability. With this approach, the Approval voting winner will probabilistically be the Score voting winner so long as there are many voters. In some sense, cardinal utility is tied to randomness in that it is often considered a better measure than ordinal utility when analyzing decision-making under uncertainty.

Score is probably the only major deterministic voting method which can fail the majority criterion in the two-candidate case. Oftentimes, voting reform proposals for governmental elections implement an alternative voting method when 3+ candidates run, but allow or mandate using [[FPTP]] when only two candidates run, ostensibly for simplicity and because it will elect the pairwise winner anyways; this is not as good an idea if Score is the reform proposal. Indeed, some who prefer Score argue that FPTP is fine for two-candidate elections, but this can lead to an illogicality, which is failing [[Independence of irrelevant alternatives]]: when there is a [[Condorcet cycle]] involving the Score winner when 3+ candidates are running, then if all candidates except the Score winner and the candidate they pairwise lose to drop out of the election, then the use of FPTP will lead to the Score winner now losing even if every voter was honest and had the same preferences. This can be averted by the voters if they use a probabilistic strategy to decide how to vote in the FPTP election however, since they can simulate their margin of strength of preference between the two candidates by choosing to either vote for their preferred candidate between the two or not vote. See the [[Utility]] page for an example.

== References ==