A modified "winner-take-all" rule for awarding state electoral votes in US presidential elections and a game model for its analysis

A modification of the ''winner-take-all'' rule for awarding state electoral votes in US presidential elections is proposed. The modified rule has the potential of turning a state that is currently ''safe'' for either major party candidate into a ''battleground'' one, forcing presidential candidates to compete in the state and encouraging state voters (interested in the election result) to vote in presidential elections. A model for estimating the chances of a candidate to win state electoral votes in presidential elections with two major party candidates under the modified ''winner-take-all'' rule is proposed. This model has the form of a two-person game on a polyhedral set of connected strategies with payoff functions each being a sum of two linear functions and a bilinear function. The model is one of the two models applicable for analyzing the proposed rule that are discussed in the article.