Rated, evaluative,[1] graded,[1] or cardinal voting systems are a class of voting methods which allow voters to state how strongly they support a candidate,[2] which involves giving each one a grade on a separate scale.[1] Cardinal methods (based on cardinal utility) and ordinal methods (based on ordinal utility) are the two categories of modern voting systems.[2][3]
The distribution of ratings for each candidate—i.e. the percentage of voters who assign them a particular score—is called their merit profile.[4] For example, if candidates are graded on a 4-point scale, one candidate's merit profile may be 25% on every possible rating (1, 2, 3, and 4), while a perfect candidate would have a merit profile where 100% of voters assign them a score of 4.
There are several voting systems that allow independent ratings of each candidate, which allow them to avoid Arrow's theorem and satisfy spoilerproofness. For example:
However, not all rated voting methods are spoilerproof:
In addition, there are many different proportional cardinal rules, often called approval-based committee rules.
Ratings ballots can be converted to ranked/preferential ballots, assuming equal ranks are allowed. For example:
Cardinal voting methods are not subject to Arrow's impossibility theorem,[9] which proves that ranked-choice voting methods cannot eliminate the spoiler effect.[10][dead link][11]
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 reversed his opinion, stating that he is "a little inclined to think that [cardinal methods are] probably the best".[11]
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.[14][15][16][17]
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,[18] 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).
A key feature of evaluative voting is a form of independence: the voter can evaluate all the candidates in turn ... another feature of evaluative voting ... is that voters can express some degree of preference.
Ordinal utility is a measure of preferences in terms of rank orders—that is, first, second, etc. ... Cardinal utility is a measure of preferences on a scale of cardinal numbers, such as the scale from zero to one or the scale from one to ten.
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.
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.
I favor 'evaluative voting' under which a voter can vote for or against any alternative, or abstain.
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(help)under CAV he has three options—cast one vote in favor, abstain, or cast one vote against.
But Arrow only intended his criteria to apply to ranking systems.
CES: you mention that your theorem applies to preferential systems or ranking systems. ... But the system that you're just referring to, Approval Voting, falls within a class called cardinal systems. ... Dr. Arrow: And as I said, that in effect implies more information. ... I'm a little inclined to think that score systems where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best.
Many voting theorists have resisted asking for more than a ranking, with economics-based reasoning: utilities are not comparable between people. ... But no economist would bat an eye at asking one of the A voters above whether they'd prefer a coin flip between A and B winning or C winning outright...
the scale-of-values method can be used for approximately the same purposes as the order-of-merit method, but that the scale-of-values method is a better means of obtaining a record of judgments
The extremely high degree of correspondence found between ranking and rating averages ... does not leave any doubt about the preferability of the rating method for group description purposes. The obvious advantage of rating is that while its results are virtually identical to what is obtained by ranking, it supplies more information than ranking does.
Many value researchers have assumed that rankings of values are more valid than ratings of values because rankings force participants to differentiate more incisively between similarly regarded values ... Results indicated that ratings tended to evidence greater validity than rankings within moderate and low-differentiating participants. In addition, the validity of ratings was greater than rankings overall.
the test-retest reliabilities of the ranking items were slightly higher than were those of the rating items, but construct validities were lower. Because validity is the most important consideration ... the findings of the present research support the use of the rating format in assessing health values. ... added benefit of item independence, which allows for greater flexibility in statistical analyses. ... also easier than ranking items for respondents to complete.