At 08:22 PM 2/12/2010, Chris Benham wrote:
Rob LeGrand wrote (11 Feb 2010):
<snip>
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.
Well I can't. Electing A would be a violation of the Minmal Defense criterion,
and electing B would violate Woodall's Plurality criterion and
Condorcet Loser.
What "good method" do you have in mind that might not elect C?
And what's good about it?
Standard deliberative process, used for elections by every
deliberative body I'm aware of, including those in Australia....
What they would normally do is allow only vote for one, which with
the profiles shown, would result in
35:A
32:B
33:C
which is majority failure. And then they would continue balloting,
same rules, until one candidate has a majority.
For efficiency, they could use a ranked method. Bucklin, in fact, is
the most efficient, but IRV might seem to work. Let's use IRV on this:
35:A
32:B>C
33:C
B is eliminated, leaving C the winner, with a majority, 65:35. It is
obvious that this method allows truncation. So if the B voters were
really approving C by voting for C, then the result of C is
legitimate. But if they were not, then it is not legitimate. In the
use of such a method for election under parliamentary procedure, it
would be proper for the election to be ratified by vote as a yes or
no on the question, "Shall C be elected." This might merely be a vote
on the question of accepting the report of the clerk or other
election official.
The answer to Chris's question is repeated ballot until a majority is
found. With such a process, and if a preferential ballot is used,
voters may have an incentive to truncate, because the later-no-harm
property of IRV, as an example, fails if a true majority is required.
We can see in this example that the B voters, by ranking a second
choice for C, have elected C, whereas if they did not, balloting
would have been repeated, and B might have won. Indeed, there is very
little difference between B and C in first preference, nor between
any of these candidates in that respect. There might even have been a
Condorcet cycle:
35:A>B
32:B>C
33:C>A
What's the best result? To my mind, it's impossible to tell from the
preferences without knowing preference strengths. It would seem,
however, from the voting pattern that *probably* we'd have something like:
35:A>>B>A
32:B>C>>A
33:C>>A>B
In a range approximation, using Range 3:
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
C is the utility optimizer, by a decent margin. But this is based on
a speculation about preference strengths. This election is really so
close, as far as what can be seen from preferential ballot, that the
electorate does not appear to me to be necessarily ready to make a
decision, unless we can truly take the B>C votes as approval of both
candidates. C's a good choice, though, from the votes, and it might
be enough to submit the matter to ratification under the rules.
That's one reason I like asset. In this case, though, Asset would not
have made a difference, because the B voters explicitly provided a
second choice, thus resulting in a true majority of votes for C.
That they violated LNH doesn't matter, does it?
LNH is incompatible with a majority requirement. I think that should
be explicitly understood and acknowledged. (Coercing votes, as in
some Australian elections where Optional Preferential Voting is not
used, does not generate true majority results, it creates a majority
of the votes, all right, as a mathematical certainty, but by tossing
any votes that result from voters refusing to vote for a candidate
when, perhaps, they detest the candidate. All that has to happen is
that they detest more than one....)
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