more on fairness & votes-against
dfb at bbs.cruzio.com
Sat Apr 20 14:45:24 PDT 1996
I promised that I'd say more about the possible method mentioned
by Steve, by which the alternative with worse Condorcet score is
eliminated, and this is repeated.
In the Dole, Clinton, Nader examples we've discussed, Clinton
, in the order-reversal examples, would immediately be eliminated,
leaving only Dole & Nader. Dole beats Nader, so Dole wins, as
I understand that method. So that method would reward the order-reversal
of the Dole voters. I haven't checked Condorcet-Elimination's results
in enough truncation situations to know if it fails there too, but
the fact that it doesn't do as well as the Condorcet's method that
I've already proposed when it comes to order-reversal is reason
enough for me to prefer the method that I've been proposing as
One other thing: You mentioned a defensive strategy, against
order-reversal, that could be used by the Clinton voters: If they
expect order-reversal by the Dole voters, then the Clinton voters
could insincerely rank Nader over Dole. I already pointed out that
insincere defensive strategy is what we want to get away from the
need for, and that, with methods other than Condorcet's method,
such strategy is needed not only for order-reversal, but also for
the very common practice of truncation.
But what I didn't add is that if the Clinton voters used that
general Pairwise defensive strategy to protect against order-reversal
&/or truncation by the Dole voters, then they'd be setting themselves
up for order-reversal &/or truncation by the Nader voters. If the
voters who believe their favorite to be middle Condorcet winner
don't know from which side the offensive strategy (or innocently-
intended truncation) will occur, then they don't know how to vote.
A defensive strategic dilemma, just what we want to avoid.
Sure, in _any_ method, including the Pairwise methods, voters with
sufficiently accurate & complete predictive information can protect
the Condorcet winner & guarantee its victory. But the problem is
when such information isn't available. The best methods, therefore,
are the ones that don't require defensive strategy under common
conditions, and that don't require drastic defensive strategy
(which I define as voting a less-liked alternative equal to or
over a more liked one).
So yes, Pairwise method (using using the definition that excludes
non-Condorcet-criterion methods) have certain general Pairwise
defensive strategies, but their general strategic situation is
nowhere near as good as Condorcet's method (When I use the term
"Condorcet's method", I'm of course referring to it as I've defined
So then, what could the Clinton voters do if they didn't know
from which side the truncation &/or order-reversal would be done?
Well, they could vote probabilistically in such a way that, based
on the best predictive information available, no one could predict
whether Dole would beat Nader or vice-versa. That way order-reversal
or truncation would have a risk. But if a Nader voter values
Clinton very low, rating him quite close to Dole, that Clinton
strategy might well not deter a Nader voter from truncation or
(Of course, not wanting to screw up the outcome by making a
circular tie, and defeating the Condorcet winner by strategy,
thereby fueling criticism of rank-balloting, is something
that _would_ deter Nader voters from using order-reversal.
In Condorcet's method truncation is harmless, so Nader voters
would have no reason to feel compelled to vote for Clinton for
the above reason. Of course they might (or might not) vote
for him they felt they needed him to defeat Dole).
The Nader voters also have a general Pairwise defensive strategy
against order-reversal &/or truncation by Dole voters: They
could rank Clinton in 1st place, equal to Nader, to defend against
Dole-voter truncation. To defend against Dole-voter order-reversal,
they could rank Clinton alone in 1st place. Those, by the way, would
be their strategies against truncation & order-reversal in Copeland
or Regular Champion. That doesn't have much appeal to anyone who
wants to get rid of the lesser-of-2-evils problem.
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