A Median Voter Theorem with Voter Abstention

We study a two-party spatial competition model that extends the Hotelling–Downs framework by allowing voter abstention. Voters share a common voting window size and participate only if at least one party lies within that window. Parties choose policy positions to maximize their vote-share margin. We show that if a pure-strategy Nash equilibrium exists, both parties must choose the same policy position that generalizes the median voter principle. In the classical model, the median splits the total electorate into two equal halves; here, the equilibrium position must split the participating voters within a fixed voting window into two equal parts. We then give necessary and sufficient conditions on the voter distribution for the existence of pure-strategy Nash equilibria. We identify broad classes of voter distributions under which pure-strategy equilibria exist.Length: 20 pages