There Are D Democrats And R Republicans Voting In The Us Presidential There are d democrats and r republicans voting in the US Presidential election. Each person decides whether to vote or not vote. The voters get a payoff of 2, 1, 0 if their preferred candidate wins, ties, or loses (respectively). Voters that vote incur a cost of 0.
Paper For Above instruction In analyzing the voting behavior of Democrats and Republicans in U.S. presidential elections, it is insightful to model the situation as a strategic game where individual voters choose whether to participate or abstain, considering potential payoffs based on election outcomes. This paper explores the structure and equilibria of such a game under varying assumptions about party sizes, specifically when the numbers of party supporters are equal and small (d = r = 1) and when they are large and equal (d = r > 1). Part A: The Case of Single Voter per Party (d = r = 1) When each party has exactly one supporter, the game simplifies to a two-player, two-strategy game where each player—representing a supporter—can choose to vote or abstain. The players are the Democrat and Republican supporter, each with preferences aligned with their party. The possible strategies are Voting (V) or Not Voting (NV). Payoff structure: If a supporter votes and their preferred candidate wins, they receive a payoff of 2. If there is a tie, supporters receive 1. If their candidate loses, the payoff is 0. Voting incurs no cost for supporters, so the only considerations are the potential benefits based on election outcomes. Constructing the normal form game table, the strategies are: Repub Exists: V Repub Exists: NV Democrat: V (2,2) — both vote; candidate with majority wins