Rated voting

There are several voting systems that allow independent ratings of each candidate, which allow them to be immune to the spoiler effect given certain types of voter behavior. For example: • Score voting systems, where the candidate with the highest average (or total) rating wins. • Approval voting (AV) is the simplest method, and allows only the two grades (0, 1): "approved" or "unapproved". • Combined approval voting (CAV) uses 3 grades (−1, 0, +1): "against", "abstain", or "for." • Range voting refers to a variant with a continuous scale from 0 to 1. • The familiar five-star classification system is a common example, and allows for either 5 grades or 10 (if half-stars are used). • Highest median rules, where the candidate with the highest median grade wins. The various highest median rules differ in their tie-breaking methods. However, other rated voting methods have a spoiler effect no matter what scales the voters use: • Quadratic voting is unusual in that it is a cardinal voting system that does not allow independent scoring of candidates. • Cumulative voting could be classified as a cardinal rule with unconditional spoiler effects. • STAR (score then automatic runoff) is a hybrid of ranked and rated voting systems. It chooses the top 2 candidates by score voting, who then advance to a runoff round (where the candidate is elected by a simple plurality). • Any hybrid of a ranked and rated voting system that reduces to majority rule when only two candidates are running fails independence of irrelevant alternatives due to the Condorcet paradox. In addition, there are many different proportional cardinal rules, often called approval-based committee rules. • Phragmen's method • Proportional approval voting (Thiele's method) • Method of equal shares == Relationship to rankings ==

Ratings ballots can be converted to ranked/preferential ballots, assuming equal ranks are allowed. For example: == Analysis ==

Arrow's impossibility theorem does not apply to cardinal rules. Psychological research has shown that cardinal ratings (on a numerical or Likert scale, for instance) convey more information than ordinal rankings in measuring human opinion. Cardinal methods can satisfy the Condorcet winner criterion, usually by combining cardinal voting with a first stage (as in Smith//Score). Strategic voting Like all (deterministic, non-dictatorial, multicandidate) voting methods, rated methods are vulnerable to strategic voting, due to Gibbard's theorem. Cardinal methods where voters give each candidate a number of points and the points are summed are called additive. Both range voting and cumulative voting are of this type. With a large number of voters, the strategic Myerson-Weber equilibria for such methods are the same as for methods where only extreme ballots are allowed. In this setting, the optimal strategy for Range voting is the same as for approval voting, and the optimal strategy for cumulative voting is the same as for first-past-the-post. For approval voting (and thus Range voting), the optimal strategy involves approving (or rating maximum) everybody above a certain utility threshold, and not approving (or rating minimum) everybody below it. == See also ==