[EM]Ranked-Pairs (wv) can lose a Cond. Winner

[Adam Tarr]

>This appears to be an example that illustrates a more stable outcome is 
>achievable
>by counting equal ranked options 1/2 vote each.

Matt, we went over this before.  By adding 1/2 of a vote for each side, you 
turn winning votes into margins.  It's not a compromise in-between the two 
at all - it becomes margins exactly.  Adding half-votes in margins does not 
change the outcome at all.  So since Stephane cooked up his example 
specifically to show when winning-votes encourages truncation (and margins 
does not) it's not surprising that adding half-votes "solves" the problem.

The reality, though, is that it's significantly easier to come up with 
examples where truncation is encouraged in margins-based methods.  Here's 
the example Stephane came up with, casted into percentages and given some 
familiar names:

36% George
9% Al>George>Ralph
18% Al>Ralph>George
18% Ralph>Al>George
19% Ralph

Ralph is the Condorcet winner, but truncation by the middle 18%, in winning 
votes, will give the election to Al.  But if you shift the percentages 
around a little, or reduce the degree of truncation a bit in the edge 
factions, then it breaks down.  Truncation only works strategically in 
winning votes when there is a lot of truncation (indifference) to start, 
and even then it only works in specific cases with fractured electorates, 
where the Condorcet winner has pretty poor support from other factions.

Contrast that to this case, which is not hard to come up with at all:

49%: George>Al>Ralph
12%: Al>George>Ralph
12%: Al>Ralph>George
27%: Ralph>Al>George

Al is the Condorcet winner.  Now, if the George voters truncate in margins, 
they win the election.  This will be true in a huge range of cases - 
basically, any time the second-place candidate's support for the winner 
allows the winner to beat another edge candidate.  You can fudge the 
numbers in the above example around a large amount and get the same results 
- provided you don't give the George faction an absolute majority of course.

Winning votes gives the election to Al, even if George voters truncate.  If 
you add half-votes, then you run into the same problems you have with 
margins -- naturally, since adding half-votes turns winning votes into margins.

-Adam


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