the anti-middle strategy examples with Condorcet

Bart Ingles bartman at
Wed Feb 23 01:19:35 PST 2000

> 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.

The first example doesn't bother me either, since it seems to do
something perfectly rational.  I don't know that it would be overly rare
though -- it looks like it would still be a reasonable strategy even if
all three groups were in a dead heat, or if the groups were of unequal
size, so long as a group's utility for B is low enough, and its favorite
has some chance of winning:

Est.   of Winning
Vote   A/C Lottery    Candidate(utility)
25%    .11      A(1.0)   B(0.1)   C(0)
23%     -       B(1.0)          A,C(0)
52%    .89      C(1.0)   B(0.1)   A(0)

Note that the vote percentages are only estimated, as they would be
before an actual election.  Group #3 needs to consider the possibility
that it really has less than 50% of the vote.

Here group #1 has a slim chance of winning, so it is still (slightly)
better off truncating.  Group #3, on the other hand, could be throwing
away an almost certain win by ranking B, in the event that it has less
than 50% of real votes.

Again, I have no problem with this result; my only concern here is that
the group which is supposed to truncate might be too naive to do so.

My second example was based on the notion that voter utilities for the
second choice candidate would be more or less evenly distributed.  In
other words, instead of:
04      A(1.0)   B(0.1)   C(0)
45      A(1.0)   B(0.9)   C(0)
you could use:
04      A(1.0)   B(<0.1)   C(0)
45      A(1.0)   B(>0.1)   C(0)

It seems to me that there would almost always be some minority sub-group
within each major group with identical _rankings_ who would prefer to
truncate, or possibly even order-reverse.  True, it's possible for the
mainstream groups to defend against order reversal, but the strategy (&
the need for such strategy) might not be obvious to most voters.  It
might actually be easier for voters who are confident of the best
approval strategy (& who have a high enough opinion of the sincere CW)
to vote as they would in approval, as a sort of routine safety measure.

I think if IRV were enacted, I would do something similar.  You can't
rank multiple candidates 1st, but you can refuse to bad candidates,
thereby possibly forcing someone else to support one of your favorites.


> 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
> candidate.
> 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
> favorite."
> 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.
> Mike Ossipoff
> ______________________________________________________
> Get Your Private, Free Email at

More information about the Election-Methods mailing list