Ensuring every candidate wins under positional voting |
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Authors: | Christopher R H Hanusa |
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Institution: | (1) Department of Mathematics, Queens College (CUNY), 6530 Kissena Blvd., Flushing, NY 11367, USA |
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Abstract: | Given a fixed set of voter preferences, different candidates may win outright given different scoring rules. We investigate
how many voters are able to allow all n candidates to win for some scoring rule. We will say that these voters impose a disordering on these candidates. The minimum
number of voters it takes to impose a disordering on three candidates is nine. For four candidates, six voters are necessary,
for five candidates, four voters are necessary, and it takes only three voters to disorder nine candidates. In general, we
prove that m voters can disorder n candidates when m and n are both greater than or equal to three, except when m = 3 and n ≤ 8, when n = 3 and m ≤ 8, and when n = 4 and m = 4 or 5. |
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