Circular Stand-Off

[Paul Dumais]

Markus Schulze wrote:
 
> You will have to explain why you think that JITW is an improvement.
> When you write that "there is no 'correct' candidate to withdraw (or
> to elect) when there is a sincere circular tie," you admit that JITW
> doesn't lead to a "better" election result than every other Smith
> Criterion election methods (since every candidate of the top set is
> equally qualified). And the claim that JITW guarantees that no
> candidate will regret having competed, is simply not true.
> 
> Example: JITW//Smith//Condorcet[EM] is used.
> 
>    A:B=48:52
>    A:C=53:47
>    A:D=43:57
>    A:E=44:56
>    B:C=45:55
>    B:D=42:58
>    B:E=62:38
>    C:D=54:46
>    C:E=41:59
>    D:E=40:60
>    A, B, and C won't withdraw under any circumstances.
>    Candidate D prefers B to C to E to A.
>    Candidate E prefers C to B to D to A.
> 
> If no candidate withdraws, candidate A is elected.

How do you get this? When A is compared to every other candidate, it
loses more than any other. Let me be more rigorous. Let us define a vote
for candidate A as being an instance where A is ranked higher than
another candidate. So if we add up all the votes, A gets the least
amount of votes (188 out of a possible 400).  

> If only candidate D withdraws, candidate B is elected.
> If only candidate E withdraws, candidate C is elected.

If only E withdraws D gets the most votes (as defined above).

> If both candidates, D and E, withdraw, candidate A is elected.
How is this possible? C gets the most votes (102) and A is second (101).
> 
> Markus Schulze
-- 
Paul Dumais