Random Ballot

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Random ballot, also known as random dictatorship, is a voting system in which the first preference candidate of a ballot drawn at random is elected.

When the drawn ballot is not decisive, then additional ballots are drawn and used only to resolve the indecision of previously drawn ballots.

Properties

Random Ballot satisfies the Plurality criterion, Monotonicity criterion, Participation criterion, Later-no-harm criterion, Clone Independence, Favorite Betrayal criterion, and Pareto criterion.

However, Random Ballot fails the Majority criterion, Condorcet criterion, Smith criterion, and Strong Defensive Strategy criterion.

Example

Tennessee's four cities are spread throughout the state

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

  • Memphis on Wikipedia, the state's largest city, with 42% of the voters, but located far from the other cities
  • Nashville on Wikipedia, with 26% of the voters, near the center of Tennessee
  • Knoxville on Wikipedia, with 17% of the voters
  • Chattanooga on Wikipedia, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
  1. Memphis
  2. Nashville
  3. Chattanooga
  4. Knoxville
  1. Nashville
  2. Chattanooga
  3. Knoxville
  4. Memphis
  1. Chattanooga
  2. Knoxville
  3. Nashville
  4. Memphis
  1. Knoxville
  2. Chattanooga
  3. Nashville
  4. Memphis

Memphis wins with 42% probability, Nashville with 26%, Chattanooga 15%, and Knoxville 17%. If the Knoxville voters had instead ranked Knoxville and Chattanooga equally, then Knoxville would win with 0% probability, since it would be impossible to draw a ballot which prefers Knoxville to Chattanooga.