Election Goals and Strategies: Equivalent and Nonequivalent Candidate Objectives

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Abstract
This essay ascertains some general conditions for equivalence and nonequivalence among six election objectives: 01, maximizing expected plurality; 02, maximizing proportion of expected vote; 02, maximizing expected vote; 04, maximizing probability that plurality exceeds some level; 05, maximizing probability that proportion of vote exceeds some level; 06, maximizing probability that vote exceeds some level. The major findings are these: (1) 01, 02, and 03 are equivalent if the election is zero-sum-like in expected vote; (2) 01 and 02 are equivalent if competition is strongly symmetric. A necessary condition for this equivalence is also presented for 2-candidate elections: (3) 01 and 04 are equivalent, as are 03 and 06, if the candidate's forecasting error is independent of all strategies; (4) 01 and 04 are equivalent for two-candidate elections, and for n-candidate elections 02 and 05 are equivalent, as are 03 and 06, if the distribution of a candidate's forecasting error is multivariate normal, and if the level of plurality, proportion, or vote to be exceeded is the minimax value of the election game under 01, 02, or 03; (5) findings of equivalence and nonequivalence depend upon the definition of equivalence (findings 1 and 2 rely upon an election with all candidates at equilibrium strategies, while findings 3 and 4 do not); (6) equivalence and nonequivalence among election objectives may be sensitive to the candidate's attitude toward risk, i.e., to the functional form of his utility function in pluraliy, vote proportion, or vote; election objectives depend on information, competitive environment, and constitutional arrangements. Hence, statements of preference for alternative election systems, laws, and reforms perforce entail reasonable theoretical expectations about the way in which these systems, laws, and reforms affect the candidates' campaign objectives, as well as about equivalence and nonequivalence among these objectives.