Dark horse plus 3 rivals

The acronym DH3 refers to the "Dark Horse plus 3" scenario, where a candidate universally considered worst is elected due to a strategic arms race. This can happen when a voting system encourages burying your "true" (strongest) opponent underneath weaker opponents. If this is the case, then in an election between three strong candidates and a weak "dark horse", the "dark horse" can win precisely because they were the weakest. Each strong candidate votes the dark horse in second place, in order to better bury the stronger opponents; and then the dark horse, with second-place support from all voters, is the strategic Condorcet winner.

This is one of the most pathological possible voting scenarios, as it could lead even the most universally-despised candidate to win.

There are documented cases of this happening in elections using the Borda count, a system particularly subject to DH3.

A method that passes dominant mutual third burial resistance provides no incentive to bury an opponent under a dark horse: it either does nothing or backfires. In this sense, it is immune to the scenario because the escalation never occurs.

In a 2001 presentation paper, Burt Monroe defined a Nonelection of Irrelevant Alternatives criterion that requires that a method never elects universally despised candidates in a strategic equilibrium. All methods passing this criterion are automatically immune to the DH3 problem.

James Green-Armytage first discussed the scenario, though not by that name, in the context of Monroe's paper, in 2003.