[EM] reply to earlier letter re: H,M,S example
dfb at bbs.cruzio.com
Tue Mar 5 05:53:26 PST 1996
Steve Eppley writes:
> keywords: single winner election reform Condorcet pairwise
> approval disapproval NOTB "None of the Above" dilemma
> Demorep1 wrote:
> >Condorcet fans seem unable to comprehend that with 2 of 3
> >candidates being "extremists" on a ballot that each "middle" voter
> >will be in a tough situation about what to do about their second
> >choice vote (if any).
> There *is* a minor voter dilemma here, I think. If you slightly
> prefer Hitler to Stalin you want to rank Hitler over Stalin. But if
> you think Hitler has more support than Stalin then you want to rank
> Stalin over Hitler, hoping to make Hitler "more beaten" than Middle
> in the tie-breaking. If I'm wrong, then I need to work through some
> tie-breaking examples until I get it.
Middle voters have no real need to vote for either extreme. If
Middle isn't Condorcet winner then an extreme has a majority, in
which case it doesn't matter about Middle voters' 2nd choices. If
Middle is Condorcet winner then he's the rightful winner, and Middle
voters don't need to vote for an extreme, because 1 of the extremes
needs Middle. The election of the opposite extreme would hurt Middle
voters less, and all the voters know that.
But, unless large-scale order-reversal is likely, there's no penalty
for Middle voters voting in 2nd place whichever extreme canddiate
they prefer to the other. With that lineup, however, as a Middle
voter, I'd not vote a 2nd choice, for the reasons I gave above.
By the way, if Middle, is bigger than the difference between the
extremes, that's all it takes to make Middle the Condorcet winner.
A sufficient, but not necessary, condition for this is for all
the candidates to be within a factor of 2 of eachother.
Another thing: If we're talking about dilemma about whether or
not to vote a 2nd choice, it's Approval that has a problem here,
not Condorcet. With just 3 candidates, in Condorcet, no one has
a dilemma. But with Approval, the extreme voters have a dilemma,
since they have to try to guess whether their favorite has a win,
and whether, if not, the opposite extreme will win if they don't
Now, if we want Condorcet to have a strategy dilemma, we need to
have 1) at least 4 candiates, with uncertainty about which one is
middle Condorcet winner; & 2) The likelihood that the devious
offensive strategy of order-reversal will be attempted on a
scale sufficient to change the election result. This is improbable
for several reasons: a) Order-reversal is risky, and well-deterred;
b) If a group wanted to organize such cheating on a large scale,
it's unlikely that they could keep that campaign secret from the
intended victims of the strategy, and those intended victims
could easily make it backfire with the simple countermeasure of
not ranking the candidate of the order-reversers; c) Order-reversal,
since it only works if the victims vote for the perpetrators' candidate,
is a really dastardly betrayal. The victims would never again
support the perpetrators' candidate.
But say we have lots of candidates, and suppose that order-reversal
is considered likely. Then Condocet's method does indeed have
a strategy dilemma. But its strategy dilemma, in that situation,
is the same dilemma that Approval has all the time, without anyone
cheating. So Approval has the same dilemma all the time, which
Condorcet's method has only if devious & risky offensive strategy
is attempted on a large scale. This strategy dilemma that Condorcet
has under those improbable conditions is, in fact, quantitatively
the same as the one that Approval has all the time.
So it isn't fair to criticize Condorcet's method because it can,
under some rare conditions, have a strategy dilemma. Other methods
have strategy dilemma under much more common ordinary conditions.
Approval has one in typical conditions.
I should add that Condorcet's strategy problem under those
conditions isn't really as bad, though, because the would be
cheaters know that their intended victims have access to the same
predictive information, and that they know what's going on just
as well, and that their defensive strategy will be accordinglyk
well-informed. Considering the other reasons I gave why
order-reversal on a significant scale is unlikely, it can be
said that Condorcet never has a strategy problem as bad as
Approval--due to the fact that cheating is well-deterred.
> Demorep's real point, missed by Rob and Mike since it wasn't clearly
> stated, is that ordinary Condorcet allows a candidate disapproved by
> majority to be declared the winner.
But, as I said, a candidate who has another candidate ranked over
him by a full majority can't win in Condorcet's method unless every
candidate is similarly majority-rejected. And that's improbable.
Improbable for people to attempt & succeed at electing a majority=
rejected candidate by order-reversal; & improbable for a natural
circular tie to have everyone majority-rejected.
And if the selection is so bad that the winner is someone disapproved
by a majority, the electorate have no one to blame but themselves,
for not running someone they like.
> Condorcet+NOTB provides for a stronger vote against the disapproved
> than leaving them unranked in ordinary Condorcet.
I don't object to NOTB, or to the disapproval count, in a Condorcet
But adding even the small paragraph needed to define that
option could be enough to make people consider the overall method
too complicated. Also, I'm not completely sure whether or not
it could be abused by offensive strategizers, especially if NOTB
can disqualify a candidate merely by beating him. I don't know.
If there isn't an obvious big probem about that, then maybe
there isn't a problem.
Anyway, since Condorcet does a good job of defeating candidates
who are _relatively_ disapproved by a full majority, and because
there's no excuse to not have a candidate selection that includes
candidates who aren't absolutely dispproved by a majority, I don't
think majority disapproval would be a problem anyway.
All-in-all, I don't object to NOTB or disapproval count, but I
don't really consider them necessary.
> Condorcet+NOTB provides protection against majority-disapproved
> candidates as strong as Approval's, and it doesn't have Approval's
> tactical voting problems.
True. In fact it provides better protection.
> My dilemmaless vote: 1=Middle 2=NOTB
> (I would vote 1=NOTB if I disapprove of Middle too.)
> Rob & Mike et al, what's wrong with Condorcet+NOTB? Is it so
> unlikely that all candidates will be disapproved that you're
> comfortable with a dumbed-down ballot? Why the silence?
With the good selection that would become available, when we're
using Condorcet's method, it seems to me very unlikely that all
the candidates would be absolutely dispproved by majorities. But,
as I said, I don't object to NOTB or the disapproval count, especially
if they'd make Condorcet's method more acceptable, and would get rid
of some objections that would otherwise be used against it.
> ---Steve (Steve Eppley seppley at alumni.caltech.edu)
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