Random ballot

Random ballot, also known as random dictatorship or single stochastic vote, 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.

Random Ballot is strategy-proof: this follows from Gibbard's 1978 theorem.

Example
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.