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Kevin,<br>
<!---->You wrote:<br>
<pre wrap=""><!---->I'm not sure I've understood your idea, but I'm sure such ideas are worth
exploring. The most intuitive change, it seems to me, would be to actually
eliminate "eliminated" candidates (not just bar them from victory) and start
the process over. Maybe you're saying that. (But I also imagine there must
be a cost to altering the method in such ways. I'm eyeing Participation, of
course.)
CB: Yes, that is what I said. Also I notice in the example you gave,
23 A>C>D>B
29 B>A>D>C
48 D>A>C>B
that the method seems to work ok if it is repeatedly used to one-at-a-time eliminate candidates
until one is left.(First B(71) is eliminated, then C(77) and then D(52), and so A,the CW wins.)
KV:Another idea I haven't thought through would be to change the way the members
of an acquiescing coalition are counted. For instance, in DAC, it bothers me
that an A>B>C=D voter contributes to set ABC as surely as A>B>C>D would.
CB: This doesn't bother me because I think it is this quality that makes the method resistant
to insincere truncation.
In his article, Woodall claims that Condorcet is incompatible with <span
class="moz-txt-citetags"></span>Participation, 4 out his 7 different types of <span
class="moz-txt-citetags"></span>Monotonicity, Later-no-harm and Later-no-help. For the Condorcet <span
class="moz-txt-citetags"></span>die-hards, would DAC (either version) <span
class="moz-txt-citetags"></span><!---->be a good Condorcet-completion method?
KV:I'm not sure what you're thinking here. Completing with DAC wouldn't permit
the method on the whole to meet Participation or later-no-help. DAC's order-
reversal incentive would no doubt rub off to some extent, as well.
CB: I had in mind Diana Galletly's problem, where it might be decided that Condorcet is more
important than Participation. I agree with what you recently wrote about resolving Condorcet
cycles by eliminating candidates, so maybe Condorcet completed by reversed DAC elimination
(stop eliminating as soon as there is no more cycle).
In this paper, Woodall introduces the so-called
<span class="moz-txt-citetags">> </span> "plurality criterion":
<span class="moz-txt-citetags">> </span>
<span class="moz-txt-citetags">> </span> Plurality: If some candidate x has strictly fewer votes
<span class="moz-txt-citetags">> </span> in total than some other candidate y has first-preference
<span class="moz-txt-citetags">> </span> votes, then x should not have greater probability than y
<span class="moz-txt-citetags">> </span> of being elected.
<span class="moz-txt-citetags">> </span>
<span class="moz-txt-citetags">> </span>"I do like this. It seems to acknowledge meaning in being ranked non-last."
<span class="moz-txt-citetags">> </span>
<span class="moz-txt-citetags">> </span>CB: While I of course know what "first-preference votes" are, I am not
<span class="moz-txt-citetags">> </span>at all clear on exactly what the
<span class="moz-txt-citetags">> </span>phrase "strictly fewer votes in total" means (in a ranked-ballot
<span class="moz-txt-citetags">> </span><!---->context). What does it mean ?
KV:For me, "votes in total" or "non-last votes," or "being voted preferable to at
least one candidate," means the number of ballots which acknowledge the candidate,
support him, in any way at all. The other ballots, in my view, most likely
truncated the candidate.
So the criterion means that if X is mentioned on fewer ballots than Y received
first-place votes, we can't pick X. It sounds like a good criterion to me,
because it seems unlikely that, in this case, we could possibly have a good
reason, sufficient information, to think that X is a better pick than Y.
But the main reason I noticed this criterion is because I think "number of
ballots which acknowledge the candidate in any way" can be useful information.
CB: For the time being I am skeptical. I don't see why we need this as well as Monotonicity.
This is the first election-methods criterion that I have seen that employs the word/concept
"probability". I think that there might be a place for "Weak Monotonicity" as a fundamental
standard for those who like to rigorously avoid any reference to sincerity/insincerity in
their criteria. Something which just says that a candidate X generally placed higher on the
ballots than candidate Y should have a greater probabilty of winning, just to knock on the
head any absurd method like "elect the candidate with the greatest number of second preferences".
Chris Benham
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