Abstract
We introduce and discuss the most common voting procedures. Our starting point is the observation that voting rules can make a significant difference in the voting outcomes. First we deal with the ambiguity of the notion of majority outcome in cases involving more than two alternatives or candidates. The concepts of Condorcet winner and core are introduced. We then define the voting procedures and present some descriptive devices for the analysis of voting situations.
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Notes
- 1.
There are a couple of minor restrictions. Firstly, it does not hold when the number of alternatives is 2 and the number of voters is even. Secondly, it is not known if the result holds when the number of voters is a multiple of 4 and the number of alternatives is 3.
- 2.
The definition of the Condorcet winner differs from the usual one in accepting alternatives that beat or tie with all the others as Condorcet winners. This allows for the possibility that there is more than one Condorcet winner in a profile. The concept of Condorcet winner in the sense of Dasgupta and Maskin is thus the set of majority undominated alternatives. This set is generally known as the core of the majority voting game.
- 3.
Pareto means that whenever an alternative x is strictly preferred to alternative y by all individuals, then y is not elected. IIA requires that the collective preference between any x and y depends on the individual preferences between these two alternative only. In other words, if in two profiles with the same number of voters, each voter has an identical preference for x with respect to y, then the collective preference between these two alternatives is the same in the two profiles. Generic decisiveness means that the rule results in an outcome under all preference profiles.
- 4.
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de Almeida, A.T., Morais, D.C., Nurmi, H. (2019). More Than Two Alternatives. In: Systems, Procedures and Voting Rules in Context . Advances in Group Decision and Negotiation, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-30955-8_4
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