Random Pair

Random Pair is a voting system where two candidates are drawn uniformly at random, and then the winner is the candidate who beats the other one pairwise.

If the two candidates are tied, the process is repeated unless every pairwise contest is a tie.

Properties
Random Pair satisfies the monotonicity criterion, Condorcet loser criterion, and independence of irrelevant alternatives. It is strategy-proof, as shown by Gibbard's 1978 theorem.

However, it fails the majority criterion, mutual majority criterion, Condorcet criterion, and has a teaming incentive.

Example
The results would be tabulated as follows:


 * [A] indicates voters who preferred the candidate listed in the column caption to the candidate listed in the row caption
 * [B] indicates voters who preferred the candidate listed in the row caption to the candidate listed in the column caption
 * [NP] indicates voters who expressed no preference between either candidate

Each cell in the matrix is equally likely to be chosen, and the winner of the two candidates of a cell wins the election if that cell is chosen. By labeling each cell with the winner, the table becomes:

Nashville is the winner in six cells, Chattanooga in four, Knoxville in two, and Memphis in none.

Thus Nashville wins with 50% probability, Chattanooga with 33.33% probability, and Knoxville with 16.67% probability. Memphis is the Condorcet loser and has no chance of winning.