Multicriteria Ranking

In this chapter, the majority judgment is extended to multicriteria problems. The most reasonable application of the majority judgment to multicriteria evaluation can be achieved by using a common language. The use of a particular procedure for multicriteria inputs will depend on the particular application. The chapter also describes several types of multicriteria majority judgments, including the judge-based majority judgment in which majority-grades of the sum of the points are calculated, and the criterion-based majority judgment in which first majority-grade of each criterion’s grades are calculated. It furthermore defines judge-based and criterion-based majority judgment procedures, which include a judge-based procedure and criterion-based procedure.

The Game of Voting

This chapter compares majority judgment mechanism to other methods, including first-past-the-post and Borda’s method, among others, in the context of the game of voting. The concept of utilities, which depends on grade distribution of the electorate, is extended to election output. When the identity of the election winner is dependent on the utilities of voters, Condorcet-winner is elected by a large number of strong-equilibria strategy-profiles. The chapter explores best-response correspondence, according to which, if the number of possible equilibria is very small and sometimes unique, the Condorcet-winner emerges as the unique, possible equilibrium outcome and honest votes determine the election outcome.

Approval Voting

This chapter discusses and analyzes approval voting, one of the point-summing methods where each voter is allowed to cast as many votes as he wishes. The form in which approval voting is practiced currently is an example of range-voting, in which there are only two meaningless scores. The approval voting experiments conducted under the conditions of the Orsay experiment of 2007 demonstrates support to the theoretical claims for and against it. The concept of approval judgment, which differs from approval voting in its traditional practice, which makes clear that the evaluations are absolute grades, is also discussed. One of the drawbacks of approval voting is that a candidate preferred by only one voter of the electorate is likely to be elected when strategic behavior is ignored.

Point-Summing Methods

This chapter discusses and analyzes reasons why point-summing methods are not acceptable methods for electing and ranking. Points invite comparisons and not evaluations, and when they are in large numbers, there is a large difference in their meanings and uses among the voters. Summing or averaging numbers, without constituting an interval measure, is of no use, as these numbers are not drawn from a bona fide interval scale. Point-summing methods are not used in political elections because such methods that favor and penalize centrist candidates are not accepted for electing or grading political candidates. Another reason is that such methods maximize manipulability as both judges and voters can make changes easily in the final scores of any candidate or competitor. The chapter also compares point-summing methods with other traditional methods or approval voting.

Large Electorates

This chapter emphasizes the simplification of majority-ranking, stating that an increased number of judges in the jury or voters in an electorate or use of simplified common language help to simplify majority-values of competitors or candidates. Ordered set grades help obtain majority-value by beginning with the majority-grade or the lower middlemost grade and following alternating grades. Unambiguous order among the competitors can be determined with certainty given an increased number of judges or voters and relatively few grades. The competitor’s majority-gauge, which is strategy-proof-in-grading, is explained with the help of a theorem. Upper, lower, and difference tie-breaking rules that are strategy-proof-in-grading share properties with the majority-gauge-ranking.

New Model

This chapter presents a new basic model, which consists of a common language of evaluation, a set of judges, and a set of competitors. It expresses the problem of what to do with judges’ scores and how to resolve them into a single score in a concise or systematic way. The model identifies the shortcomings of traditional models of social choice theory and provides a new model as an alternative. Six axioms of the basic model are satisfied in a method of grading called social grading function f, in which there is no ambiguity in grading, and the final grade assigned to every single alternative is independent of all other alternatives. The deep preferences or utilities of a judge or a voter play an important role in voting and judging as every decision-maker tries to maximize his utility.

Judging in Practice

This chapter presents mechanisms that help in transforming scores, measures, or grades of judges into the jury’s scores to determine the final rankings in wine, figure skating, diving, and other competitions. It also focuses on the common languages used by judges in permitting meaningful measurement in these competitions. The chapter discusses how these mechanisms are applied when evaluating and ranking students in their examinations, essays, and class performances, and also when evaluating and ranking employees, musicians, divers, and skaters in related competitions. It also describes how a quality-of-life index is prepared by the Economist Intelligence Unit in which rankings are given to specific countries. It is demonstrated in theory and practice that different approaches are used by judges in assigning scores to an individual competitor when they combine them in the competitor’s total jury score.

Objections to Majority Judgment

This chapter focuses on majority judgment drawbacks. Properties, including participant-consistency, join-consistency, and proper cancellation, which majority judgment does not satisfy, are also lacking in other traditional models of social choice theory. The chapter concludes that majority judgment is a practical method for ranking and electing, and is a choice-monotonic, rank-monotonic, and strongly monotonic method. Drawbacks of traditional models are also highlighted, and it is stated that the traditional models lack guarantees of change in the estimation of voters without affecting the outcome of the election or ranking. The chapter discusses the critics of the majority judgment, who do not take into consideration the strategic behavior of judges and voters.

Common Language: Voting

This chapter focuses on the importance of a simplified common language with clear cultural meanings for grading political candidates. Voters using majority judgment are better at expressing their opinion about a candidate compared with giving rank-orders. The 2007 Orsay experiment in the context of the majority judgment ballot that took place during the French presidential elections in 2007 is also discussed, with a focus on the use of language in which the hypothetical voting process was explained to voters. Analysis on the grades allotted during the experiment is presented along with homogeneity of voters’ grades to consider the use of language by the voting population.

Comparisons of Voting Methods

This chapter analyzes fundamental differences among different voting methods by comparing their qualitative properties, and also demonstrates how strategic manipulation is controlled by the majority judgment. Borda’s and point-summing, the methods that have gained substantial support by reformists, are manipulated and biased in favor of election of moderate candidates. The methods that are least manipulable include Condorcet, approval judgment, and the majority judgment. Manipulation is difficult in Condorcet due to the creation of Condorcet-cycles. The majority judgment is also considered the most balanced with regard to the left–right spectrum. Bias in favor of centrist candidates is a serious drawback of approval judgment.