"votes against" in pair-defeats? in all pairings?

[Mike Ossipoff]

Looking at a candidate's votes-against in all of his pairwise
comparisons doesn't work as well, when it comes to strategy
situations. 

For instance, in my standard 40,25,35 example, with
Dole, Clinton & Nader, where sincere rankings are:

40%: Dole, Clinton, Nader
25%: Clinton
35%: Nader, Clinton, Dole


..and where the Dole voters truncate, ranking only Dole,
Condorcet picks Clinton, the Condorcet winner, while
Simpson-Kramer (the relative of Condorcet that looks at
all pairings instead of just defeats) makes it a tie
between Clinton & Nader. If the simple tiebreaker of
Plurality is used, then Nader wins. In any case, the
method would either be indecisive, or its choice between
Clinton & Nader would depend on some other tie-breaker
which might not do what we'd most like, and may not
do as good a job of picking the Condorcet winner.

Someone could say: "If the Dole voters didn't rank Clinton,
then they sure have no right to complain when Nader wins.
But truncation by _some_ Dole voters could give it to Nader
in Simpson-Kramer. The other Dole voters are getting penalized
for a mistake that wasn't theirs. In fact, so, of course, are
the Clinton voters.

And the Clinton voters then might have to get involved with
strategy about their 2nd choice. When Simpson-Kramer is
used in the 40,25,35 example, the Clinton voters could knock
Nader out by voting Dole over him, even if they really like
Nader better than Dole. Do we want them to have to worry
about that?

Trunction, unlike order-reversal, can, & in any election always
will, often be done without strategic intention. It's not
a form of cheating. Should it be punished by the election
of the opposite extreme? That means that we might hesitate
to leave someone out of our ranking, even though that's
Condorcet's non-drastic defense against order-reversal. So,
with Simpson-Kramer, Condorcet's non-drastic order-reversal
defense becomes more risky than it was (not ranking the
compromise is a mistake in any method if your extreme is
the one that can't beat the other--but in Simpson-Kramer
you can regret not ranking the middle either way). In a
more-than-3-candidate election, then, Simpson-Kramer
creates more of a problem, under the worst conditions--
in a devious electorate where order-reversal can happen.

But it also creates problems when only truncation happens,
as I showed earlier.

And not only does it punish truncation where Condorcet
wouldn't, but it doesn't deter order-reversal as strongly
as Condorcet does, for the following reason:

In the 40,25,35 example, if the Dole voters order-reverse
against Clinton, and the Clinton voters have refused to
rank Dole, then, with Condorcet, Nader wins. The order-reversal
has not only been thwarted, but it has been well penalized.

One thing I like about Condorcet, under the worst-case conditions
where order-reversal might happen, is that it punishes the order-reversal,
and thereby deters it. In Simpson-Kramer, in that example, 
When the Dole voters order-reverse, the result is a tie between
Clinton & Nader. Sure, if Plurality is the tie-breaker, Nader
wins. But wouldn't it be better if the main method deterred
order-reversal on its own?

These pairwise ties wouldn't be happening in Condorcet. Simpson-
Kramer returns automatic pairwise ties under the conditions
of those 2 examples.

These are some of the reasons I like Condorcet better than
Simpson-Kramer.


Mike



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