19.12 Probabilistic voting Probabilistic voting is a way of modeling the voting process that introduces continuity into individuals' voting decisions. In this way, calculus-type derivations become possible. To take an especially simple form of this approach, suppose there are # voters and two candidates (labeled A and B) for elective office. Each candidate proposes a platform that promises a net gain or loss to each voter. These platforms are denoted by 04 and 0, where i = 1,..., . The probability that a given voter will vote for candidate A is given by U(0) U(0)], where f>0>f". The probability that the voter will vote for candidate B is 1-.

a. How should each candidate chose his or her platform so as to maximize the probability of winning the election subject to the constraint 04 00? (Do these constraints seem to apply to actual political candidates?)

b. Will there exist a Nash equilibrium in platform strategies for the two candidates?

c. Will the platform adopted by the candidates be socially optimal in the sense of maximizing a utilitarian social welfare? [Social welfare is given by SW, U(0,).]