[EM] Example Demorep requested

[MIKE OSSIPOFF]

When I began writing this the 1st time, it vanished and the
inbox returned. If that meant that an incomplete reply was sent,
I don't know how it happened.

Demorep wrote:

Mr. Ossipoff wrote in part-

In the ideal best category I vote for BeatpathWinner(wv)/CSSD.
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D- Could an example with about 5 choices be done ???

I reply:

I'm glad you said _about_ 5, because 4 candidates is all it takes
to be able to distinguish the wv versions, though I haven't
checked this example to find out if it does. It probably doesn't.
I suspect that in this example all the wv methods would get the same
result. Four candidates give an easier count than 5.

You'll say this is an optimistic example. I've adapted a previous
example of mine to 4 candidates. It's an order-reversal example,
but any example illustrates the use of the method:

Actual rankings:

10: BRN
90: RBN
49: D
75: N

Pairwise defeats: ND175, DR124, DB124, RN100, BN100, RB90

First using the CSSD procedure, then the BeatpathWinner procedure.

Initially all the candidates are in the Schwartz set. The weakest defeat
in the Schwartz set is RB90. We drop it, but the Schwartz set still
includes all of the candidates.

Now the 2 equally weakest defeats in the current Schwartz set are
RN100 & BN100. It doesn't matter in which order we drop them, and
my rule, in any case, is to drop them simultaneously if they're
equally weakest in the current Schwartz set.

R & B are no longer in the current Schwartz set.

Now the current Schwartz set is {N}. Since there's only one
candidate in that set, there are no defeats among its members, and
so it's 1 member wins. Nader wins this election.

Looking at it in terms of BeatpathWinner, Nader's only defeats are
smaller than any of the defeats in Nader's strongest beatpaths to the other 
candidates, and so Nader wins by BeatpathWinner.

Demorep continued:

What is the strategy to play games with BeatpathWinner(wv)/CSSD ???

I reply:

I've been posting about that. This election, by this method,
has equilibria in which defensive truncation is used to protect
the Democrat, as in my example. Adam pointed out that there's another
reliable order-reversal countermeasure that's also part of an
equilibrium: The Nader voters could rank the Democrat equal to Nader,
so that the Democrat's defeat can't be a majority defeat, since the
offensive order-reversers, the voters who prefer R & B to D, aren't
a majority. In general, a group who prefer someone else to the CW
of course can't be a majority, and can't, by themselves, give the
CW a majority defeat.


The adavntage of the equal-1st-ranking is that it elects the CW.
The advantage of the truncation is that it's a milder strategy. It
also results in the CW winning if it's made public in advance.

So, if you prefer the CW, the Democrat, to the Republican &
to Buchannan, then don't rank any lower than the Democrat. That's
the strategy that I suggest if falsification isn't ruled out as
an offensive strategy.

Refusal to rank anyone over the Democrat will work too, and will
elect that CW, but the truncation, as I said, will get that result too
if it's announced before the election, and the truncation is a milder
defensive strategy.

If we rule out falsification as an offensive strategy, then
under the conditions in the premise of SFC, this method has no
strategy.

Demorep rashly continues:

I will make the rash assumption that there is such a strategy and that Mr.
Ossipoff has not quite yet deemed Mr. Arrow to have made some sort of
fundamental error.

I reply:

Gibbard & Satterthwaite are right, so far as I'm aware, if they
showed that all nonprobabilistic methods have situations where
someone can benefit from strategy.

But, as I mentioned above, the wv methods can be strategy free
under certain conditions.

Mike Ossipoff


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