Advances and Applications in Statistics
Volume 64, Issue 1, Pages 75 - 85
(September 2020) http://dx.doi.org/10.17654/AS064010075 |
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MAXIMUM BINOMIAL PROBABILITIES AND GAME THEORY VOTER MODELS
Jeffrey S. Rosenthal
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Abstract: We consider the simple voter model where two candidates A and B have nA and nB supporters, who each vote independently with probabilities pA and pB. We provide estimates and bounds on the probability that the vote ends in a tie, or within some fixed margin α. To do this, we derive bounds on the maximum values of certain binomial probabilities, which in turn allow us to bound probabilities of differences of pairs of independent binomial random variables. |
Keywords and phrases: binomial distribution, voter model, game theory, tie probability.
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