mgf1107lecture3 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 3 Flaws of Voting We have found in this chapter that the voting method chosen can be as important to the outcome as the preferences in the voting. It is possible for all four methods to yield a different result, and while each system seems reasonable, we shall see in this section that there are inherent flaws with each method. We will examine four criteria that mathematicians have agreed that a voting system should meet in order for an election to be considered fair. Majority Criterion If a single candidate is the first choice of a majority of voters, then that candidate should be declared the winner. If this does not happen, then that voting method is said to violate the majority criterion. Ex. 15 orchestra members are asked to nominate which composer’s music, either Mozart (M), Beethoven (B) or Schubert (S), is to be played during their upcoming concert. The preference table is shown below. Number of votes First M B B Second B S M Third S M S If we use the Borda count method: Mozart gains points Beethoven gains points Schubert gains points. Thus using this method, the music of would be played at the concert. However this result violates the majority criterion since 8 of the 15 voters (a majority) ranked as their first choice.
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Head-to-Head Criterion If one candidate is favored over each of the other candidates using head- to-head comparisons, then that candidate should be declared the winner. As we will see below though, this is not always the case. Ex. Students at a small high school are asked to vote on a new nickname for their football team. The options are Lions (L), Tigers (T), Eagles (E), and Bulldogs (B). The preference table is shown below. Number of
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mgf1107lecture3 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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