Rated voting



Rated voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as cardinal, evaluative, or graded voting systems. Cardinal methods (based on cardinal utility) and ordinal methods (based on ordinal utility) are the two modern categories of voting systems.

Variants
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:


 * 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, not all rated voting methods are spoilerproof:


 * Quadratic voting is unusual in that it is a cardinal voting system that does not allow independent
 * Cumulative voting is a technically-cardinal voting system that, in practice, behaves like first-past-the-post voting.
 * 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).

In addition, there are many different proportional cardinal rules, often called approval-based committee rules.


 * Phragmen's method
 * Proportional approval voting (Thiele's method)
 * Fair majority voting
 * Method of equal shares
 * Expanding approvals rule

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

Analysis
Cardinal voting methods are not subject to Arrow's impossibility theorem, which proves that ranked-choice voting methods cannot eliminate the spoiler effect.

Others, however, argue that ratings are fundamentally invalid, because meaningful interpersonal comparisons of utility are impossible. This was Arrow's original justification for only considering ranked systems, but later in life he reversed his opinion, stating that cardinal methods are "probably the best".

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.

Cardinal methods can satisfy the Condorcet winner criterion, usually by combining cardinal voting with a first stage (as in Smith//Score).

Strategic voting
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, 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).

Cardinal methods that satisfy spoilerproofness, including score or approval voting, pass the Condorcet and Smith criteria if voters behave strategically. As a result, cardinal methods with strategic voters tend to produce results similar to Condorcet methods with honest voters.