Problem #PRU-65351

Problems Probability and statistics Probability theory Discrete distribution Methods Examples and counterexamples

Problem

In Anchuria, presidential elections are being prepared, in which President Miraflores wants to win. Exactly half of the voters support Miraflores, and the other half support Dick Maloney. Miraflores is also a voter. According to the law, he has the right to divide all of the voters into two constituencies at his own discretion. In each of the districts, the voting is conducted as follows: each voter marks the name of their candidate on the ballot; all ballots are placed in the ballot box. Then one random ballot is chosen from the ballot box, and the one whose name is marked on it will win in this district. The candidate wins the election only if he wins in both districts. If the winner does not appear, the next round of voting is appointed according to the same rules. How should Miraflores divide the electorate in order to maximize the probability of his victory on the first round?