Rated voting

The distribution of ratings for each candidate—i.e. the percentage of voters who assign them a particular score—is called their merit profile. 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.

Since rated methods allow the voters to express how strongly they support a candidate, these methods are not covered by Arrow's impossibility theorem, and their resistance to the spoiler effect becomes a more complex matter. Some rated methods are immune to the spoiler effect when every voter rates the candidates on an absolute scale, but they are not when the voters' rating scales change based on the candidates who are running.

Variants

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