Nobody votes, together

In majoritarian two-party elections, rather than tallying the total votes received by either candidate, we could consider the margin by which one candidate surpasses the other. In that sense, you can look at each vote up to that margin as “cancelling out” a vote for the other party. For example, consider an election between two candidates, A and B, where I am dead set on voting for candidate B while my roommate is a fervent supporter of candidate A. For whatever reason, we might both choose to shoulder the costs associated with voting for our preferred candidate. The issue with this arrangement is that we essentially cancel each other’s votes out — the election would have the same outcome if we both abstained. Knowing this, I could propose that we both stay home and watch a movie together, avoiding the costs while still achieving the same outcome.

Expanding this logic to a macro level, elections can be thought of as a prisoner’s dilemma between two blocs of voters (e.g. Democrats and Republicans). If every voter in the smaller constituency matches up with voters in the larger constituency and mutually agree to abstain, we arrive at a cooperative equilibrium that arrives at the same electoral result, while avoiding a majority of the costs. Note that from the cooperative cell, each has an incentive to unilaterally defect — so abstention contracts must be enforceable, otherwise the game will reach a Nash equilibrium at (Defect, Defect), even if everyone would be made better off by mutual abstention.

With the power of the internet, an arrangement like this could actually be feasible (similar to vote trading) by matching strangers with opposing politics (though enforceability would be a problem). In the case where the only benefits derived from voting are from the probability of determining the outcome, the costs associated with voting are significant, and abstention contracts are enforceable, “mutual abstention” could minimize needless costs imposed on voters (and minimize the total number of votes cast). In the extreme case with full participation and information, every election would be won 1 vote to 0, decided by the only person to cast a ballot.