Rated, evaluative, graded, or cardinal voting rules are a class of voting methods that allow voters to state how strongly they support a candidate, by giving each one a grade on a separate scale. The

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...

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 Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy the ind ...

, and their resistance to the

spoiler effect In social choice theory and politics, a spoiler effect happens when a losing candidate affects the results of an election simply by participating. Voting rules that are not affected by spoilers are said to be spoilerproof. The frequency and se ...

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 Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approva ...

systems, where the candidate with the highest average (or total) rating wins. **

Approval voting Approval voting is a single-winner rated voting system where voters can approve of all the candidates as they like instead of Plurality voting, choosing one. The method is designed to eliminate vote-splitting while keeping election administration ...

(AV) is the simplest method, and allows only the two grades (0, 1): "approved" or "unapproved". **

Combined approval voting Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate. The winner is the candidate with the highest score, which is determined by subtracting the number of ap ...

(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 The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...

grade wins. The various highest median rules differ in their tie-breaking methods. However, other rated voting methods have a

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 Cumulative voting (sometimes called the single divisible vote) is an election system where a voter casts multiple votes but can lump votes on a specific candidate or can split their votes across multiple candidates. The candidates elected are tho ...

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 Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several dif ...

due to the

Condorcet paradox In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarante ...

. In addition, there are many different proportional cardinal rules, often called approval-based committee rules. * Phragmen's method *

Proportional approval voting Proportional approval voting (PAV) is a proportional electoral system for multiwinner elections. It is a multiwinner approval method that extends the D'Hondt method of apportionment commonly used to calculate apportionments for party-list prop ...

(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

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 In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properti ...

. Cardinal methods where voters give each candidate a number of points and the points are summed are called ''additive''. Both

range voting Score voting, sometimes called range voting, is an electoral system for single-seat elections. Voters give each candidate a numerical score, and the candidate with the highest average score is elected. Score voting includes the well-known approva ...

and

cumulative voting Cumulative voting (sometimes called the single divisible vote) is an election system where a voter casts multiple votes but can lump votes on a specific candidate or can split their votes across multiple candidates. The candidates elected are tho ...

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 First-past-the-post (FPTP)—also called choose-one, first-preference plurality (FPP), or simply plurality—is a single-winner voting rule. Voters mark one candidate as their favorite, or First-preference votes, first-preference, and the cand ...

. 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.

References

External links