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Marquis de Condorcet | Jean Borda | Charles Dodgson | John Kemeny |

The images above are available with permission from the The MacTutor History of Mathematics archive at the University of St Andrews, Scotland

If one is to do a mathematical analysis of any subject, one has to carefully examine phenomena related to what one is investigating and make simplifying assumptions, to construct what today are called mathematical models. Voting is carried out in a surprisingly large array of situations: selection of candidates for municipal, state, and national elections; votes that legislators make when choosing among alternative courses of action; decisions by economic planners about what course of action to take; selection by judges of the winner for a skating competition; selection of a movie for best film of the year; or selection of what should be served at the company picnic. What are the salient phenomena involved in elections and voting? Elections require voters and alternatives to choose from (typically people, but there are many other possibilities). To express voter opinions about the alternatives requires a ballot of some kind. After the voters make their judgments on the alternatives (candidates), it is required that some decision method be used to arrive at the winning candidate, winning candidates, or a collection of selected alternatives.

There are many interesting aspects of elections that probably will not play a part in a first pass at using mathematics to study elections. Should felons be restricted from voting? Should people who can not be present when the voting is to take place have a way to cast a ballot in some other way? Are the machines (or physical mechanism) currently used for voting the best choice possible? (Best choice from what point of view?)

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