Hunting The Muse

The "Third Party Presidential Spoiler" is a type of candidate (referred to as a "spoiler") that can make one winnable candidate lose to another, when they might otherwise beat the other. Not all presidential candidates are spoilers. Not all third party presidential candidates are spoilers. There nonetheless exists a type of candidate that is a spoiler, and this is the definition and proof.

We can define a spoiler as a candidate that fits all the below criteria.

• The spoiler is running for president
• The spoiler does not have a shot at winning the election
• The spoiler is running against other candidates who do have a clear shot at winning ("winnable candidates")
• The spoiler is clearly ideologically closer to one of the winnable candidates than the other(s), in terms of voter support
• The spoiler is participating in an election that does not allow the spoiler's supporters to register preference between the winnable candidates.

Reasoning:

A spoiler gets support from a variety of supporters. We define a "preferenced supporter" as a supporter of the spoiler, that also has a preference among the winnable candidiates.

Since the spoiler is ideologically closer to one party, some of the spoiler's support would come from preferenced supporters of that party's candidate. The spoiler would also have more preferenced supporters from that candidate than from another.

If so, then an otherwise winnable candidate could then lose to another winnable candidate, even though the population as a whole preferred that losing winnable candidate.