Downsian Competition for the Myerson Value

This paper studies an electoral competition model in which parties maximize legislative power rather than vote shares. Voters are uniformly distributed on the unit interval and vote for the party proposing the closest policy platform. After the election, parties form coalitions through a communication network arising from ideological proximity: two parties are directly linked if their policy distance is at most $d$. A party's objective is its Myerson value in the resulting graph-restricted voting game. I characterize symmetric pure-strategy equilibria in two-, three-, and four-party systems. The two-party case yields convergence to the median. The three-party case admits a continuum of symmetric equilibria in which the two extreme parties are directly linked. In the four-party case, the unique symmetric equilibrium places two parties at $(1-d)/2$ and two parties at $(1+d)/2$. In both three- and four-party systems, more restrictive coalition communication, represented by a smaller $d$, generates a centripetal force, and the median voter theorem holds in the limit despite the multiparty setting.