As a matter of practice, though, we don't much use simple majority rule in American elections. Instead we use plurality rule often termed "winner-take-all" or "first-past-the-post" voting where the winner is the candidate or alternative that receives more votes than any other. In circumstances where the choice is between two alternatives represented in the U.S. by the two major parties plurality rule usually gives the same results as simple majority rule. But not always.
More generally, the question of which voting procedure is best involves questions of fairness. The phrase "one person, one vote" encapsulates a core idea of procedural fairness. But, given procedural fairness, what's a fair way to add up votes to determine social choices, particularly when we allow for more than two alternatives?
In general, we believe that the candidate with the most support should win. But what is the fairest way to judge support? There is no simple answer. Simple majority rule and plurality rule consider only each voter's top choice ignoring lower ranking choices. Variations on simple majority and plurality voting called full preference voting rules attempt to take into account each voter's second, third, and fourth choices, and so on among a list of candidates. As we shall see, different voting procedures many arguably as or more fair than simple majority rule can produce very different outcomes, even when used by the same group of voters to decide among the same list of candidates.
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