the anti-middle strategy examples with Condorcet
nkklrp at hotmail.com
Tue Feb 22 18:51:27 PST 2000
Bart (& EM):
The 2 examples that you posted could conceivably happen, but
they wouldn't bother me if they happened, because someone gets
an outcome that he likes less than the middle compromise, after
he refuses to support the middle compromise, then that voter has
no one to blame but himself.
One thing about Condorcet is that truncation can't elect a
candidate over whom a majority have ranked the CW, when there
is no voting of unfelt preferences. Other pairwise methods can't
make that claim. That property can be generalized to a claim
that no other rank-method can make, a criterion that I'll
post within a few days, when I discuss criteria & demonstrations
In the first example, the middle candidate, B is little liked
by either extreme. They each rate B barely over the opposite
extreme. That could happen if B has some sort of non-positional
disutility like corruption or a scandal. But the voter median
position will be a popular & crowded place for candidates, and
there'd likely be a good selection there, including candidates
who are well-like and well-known.
I'm just saying that the examples aren't something that can be
expected to happen a lot, and so they aren't a worry for
Condorcet. Typically the A voters or the C voters would feel that
the utility expectation from supporting B is better than that
of the AC lottery. If, as would usually be the case, there's
a middle candidate who doesn't have more non-positional disutility
than the extremes, then if the A voters perceive him close to
C in merit, then the C voters likely would also--if he doesn't
have disutility apart from his actual position on the spectrum.
The probability estimates about whether A beats C pairwise, or
vice-versa, and the utilities for the various candidates, as
judged by the various voters, would have to balance just right
in order for that situation where both sides consider defection
against B to have better utility expectation than support for B.
I too have sometimes noticed similarities in some strategy situations
with Condorcet & Approval, the best methods.
I should add that order-reversal, in Condorcet, is likely to
backfire if the intended victims know what's going on as well
as do the reversers, as they'd be likely to. And if the intended
victims don't actively help their victimizers. In the reversal
example, if the A voters reverse against B, and the C voters
support B, and the B voters don't vote a 2nd choice (the non-drastic
defensive strategy of someone expecting order-reversal strategy),
then that reversal will elect C, where sincere voting would
have elected B.
Additional disadvantages of order-reversal are that it would
discredit one's candidate and that candidate's party. And,
since reversal normally works only by taking advantage of people
who'd helped the reversers' candidate, those people are unlikely
to give that support again.
And order-reversal, in fact, could discredit the voting system
itself, and that would be a reason for people who like the
voting system to not order-reverse.
The reason why it took so few reversers to have an effect in
the 2nd example is that there are so few B voters. That's possible,
and some of our IRV bad-examples are somewhat like that. But
it doesn't sound typical. We have IRV bad-examples in which
the median CW candidate that IRV eliminates is also the one
with more first choice support than any other candidate.
The 2nd example shows one kind of situation that explains why
no method can meet a criterion that requires that no voter ever
have strategic incentive to vote a less-liked candidate equal to
or over his favorite.
Approval is a remarkably good voting system, in terms of the
criteria that it meets. It meets one of the strategy criteria
that Condorcet meets, which is met by few if any methods other
than Approval, Condorcet & Bucklin:
If a majority of all the voters prefer A to B, then they should
have a way of voting that will ensure that B won't win, without
any of them having to vote a less-liked candidate over a more-liked
That criterion has been named Weak Defensive Strategy Criterion
(WDSC). But it should perhaps be renamed more descriptively; maybe
something like Defensive Order-Reversal Criterion, though
I'm looking for one with a better acronym. Maybe "Drastic Defensive
Strategy Criterion" (DDSC).
Approval also meets criteria met by no other method. For instance:
"By voting a less-liked candidate over his favorite, a voter should
never elect a candidate whom he likes more than any that he could
have elected without voting a less-liked candidate over his
But Condorcet has exclusive criterion compliances too, and I
personally prefer those. If it were up to me, I'd enact Condorcet.
But Approval's criteria compliances make it one of the 2 best
methods, and that, combined with its minimal change from
Plurality (less change to ask for), and its 0-cost implementation
statewide, make it one of the 2 best proposals, and a proposal
possibility that can't be ignored; it's nothing other than
Plurality done right. Proposal options & contingency plans should
be kept open. No one knows how good or how fancy a method the
public will accept. Nothing wrong with having having more than
1 tool in the box.
Actually, Bucklin may be a little better than Approval, but
Bucklin is in the middle; it requires rank-balloting, it requires
significant change from Plurality. But it doesn't share all
the merit of Condorcet. So it doesn't share the advantages of
Approval or Condorcet.
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