At 12:55 AM 6/23/2008, Chris Benham wrote:
Kathy,
Imagine that Approval is used to elect the US President and
as in the current campaign the Republicans are fielding one
candidate, McCain. Does that mean that the big fight for the
Democrat nomination between Clinton and Obama we've just
seen would in the Approval scenario be completely unnecessary?
No. That fight is over the Democratic Party nomination and
endorsement. It means that the whole apparatus of the Democratic
Party is devoted to one candidate, which is, of course, strongly in
the interest of the Democratic Party.
Why not simply endorse both candidates? After all, one cannot
possibly spoil the election for the other because Approval has
no spoiler problem. Voters simply approve candidates or not
completely regardless of what other candidates are on the ballot,
right?
Sure. If we imagine that somehow the parties have decided not to
nominate candidates, snowballs in hell nevermind, running both Obama
and Clinton against a single McCain would probaby result in very
common double-voting. Now, if Obama and Clinton heavily campaign
against each other, slinging mud, etc, trying to convince the voters
that the other one is practically the devil, nobody would benefit
from this except McCain. Which is quite why we don't do things this
way. Parties in Australia don't run multiple candidates for the same
single-winner office, do they?
The problem, were it Approval, wouldn't be so much the voting method.
(Which, by the way, loses most of the problems it has if a majority
is required or there is a runoff). It would be the rest of the
system, the process by which voters become informed, or deluded,
depending on your point of view.
I think that in practical effect Approval does have a "spoiler" or
split-vote problem that would be sufficient for the Democrats to
still want to endorse one candidate only.
There are *lots* of reasons why the Democrats would want to do that.
Or any party. This is a red herring argument. The "split vote
problem" in Approval is a very different animal than the split vote
problem in Plurality, or, for that matter, in IRV.
What I actually wrote in my initial post on the 5 "fairness
principles in your paper (regarding IIA):
In practical effect *no* method meets this.Approval and Range can
be said to meet
Independence of Irrelevant Alternatives (IIA) only if the votes are
interpreted as the voters giving
ratings on some fixed scale that is independent of the actual candidates.
No, that's not correct. Perhaps it would be useful if you actually
state the version of IIA you are using. Usually, it refers to adding
or subtracting a candidate without changing the "preference order" of
the other candidates, but if you are going to use it with Range and
Approval, you have to modify it; the basic modification is that the
Range Votes or Approval Votes don't change, and all that happens is
that a new candidate is added to the ballot or taken off the ballot.
If voters are allowed to actually change their votes, *no method
meets IIA.* Simple proof: there is a candidate whose name is a
trigger for a long-hidden internal program that causes human beings
to fall into a trance when they contemplate whether or not to vote
for a candidate, and they leave the booth with false memories of what
happened (really happens with trance, sometimes, i.e, false memory).
The voters see this new name on the ballot, and regardless of how
they would have voted, they become incapable of voting, so all
candidates tie with no votes. And thus the winner could change.
On this perverse interpretation Approval and Range do not reduce
to FPP in the 2 candidate election,
in violation of Dopp's "fairness principle 4":
"Any candidate who is the favorite [first] choice of a majority of
voters should win."
(approval or non-approval counts as "rating" on a 2-point scale).
Chris, you should look at Dhillon and Mertens, "Relative
Utilitarianism," where they purport to prove that Range Voting is a
unique solution to a version of Arrow's voting axioms that
accommodate Range Voting. Relative Utilitarianism refers to "votes"
which are "normalized von Neuman-Morgenstern utilities in the range
of 0-1. I.e., Range Voting. Warren Smith is actually not in outer
space on this (their work preceded his).
Because of the normalization, in the two candidate case, Majority is
satisfied. Because vN-M utilities are modified by probabilities, it
gets complicated in the three-candidate case, where RU is considered
the unique solution. If I remember correctly. I'm hoping to help get
a popularization of Dhillon and Mertens prepared, it's needed. Smith
calls their use of symbols "Notation from Hell." And he's familiar
with the conventions!
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