[EM] "good method" ? , was "IRV ballot pile count (proof of closed form)"

[Abd ul-Rahman Lomax]

At 03:29 PM 2/13/2010, Kathy Dopp wrote:
> > From: Chris Benham <cbenhamau at yahoo.com.au>
> > 35:A
> > 32:B>C
> > 33:C,
> >
> > by which I mean
> >
> > 35:A>B=C
> > 32:B>C>A
> > 33:C>A=B.

Kathy doesn't seem to recognize this, or maybe she does, but the two 
statements are equivalent. By not ranking B and C, the voter 
equal-ranks them bottom. That is the exact effect of the vote.

>I agree with Chris (below), If you require every winner to "have a
>majority *over*" ever other candidate, then there is no system that
>would give you any winners.  Clearly above, C has 65 votes and B only
>has 35 votes, at least in scenario #1 above.

Actually, with the votes above, C has a plurality over every other candidate:
A:B 35:32, A
B:C 32:33, C
C:A 65:35, C

C wins every pairwise election, C is the Condorcet winner. "Condorcet 
winner" does not at all require a majority in every pairwise 
election, and, in fact, that was part of my point. It's possible that 
the Condorcet winner only has a plurality in all of them. But in this 
particular case, a majority of voters have chosen to cast a vote that 
can be read as a vote for the Condorcet winner. All we have to do is 
take the B>C votes as such. They are clearly votes against A. So 
two-thirds of the voters have voted against A. A's out.

65 voters have voted for C, but only 35 have voted for B.

"Vote for" means "cast a vote that can be used to elect."

>Guessing as to what voters really mean, by assuming scenario #2 from
>scenario #1 -- you may have read the minds of all those voters who you
>believe all think exactly alike in each category, incorrectly.
>However, in scenario #2, I think A is the correct winner.

They are the same scenario, in fact. I think you misread this, Kathy. 
Equal-bottom is the same as not expressing the candidate's rank at all.

>I think election methods enthusiasts too often think they can read
>voters' minds and translate votes between between two different
>scenarios for voters.

Perhaps you mean that the B=C part of A>B=C means that the voter 
really did mean to actually equate them. Okay, let's look again. I 
assumed in a previous mail, Range utilities of

35: A, 3 / B, 1 / C, 0
32: B, 3 / C, 2 / A, 0
33: C, 3 / A, 1 / B, 0

Range totals:

A: 138
B: 131
C: 163

This allows the A voters to still have a preference between B and 
see, but at a lower level. If, in fact, they had no preference, the 
result becomes simply a lower sum of ratings for B. And if the C 
votes really did mean that A and B were equal, the result becomes 
fewer votes for A.

C still wins.

If the method were Bucklin, then, again, C would win, easily, with 
65/100 voters approving of C, if the votes were as writ.

With Bucklin, would more of the B voters truncate? Maybe. Maybe not. 
Depends, doesn't it?

It depends on how strong their preferences are. If it's Bucklin and 
everyone truncates, A wins, by a narrow margin. Same as with 
Plurality. But if a majority is required, it would go to a runoff.

Do we know, then, who would win? No, we do not. We do not have enough 
information! If the B votes really do show a higher approval of B 
voters for C, then C might win, but in that case some of them would 
probably also approve of C in Bucklin.... and then C could still win 
in the first round.

The scenario I worry about here is that B is really the Condorcet 
winner, and the Range winner, and the B voters were merely more 
willing to disclose lower preferences. IRV will choose A and C for 
the instant runoff, and top-two runoff for a real runoff, which is 
fine, except for that contingency.

I do believe that Bucklin would handle this well, in general. Some 
voters will add lower preferences, enough to show, even if there is 
majority failure requiring a runoff, what the best two candidates 
would be for the runoff. Again, if write-ins are allowed in the 
runoff, and the wrong two candidates get there, and there is real 
preference strength behind that error, the voters can fix it.

They will be in a better position to do so if the ballot is actually 
a range ballot, they will have a better idea of the chances of a 
write-in campaign in the runoff.