Abstention in two-candidate and three-candidate elections when voters use mixed strategies

Conclusions

In re-analyzing the Ferejohn and Fiorina (1974) examination of ‘rational’ abstention we found that admitting mixed strategies does not affect findings as to the optimal behavior of voters who are expected utility maximizers but does significantly affect our expectations as to behavior of voters using a minimax regret rule. We found that minimax regretters with admissible mixed strategies would always have some probability of voting rather than abstaining, except under the quite restrictive condition that c > 1/2. Thus, to the extent that some voters can be seen as operating from a minimax regret perspective, a decision to vote on their part can be understood without recourse to ideas like the ‘psychic benefits of voting’ or ‘citizen duty’.

An important difference between the Ferejohn and Fiorina (1974) analysis and our own is that their models all have step-function threshold effects, while ours is probabilistic in nature and behavior is gradient-like. In the usual rational choice modeling of voter behavior (including the minimax regret model restricted to the pure strategy case) voters behave deterministically: e.g. if p ₃ + p ₄ > 2c then expected utility maximizing voters always abstain in two-candidate plurality elections; if p ₃ + p ₄ < 2c then they always vote for their first choice. In the mixed strategy minimax regret model, on the other hand, raising c (or k) does not operate in a dichotomous fashion — instantaneously shifting the voter from voting to abstention once a critical threshold is passed. Rather, as c (or k) increases, the probability of voting decreases.

We believe that probabilistic choice mechanisms are more descriptive of human choice behavior (including voter behavior) than are deterministic ones. Thus, while the mixed strategy minimax-regret model we propose may only account for the behavior of some voters, we believe it is desirable to pursue other models for voter choice which, unlike those now current in the literature, do not postulate sharp ‘on-off’ effects but make use instead of response-gradient notions.