The Burr Dilemma or chicken dilemma is a dilemma that exists in electoral systems based on approval ballots.

A set of voters prefer two candidates over all others, while at best, only one is likely to win. Both candidates are incentivized to publicly encourage voters to support the other candidate while privately encouraging some supporters to only vote for themselves. When taken too far, this strategy may cause too many defections from both candidates' support such that both lose, while avoiding defections prevents an effective choice between the two candidates.

It is named after Aaron Burr in the U.S. Presidential election of 1800, by Professor Jack H. Nagel,[1] where both Thomas Jefferson and Aaron Burr ran as Democratic-Republicans.[2] The other name, "chicken dilemma", comes from the game of chicken.

History

The 1800 United States presidential election was conducted using a voting-rule similar to approval voting. Each member of the Electoral College should cast two votes, with no distinction made between electoral votes for president and electoral votes for vice president. The candidate winning the highest number of votes would be the president, and the one winning the second-highest number would be the vice-president.

There were four candidates: the Democratic-Republicans nominated a ticket consisting of Thomas Jefferson and Aaron Burr, while the Federalists nominated a ticket consisting of Adams and Charles C. Pinckney. Each party formed a plan by which one of their respective electors would vote for a third candidate or abstain, so that its preferred presidential candidate (Jefferson for the Democratic-Republicans and Adams for the Federalists) would win one more vote than the party's other nominee.

At the end of a long and bitter campaign, Jefferson and Burr each won 73 electoral votes, Adams won 65, and Pinckney won 64. The Democratic-Republicans' failure to execute their plan to award Jefferson one more vote than Burr resulted in a tie, which necessitated a contingent election in the House of Representatives. Under the terms laid out in the Constitution, the outgoing House of Representatives chose between Jefferson and Burr. Burr was accused of campaigning for the presidency himself in the contingent election, despite being a member of Jefferson's party. Each state delegation cast one vote, and a victory in the contingent election required one candidate to win a majority of the state delegations. Neither Burr nor Jefferson was able to win on the first 35 ballots of the contingent election, as most Federalist representatives backed Burr and all Democratic-Republican representatives backed Jefferson. Hamilton favored Jefferson over Burr, and he convinced several Federalists to switch their support to Jefferson, giving Jefferson a victory on the 36th ballot.

Following this political crisis, in 1804 the 12th Amendment was ratified: it required each member of the electorate to cast one vote for president and one vote for vice-president, rather than two indistinguishable votes.

Decapitation

Another related term is decapitation. [3]: Sec.7  Suppose a party sends several candidates to compete in an election using approval voting. If all supporters of the party vote naively, all party candidates will get the same number of votes. If there are more candidates than winners, the winners will have to be selected randomly. But usually, the party wants its leader to be elected first. They can arrange for it by asking some of their supporters to vote only for the leader, but the opponents of the party might try to vote for other party members, thus effectively "decapitating" the party (removing its head, as in the military strategy of decapitation).

Solutions

The 12th Amendment to the United States Constitution[3]: Sec.7  prevented a recurrence of the Burr dilemma by having the Electors vote separately for President and Vice President.

The Burr dilemma can also be avoided by switching from approval ballots to ranked ballots.

See also

References

  1. ↑ The Burr Dilemma in Approval Voting Jack H. Nagel, University of Pennsylvania - Political Science
  2. ↑ Simeone and Pukelsheim (2006) p. 142 3.1 The Burr Dilemma.
  3. 1 2 Janson, Svante (2018-10-12). "Phragmén's and Thiele's election methods". arXiv:1611.08826 [math.HO].
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