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Suppose that a Condorcet winner exists in an election. Certainly it is possible that an individual voter prefers some other candidates to the Condorcet winner. They might even prefer most, or all, other candidates to the Condorcet winner.

But what is the upper bound, if any, on how many such voters are possible?

More specifically:

  • Is there an upper bound on how many voters can prefer at least one other candidate?
    • Per vadim123, there is not
  • Is there an upper bound on how many voters can prefer most other candidates?
  • Is there an upper bound on how many voters can prefer every other candidate?

Bonus points for establishing a general relationship that answers all questions of this type.

Colin P. Hill
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  • If there are many candidates and the Condorcet winner is just one vote ahead with respect to any other, your scenarios are possible. – Jack D'Aurizio Dec 22 '14 at 21:26
  • Normally, this site operates at the pace of one question per question. You should ask your other questions separately. – vadim123 Dec 23 '14 at 15:02
  • They're really all variants on the same question -- or cases within a single general problem, if you prefer. It seemed clearer to express it informally this way than to unify them formally. – Colin P. Hill Dec 23 '14 at 22:46

1 Answers1

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Voter 1: $A>X>B>C$
Voter 2: $B>X>C>A$
Voter 3: $C>X>A>B$

Candidate $X$ is the Condorcet winner, but every voter prefers someone else.

vadim123
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