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Simple majority voting is a common form of voting where, given two options, the option receiving a simple majority of votes wins, a well-known example of democratic procedure. It is informally used in small groups to make all kinds of practical decisions, by counting hands in a group or judging the loudness of the cheers in a crowd. However, May’s theorem states that any social choice rule that satisfies certain conditions, will turn out to be the simple majority rule.
May's Theorem
Manipulability by voters is as such unobservable, but doesn’t constitute a problem with simple majority voting, since in a two option case, it is impossible to manipulate the result by voting strategically. May states that, since group choice must depend only upon individual preferences concerning the alternatives in a set, a pattern of group choice may be built up if we know the group preference for each pair of alternatives. However, manipulability in a more options case is not as simple as it sounds.
Definition Simple majority voting is an example of a social choice rule: the winning choice is the one whose number of votes is greater than half of the voters who are not indifferent between the two choices. This is in contrast with absolute majority voting, where the winner is the option which gets more than half of all votes, including abstentions.
Properties
Simple majority voting satisfies the property of universal domain: it assigns an unambiguous value to every logically possible list of individual preferences. In other words, whatever every individual chooses, the procedure always yields a result. This trait is sometimes referred to as decisiveness.
Secondly, simple majority voting satisfies anonymity: it assigns the same value to two lists that are permutations of one another. This means that when two people change their votes in such a way that the number of voters for each option remains the same, than the result remains the same. The procedure does not care about which voter votes for an option, only about how many voters vote for that option. If the result changed, that would mean that one of those two votes overrides all the other votes, which comes down to a dictatorship.
Simple majority voting also satisfies neutrality: if everyone reverses their vote, the result is reversed, a tie remains a tie.
As fourth and last property, simple majority voting satisfies positive responsiveness. If one of the two options has more or equally many votes as the other option and one voter changes his mind in favor of that first option, then the result will also change in favor of that option: a tie becomes a win and a win stays a win.