Strategic decisions under one-stage multi-candidate voting systems

Conclusion

We have seen that under the assumptions of this study the problem of maximizing a voter's total utility for a number of one-stage decision rules for multi-candidate elections may be specified as linear (or quadratic) programs. Potentially optimal strategies emerge as extreme points of the feasible region in the sense that no other strategies can be uniquely optimal. Categorical, approval, Borda, and z-score decision rules are all minimal in the sense that for each, the feasible region (with abstentions excepted) consists entirely of potentially uniquely optimal strategies. For each of these decision rules we have determined the optimal strategies explicitly in terms of the voter's utility function. Among the minimal voting systems studies, we argue that the voter's task of estimating his optimal strategy is least difficult under approval voting.

Application of optimal strategies to the results of a thermometer scale survey suggest that the approval, Borda, and z-score decision rules can produce results very similar to one another but very different from that of categorical voting. Furthermore, for this survey, the former three systems were far less sensitive than categorical voting to the withdrawal of some of the candidates.