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Rated voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. [1] These are also referred to as cardinal, evaluative, or graded voting systems.[ citation needed ] Cardinal methods (based on cardinal utility) and ordinal methods (based on ordinal utility) are the two modern categories of voting systems. [2] [3] [4]
There are several voting systems that allow independent ratings of each candidate. For example:
In addition, every cardinal system can be converted into a proportional or semi-proportional system by using Phragmen's voting rules or Thiele's voting rules. Examples include:
Ratings ballots can be converted to ranked/preferential ballots, assuming equal ranks are allowed. For example:
| Rating (0 to 99) | Preference order | |
|---|---|---|
| Candidate A | 99 | First |
| Candidate B | 55 | Second |
| Candidate C | 20 | Third |
| Candidate D | 20 | Third |
Cardinal voting methods are not subject to Arrow's impossibility theorem, [9] which proves that ranked-choice voting methods can be manipulated by strategic nominations. [10] However, since one of these criteria (called "universality") implicitly requires that a method be ordinal, not cardinal, Arrow's theorem does not apply to cardinal methods. [11] [10]
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 stated that cardinal methods are "probably the best." [14]
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. [15] [16] [17] [18]
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, [19] 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).
Most cardinal methods, including score voting and STAR, pass the Condorcet and Smith criteria if voters behave strategically.[ citation needed ] As a result, cardinal methods with strategic voters tend to produce results similar to Condorcet methods with honest voters.[ citation needed ]
Approval voting is an electoral system in which voters can select any number of candidates instead of selecting only one.
Score voting or range voting is an electoral system for single-seat elections, in which voters give each candidate a score, the scores are added, and the candidate with the highest total is elected. It has been described by various other names including evaluative voting, utilitarian voting, interval measure voting, point-sum voting, ratings summation, 0-99 voting, and average voting. It is a type of cardinal voting electoral system that aims to approximate the utilitarian social choice rule.
Strategic or tactical voting is a situation where a voter considers the possible ballots cast by other voters in order to maximize their satisfaction with the election's results. For example, in plurality or instant-runoff, a voter may recognize their favorite candidate is unlikely to win and so instead support a candidate they think is more likely to win.
In social choice theory and politics, the spoiler effect refers to a situation where the entry of a losing candidate affects the results of an election. A voting system that is not affected by spoilers satisfies independence of irrelevant alternatives or independence of spoilers.
Arrow's impossibility theorem is a key impossibility theorem in social choice theory, showing that no ranked voting rule can produce a logically coherent ranking of more than two candidates. Specifically, no such rule can satisfy a key criterion of rational choice called independence of irrelevant alternatives: that a choice between and should not depend on the quality of a third, unrelated outcome .
In welfare economics and social choice theory, a social welfare function—also called a socialordering, ranking, utility, or choicefunction—is a function that ranks a set of social states by their desirability. A social welfare function takes two possible outcomes, then combines every person's preferences to determine which outcome is considered better by society as a whole. Inputs to the function can include any variables that affect the well-being of a society.
Independence of irrelevant alternatives (IIA), also known as binary independence, the independence axiom, is an axiom of decision theory and economics describing a necessary condition for rational behavior. The axiom says that a choice between and should not depend on the quality of a third, unrelated outcome .
The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and states that for every voting rule of this form, at least one of the following three things must hold:
Bucklin voting is a class of voting methods that can be used for single-member and multi-member districts. As in highest median rules like the majority judgment, the Bucklin winner will be one of the candidates with the highest median ranking or rating. It is named after its original promoter, the Georgist politician James W. Bucklin of Grand Junction, Colorado, and is also known as the Grand Junction system.
The majority criterion is a voting system criterion. The criterion states that "if only one candidate is ranked first by a majority of voters, then that candidate must win."
Social choice theory or social choice is a branch of welfare economics that analyzes mechanisms and procedures for collective decision-making. Social choice incorporate insights from economics, mathematics, and game theory to find the best ways to combine individual opinions, preferences, or beliefs into a single coherent measure of the quality of different outcomes, called a social welfare function.
Positional voting is a ranked voting electoral system in which the options or candidates receive points based on their rank position on each ballot and the one with the most points overall wins. The lower-ranked preference in any adjacent pair is generally of less value than the higher-ranked one. Although it may sometimes be weighted the same, it is never worth more. A valid progression of points or weightings may be chosen at will or it may form a mathematical sequence such as an arithmetic progression, a geometric one or a harmonic one. The set of weightings employed in an election heavily influences the rank ordering of the candidates. The steeper the initial decline in preference values with descending rank, the more polarised and less consensual the positional voting system becomes.
Allan Fletcher Gibbard is the Richard B. Brandt Distinguished University Professor of Philosophy Emeritus at the University of Michigan, Ann Arbor. Gibbard has made major contributions to contemporary ethical theory, in particular metaethics, where he has developed a contemporary version of non-cognitivism. He has also published articles in the philosophy of language, metaphysics, and social choice theory: in social choice, he first proved the result known today as Gibbard-Satterthwaite theorem, which had been previously conjectured by Michael Dummett and Robin Farquharson.
Kenneth Arrow's monograph Social Choice and Individual Values and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. Somewhat formally, the "social choice" in the title refers to Arrow's representation of how social values from the set of individual orderings would be implemented under the constitution. Less formally, each social choice corresponds to the feasible set of laws passed by a "vote" under the constitution even if not every individual voted in favor of all the laws.
Majority judgment (MJ) is a single-winner voting system proposed in 2010 by Michel Balinski and Rida Laraki. It is a kind of highest median rule, a cardinal voting system that elects the candidate with the highest median rating.
The term ranked voting, also known as preferential voting or ranked-choice voting, pertains to any voting system where voters indicate a rank to order candidates or options—in a sequence from first, second, third, and onwards—on their ballots. Ranked voting systems vary based on the ballot marking process, how preferences are tabulated and counted, the number of seats available for election, and whether voters are allowed to rank candidates equally.
A major branch of social choice theory is devoted to the comparison of electoral systems, otherwise known as social choice functions. Viewed from the perspective of political science, electoral systems are rules for conducting elections and determining winners from the ballots cast. From the perspective of economics, mathematics, and philosophy, a social choice function is a mathematical function that determines how a society should make choices, given a collection of individual preferences.
Combined approval voting (CAV) is an electoral system where each voter may express approval, disapproval, or indifference toward each candidate. The winner is the most-approved candidate.
The no favorite betrayal criterion, sincere favorite criterion, or simply favorite betrayal criterion is a voting system criterion which requires that it must always be safe for a voter to give their true favorite candidate maximum support. They must never have reason to worry that doing so will cause a worse outcome in the election.
The highest median voting rules are a class of graded voting rules where the candidate with the highest median rating is elected.
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.
{{cite journal}}: Cite journal requires |journal= (help)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.
{{cite journal}}: Cite journal requires |journal= (help)under CAV he has three options—cast one vote in favor, abstain, or cast one vote against.
{{cite journal}}: Cite journal requires |journal= (help)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...
CES: you mention that your theorem applies to preferential systems or ranking systems. ... But ... 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 ... is probably the best.
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.