Sequential pairwise elimination: Difference between revisions

An SPE method, emulating legislative procedure, works by first determining a base social order by some method (e.g. [[Minmax]] or [[Range]]). Then starting with the winnerloser of that order (or list), compare the current candidate at the headend of the list with the candidate next to it. Replace the two adjacent candidates in the list with the candidate who beats the other pairwise, then repeat. The candidate who is left standing at the end is the winner.

In effect, each candidate can be considered a proposal (a bill or an amendment). TheStarting with the weakest proposal, the "legislature" repeatedly votes whether to keep the current bill or to replace it with an amended bill. At the end of the procedure, the last accepted amended bill wins.

In the first round, starting at the end of the list, we compare MemphisKnoxville to NashvilleChattanooga. As the table on the right shows, more voters prefer NashvilleChattanooga to MemphisKnoxville than vice versa. So NashvilleChattanooga survives the comparison and MemphisKnoxville is eliminated.

In the second round, we compare NashvilleChattanooga to KnoxvilleNashville. As more voters prefer Nashville to KnoxvilleChattanooga, KnoxvilleChattanooga is eliminated andin Nashvillefavor staysof in the gameNashville.

Finally, we compare Nashville to ChattanoogaMemphis. ChattanoogaMemphis is eliminated.

In this example, no matter what the order is, Nashville eventually becomes the incumbent and defeats all subsequent challengers in the order. This happens because Nashville is the Condorcet winner and every SPE method passes the [[Condorcet criterion]].