King of the Hill

King of the Hill or KH is a method devised by Kevin Venzke which satisfies Later-no-help. It was devised as a Condorcet completion method that would be resistant to burial. This article describes it as a method on its own, in which case it has no burial incentive at all.

Definition

1. The voter submits a ranked ballot. Equal-ranking is not allowed; truncation is.
2. Find the candidate with the most first preferences who is involved in a majority-strength pairwise contest (i.e. >50% of the ballots) with the first-preference winner.
3. If there is no such candidate, elect the first-preference winner.
4. Otherwise, elect the winner of that pairwise contest.

Comments

KH satisfies Later-no-help. Adding lower preferences may cause the new preference to win, but it can't make any other candidate win.

Note that, although the method doesn't satisfy Later-no-harm, the supporters of the top two candidates are guaranteed both of the LNH criteria. It is only the supporters of weaker candidates (by first preferences) who have the risk of giving the election away to their second preference.

To see this, note that the supporters of the first-preference winner do not have their lower preferences counted at all. The only pairwise contests that matter are those directly involving the first-preference winner. Then, note that the second-place candidate wins if and only if he has a majority-strength win over the first-preference winner. There is no way for supporters of this candidate to affect this test by adding lower preferences.