Burr dilemma

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The Burr dilemma is a term coined by Jack H. Nagel to describe the likelihood of ties between two or more candidates in the misuse of Approval voting as a multi-member method. To quote Nagel, "Problems of multicandidate races in U.S. presidential elections motivated the modern invention and advocacy of approval voting; but it has not previously been recognized that the first four presidential elections (1788–1800) were conducted using a variant of approval voting. That experiment ended disastrously in 1800 with the infamous Electoral College tie between Jefferson and Burr. The tie, ... resulted less from miscalculation than from a strategic tension built into approval voting, which forces two leaders appealing to the same voters to play a game of Chicken."^[1] In this election, the candidate who received the largest number of votes was elected president, and the candidate receiving the second largest number of votes was elected vice-president.

It is worth noting that this was not an approval election. It was a bloc election, where electors were limited to two votes. A tie in a normal bloc election would have been irrelevant, as two people, usually of the same politically philosophy, would be elected under such conditions. The tie in this case was problematic, however, because the two positions were assigned vastly different powers, and one person must receive one office and another must receive the other. This obviously wouldn't be a problem in a single-winner approval election, especially one with a large amount of voters, which would make ties much less likely. Therefore, it is likely that the "Burr dilemna" would have little real effect if approval were used by the direct populace to elect just the president.

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