the anti-middle strategy examples with Condorcet

Wed Feb 23 20:36:22 PST 2000

First I want to emphasize that none of this should be taken to
mean that Condorcet has complicated strategy. Even Plurality
is much more demanding than Condorcet, strategy-wise. What
distinguishes Condorcet is its reduced need for defensive

I'm just commenting on what I can now, though it will likely
be possible to say more after studying the message:

>        Est.
>        Probability
>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
>away an almost certain win by ranking B, in the event that it has less
>than 50% of real votes.

But I just want to add that, if group #1 doesn't trunate, then
trucation by group #3 won't gain anything, though it won't
lose anything either.

>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.

If C really gets 1st choice ranking by 52% of the voters, as
estimated, the of course C wins no matter what.

If not, if neither extreme has a majority, then B is the CW,
the candidate with a sincere majority over each of the others.
B should then win. If the C voters don't take advantage of an
offensive strategy possibility that depends for its success
on the A voters taking a gamble, and as a result the CW wins,
that isn't a bad outcome. Condorcet has elected the CW.

>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.

If I'm a C voter, and the B voters have the same predictive
information that I have, and I consider B to be in danger from
order-reversal by A voters, then B voters will know that too,
and I can count on them to do the defensive strategy against
that order-reversal. Though I could prevent it by ranking B
ahead of C, I don't need to. As for truncation by A voters,
I don't need to do anything but sincerely rank B. No strategy
is needed to thwart offensive truncation in Condorcet.

Actually, with 3 candidates, it's especially easy, with Condorcet,
because the middle candidate's voters really have no reason to
rank anyone other than the middle candidate.

>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.

The middle voters, in IRV, could vote probabilistically in such
a way that it each of the 2 extreme candidates would have a 50%
chance of winning after B gets eliminated. Of course they'd have
to announce that beforehand. It might or might not force extreme
voters to rank B 1st, enough to prevent the elimination.
Or if they could announce a definite voting plan, voting
their favorite extreme in 2nd place, so that it would be
obvious to the members of the other extreme that they need
to vote B in 1st place. The problem is that sometimes people
will be timid, and mistakenly give the election to Middle. Avoiding
the need to do that is, for me, the main purpose of single-winner
reform, which is why I don't rate IRV as an improvement over

Mike Ossipoff

> > 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
> >
> > ______________________________________________________
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