[EM] Markus: Tideman(m) & Condorcet Criterion

[MIKE OSSIPOFF]

Yesterday I said, in answer to your question, that I didn't know whether
or not Tideman(m) is better than Plurality, because I haven't dealt
with minutiae like the possible merit difference between methods like
that. Of course I never said there _wasn't_ a merit difference.

Actually, maybe Tideman(m) is marginally better than Plurality, but
not enough to make it an adequate method.

I say that because the Condorcet Criterion, in a distant, hypothetical,
"what if" sort of a way, does relate to voters' strategy situation.

The obvious way in which it has to do with that is that if no one
uses strategy, then no one has legitimate reason to regret using
strategy.

Also, if everyone has complete information about eachother's preferences,
and so everyone knows what to do, then the sincere CW wins, no matter
what voting system is used (except that I don't want to guarantee that
for Borda), when people use the strategy that they need to get their
best ourcome for that election. Riker demonstrated that sometime before
1977. It's mentioned in the _Scientific American_ article that he wrote
with Niemi in '76 or '77, on voting systems.

So, if everyone uses completely well-informed strategy, the sincere CW
(SCW) wins. Since the SCW is what people would get if they all
knew the situation, the victory of the SCW has a certain rightness.
So there's also something right when it can be guaranteed that the SCW
will win if everyone votes sincerely. In rank methods that means
a guarantee that the SCW wins if everyone sincerely expresses all of
their preferences. For the purpose of applying the Condorcet Criterion
to rank methods only, it could be defined with reference to nothing
about voters except for their votes, as Markus would like: A
candidate who pairwise-beats each of the others must win. That too
sounds like a good thing to guarantee.

So I'm not saying that the Condorcet Criterion doesn't mean anything,
and when we're examining the bottom-end methods, something like the
Condorcet Criterion can be used to establish a merit difference between
bad and worse.

But the operative expression above was "what-if".  Truncation will
always be common, and everyone sincerely expressing every preference
is a fiction. That's why I question the value of Condorcet's Criterion
for anything other than establishing superiority to Plurality.

The defensive strategy criteria are down-to-earth, materially,
strategically practical criteria. So I claim that any one of the
defensive strategy criteria is worth more than the Condorcet Criterion.

For instance, there's an IRV mitigation that meets WDSC, and maybe
that's all it meets. Voters are allowed to split their one vote by
dividing it between more than 1 candidate, by ranking more than 1
candidate at a rank position, any rank positionn(s). Though, unlike
Approval & Condorcet, that IRV mitigation likely meets nothing but
WDSC, that's enough to make it better than Tideman(m), Dodgson,
or any other rank method other than Condorcet or Simpson-Kramer(wv).
(Where Condorcet includes Tideman(wv), SSD, etc.)

Why don't we mention Condorcet's Criterion at the website?
Anything that meets the 4 majority defensive strategy criteria
also meets Condorcet's Criterion. I don't have a proof for that,
so if you can cite an exception, feel free to do so. The reverse
isn't true: Meeting Condorcet Criterion doesn't mean meeting even
one of the majority defensive strategy criteria, or other defensive
strategy criteria.

So then, why should we mention Condorcet's Criterion? It's covered by
the more valuable & stronger criteria that we use. Why bother readers
with an additional criterion that is relatively worthless compared to
the criteria that we're already using, and whose compliance is guaranteed
by compliance with some of the criteria that we're using?

Why do I say that Condorcet's Criterion is relatively worthless?
Many agree with me that the lesser-of-2-evils problem is a real
problem. Either we get rid of that problem to the extent possible, or
we don't. Condorcet's Criterion doesn't. So the fact that Condorcet's
Criterion can be used to compare bottom-end methods doesn't make it
valuable. As I said, either we do or we don't, and Condorcet's Criterion
doesn't.  It isn't even part of the array of criteria that measure that.

Again, you might say I expect too much from a voting system, but there
are a number of voting systems that meet some of the defensive
strategy criteria, including the simple & modest Approval. So I
don't think I'm asking too much from a voting system.

Mike Ossipoff

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