Part of the Politics series |
Electoral systems |
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Rated voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade.[1] These are also referred to as cardinal, evaluative, or graded voting systems.[citation needed] Cardinal methods (based on cardinal utility) and ordinal methods (based on ordinal utility) are the two modern categories of voting systems.[2][3][4]
There are several voting systems that allow independent ratings of each candidate. For example:
In addition, every cardinal system can be converted into a proportional or semi-proportional system by using Phragmen's voting rules or Thiele's voting rules. Examples include:
Ratings ballots can be converted to ranked/preferential ballots, assuming equal ranks are allowed. For example:
Rating (0 to 99) | Preference order | |
---|---|---|
Candidate A | 99 | First |
Candidate B | 55 | Second |
Candidate C | 20 | Third |
Candidate D | 20 | Third |
Cardinal voting methods are not subject to Arrow's impossibility theorem,[9] which proves that ranked-choice voting methods can be manipulated by strategic nominations.[10] However, since one of these criteria (called "universality") implicitly requires that a method be ordinal, not cardinal, Arrow's theorem does not apply to cardinal methods.[11][10]
Others, however, argue that ratings are fundamentally invalid, because meaningful interpersonal comparisons of utility are impossible.[12] This was Arrow's original justification for only considering ranked systems,[13] but later in life he stated that cardinal methods are "probably the best."[14]
Psychological research has shown that cardinal ratings (on a numerical or Likert scale, for instance) are more valid and convey more information than ordinal rankings in measuring human opinion.[15][16][17][18]
Cardinal methods can satisfy the Condorcet winner criterion, usually by combining cardinal voting with a first stage (as in Smith//Score).
The weighted mean utility theorem gives the optimal strategy for cardinal voting under most circumstances, which is to give the maximum score for all options with an above-average expected utility,[19] which is equivalent to approval voting. As a result, strategic voting with score voting often results in a sincere ranking of candidates on the ballot (a property that is impossible for ranked-choice voting, by the Gibbard–Satterthwaite theorem).
Most cardinal methods, including score voting and STAR, pass the Condorcet and Smith criteria if voters behave strategically.[citation needed] As a result, cardinal methods with strategic voters tend to produce results similar to Condorcet methods with honest voters.[citation needed]