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 3 candidates is 9. For 4 candidates, 6 voters are necessary, for 5 candidates, 4 voters are necessary, and it takes only 3 voters to disorder 9 candidates. In general, we prove that m voters can disorder n candidates when m and n are both greater than or equal to 3, except when m=3 and n≤8, when n=3 and m≤8, and when n=4 and m equals 4 or 5.

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