[EM] IRV ballot pile count (proof of closed form)

[Rob LeGrand]

Abd wrote:
> 34 A
> 33 B>C
> 33 C>B.
>
> The Condorcet winner is A, because in the two pairwise
> elections involving A, A wins
>
> A>B, 34:33
> A>C, 34:33.

Assuming that by the above votes you mean

34:A>B=C
33:B>C>A
33:C>B>A,

A is not the Condorcet winner and is in fact the Condorcet loser, losing
both A:B and A:C by 34:66.  Perhaps you had in mind an example like

35:A
32:B>C
33:C,

by which I mean

35:A>B=C
32:B>C>A
33:C>A=B.

In this example, C is the Condorcet winner even though C does not have a
majority over B.  I can see how this example could be seen as an
embarrassment to the Condorcet criterion, in that a good method might not
choose C as the winner.

--
Rob LeGrand
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/