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• W2314560319 abstract "In a recent two-candidate Town Council election in Brunswick, Maine, the winner received 2,390 votes and the loser 2,383. After the vote had been announced, it was discovered that 16 voters had been allowed to vote at polling places where they were not officially registered, and those votes were declared invalid on the grounds that the voters had not been appropriately certified as being qualified to vote as required by state law. There was no evidence of fraud and no indication of how the invalid ballots were cast. The loser asked for a new election on the grounds that 12 or more of the 16 invalid votes could have been cast for the winner, enough to reverse the election results. In this situation, the ballot box can be viewed as an urn in which there are a few more white balls (votes cast for the winner) than black balls (votes cast for the loser). A certain number of balls (the invalid votes) are withdrawn at random from the urn. What is the probability of a reversal, i.e., that, after the withdrawal, the number of black balls in the urn will exceed the number of white balls? Of course the assumption that the balls are withdrawn at random is critical. The assumption that each ball has the same probability of being withdrawn is the assumption that each voter in the election has the same probability of casting an invalid ballot. If there is evidence of election irregularities or fraud, or if there is reason to assume that other factors, such as the time of day the invalid votes were cast or the location of the polling place, made it more likely that the invalid ballots were cast for one of the candidates, this assumption may not be tenable. The probability of reversal is simply the number of withdrawal combinations which cause a reversal divided by the total number of possible withdrawal combinations. In most close elections, there will be too many of these combinations to be readily countable, so it is desirable to be able to approximate the probability of reversal. Because the arguments about election results occur in public and legal arenas, not in mathematical journals, a simple approximation is preferable. An approximation due to Finkelstein and Robbins [2] is made as follows: suppose the urn contains w white balls and b black balls with w > b. Of the total t = w + b balls, m are withdrawn at random. Let x denote the number of these m balls which are white. There will be a reversal if, after the withdrawal, there are at least as many black balls as white balls remaining in the urn; i.e., if w-xsb-(m-x), or" @default.
• W2314560319 created "2016-06-24" @default.
• W2314560319 creator A5035179302 @default.
• W2314560319 date "1981-11-01" @default.
• W2314560319 modified "2023-09-23" @default.
• W2314560319 title "The Probability of Election Reversal" @default.
• W2314560319 cites W2276089763 @default.
• W2314560319 doi "https://doi.org/10.1080/0025570x.1981.11976937" @default.
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