Game theory time!
Imagine two voters, one conservative and one liberal, who are faced with an election in which they have to choose between their candidate and a third-party candidate (because they would never consider voting for the other major candidate). They both assign a value of +1 to their own candidate, 0 to the third-party candidate, and -10 to the other major candidate. The rules of the game are this: if they both vote third-party, then third-party wins; if one votes third party, then the other major candidate wins; if they both vote for their own candidate, it's a toss-up, and the expected value for both is an average of the two major candidates. This simple game can be put into a matrix as thus, with Player 1 (on the left) as the conservative:
Code:
1 / 2 Own Third
Own -4.5, -4.5 1, -10
Third -10, 1 0, 0
The ideal outcome overall would be to agree to vote for the third-party candidate, with an overall total value of 0, while every other outcome has an overall value of -9. However, you can easily see that, from the point of view of either voter, it is always more valuable to vote for their own candidate (e.g., if Player 2 votes for their own candidate, their own return will increase, from either 0 to 1, or from -10 to -4.5). Thus, although working together would be best, the best individual strategy is to vote for your own candidate, because if you don't, you risk helping elect that giant -10 staring you in the face from the ballot.