A fundamental problem faced by any group of people is how to arrive at a good group decision when there is disagreement among its members. The difficulties are most evident when there is a large number of people with diverse opinions, such as, when electing leaders in a national election. But it is often not any easier with smaller groups, such as, when a committee must select a candidate to hire, or when a group of friends must decide where to go for dinner. Mathematicians, philosophers, political scientists, and economists have devised various voting methods that select a winner (or winners) from a set of alternatives taking into account everyone’s opinion. It is not hard to find examples in which different voting methods select different winners given the same inputs from the members of the group. What criteria should be used to compare and contrast different voting methods? Not only is this an interesting and difficult theoretical question, but it also has important practical ramifications.
Nearly every democratic country uses a similar system for casting and counting votes—voters select one candidate per race on a ballot and the candidate that receives the most votes wins. This is known as plurality voting or winner-take-all.
Alternatives have been proposed: Ranked-choice voting, approval voting, proportional representation, single transferable vote, two-round system, and Borda count system.
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