Score voting: Difference between revisions

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about those candidates.

== Criteria ==

Range voting satisfies the [[monotonicity criterion]], the [[participation criterion]], the [[Consistency Criterion]], the [[summability criterion]], the [[Favorite Betrayal criterion]], [[Independence of irrelevant alternatives]], the [[Non-compulsory support criterion]], Mono-Add-Top, [[Pareto criterion]], Plurality Criterion, and [[Strategic nomination|independence of clones]].

Range voting satisfies the [[monotonicity criterion]], the [[participation criterion]], the [[Consistency Criterion]], the [[summability criterion]], the [[Favorite Betrayal criterion]], [[Independence of irrelevant alternatives]], the [[Non-compulsory support criterion]], Mono-Add-Top, [[Pareto criterion]], [[Plurality criterion#Plurality criterion for rated ballots|Plurality Criterion for rated ballots]], and [[Strategic nomination|independence of clones]].

=== Majority-related criteria ===

Range voting does not comply with the [[Condorcet criterion]] because it allows for the difference between 'rankings' to matter. E.g. 51 people might rate A at 100, and B at 90, while 49 people rate A at 0, and B at 100. Condorcet would consider this 51 people voting A>B, and 49 voting B>A, and A would win. Range voting would see this as A having support of 5100/100 = 51%, and B support of (51*90+49*100)/100 = 94.9%. Score voting advocates say that in this case, the Condorcet winner is not the socially ideal winner.

Range voting does not comply with the [[Condorcet criterion]] because it allows for the difference between 'rankings' to matter (though see the [[rated pairwise preference ballot]] for an alternative way to do this). E.g. 51 people might rate A at 100, and B at 90, while 49 people rate A at 0, and B at 100. Condorcet would consider this 51 people voting A>B, and 49 voting B>A, and A would win. Range voting would see this as A having support of 5100/100 = 51%, and B support of (51*90+49*100)/100 = 94.9%. Score voting advocates say that in this case, the Condorcet winner is not the socially ideal winner.

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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, so therefore Score voting passes a weak form of the [[mutual majority criterion]].

== Counting the Votes ==

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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.

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In general, unlike almost any other voting method, the only [[Strategic voting|strategies]] that are possible in Score voting are to either score a candidate higher to increase their chances of winning, or score a candidate lower to decrease their chances of winning. There is never incentive for "order-reversal" (i.e. voting as if candidate X is better than candidate Y if you prefer Y to X). Because of this, Score can be thought of as a "perfectly [[Monotonicity|monotonic]]" voting method.

⚫

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]].

⚫

In general, unlike almost any other voting method, the only [[Strategic voting|strategies]] that are possible in Score voting are to either score a candidate higher to increase their chances of winning, or score a candidate lower to decrease their chances of winning. There is never incentive for "order-reversal" (i.e. voting as if a candidate ~~you prefer~~ is ~~actually worse~~ than a candidate you ~~honestly~~ prefer ~~them~~ ~~more~~ ~~than~~). Because of this, Score can be thought of as a "perfectly [[Monotonicity|monotonic]]" voting method.

Range voting has an advantage over approval voting if

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== Notes ==

It is often argued that Score can do a much better job of electing consensus candidates than many ranked methods; one commonly discussed implication of this is that Score may neuter the effectiveness of gerrymandering (see [[Gerrymandering#Cardinal methods]]), and thus could be even better than [[Proportional representation]] in the sense of also giving voters good geographical single-winner district representation.

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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 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. See also the [[KP transform]].

=== Two-candidate case ===

Score is probably the only major deterministic voting method which can fail the majority criterion in the two-candidate case. It is, however, practically impossible to happen in practice since the scale for score voting is set by the candidates who run. With only two candidates each voter will vote one candidate at each extreme of the scale resulting in a reduction to approval voting. It is then also very unlikely that any voter would approve of both or neither candidate when voting. 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. Some who prefer Score argue that FPTP is fine for two-candidate elections since score will reduce to FPTP for rational voters.

Score is probably the only major deterministic voting method which can fail the [[majority criterion]] in the two-candidate case. It is, however, practically impossible to happen in practice since the scale for score voting is set by the candidates who run. With only two candidates each voter will vote one candidate at each extreme of the scale resulting in a reduction to approval voting. It is then also very unlikely that any voter would approve of both or neither candidate when voting. 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. Some who prefer Score argue that FPTP is fine for two-candidate elections since score will reduce to FPTP for rational voters.

Despite this, if enough voters vote in a way contrary both to how the system is intended and their honest interest there can be results similar to 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. Such a situation is virtually impossible since if a winner drops out after an election another will be held. 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.