[EM] The 101 voter A,B,C example

[Mike Ossipoff]

I've just realized that, in regards to Bruce's 101 voter example,
where 2 voters have perfect information, I made a mis-statement:

There _is_ a Condorcet winner in the election: C is Condorcet winner, 
because, when compared separately with each of the other alternatives,
C is ranked over it by more voters than vice-versa.

When I said that truncation can't work then there's a Condorcet
winner, in Condorcet's method, what I should have said (& what I've
been saying previously) is that in Condorcet's method an alternative
with a majority ranking something over it can't win if there's
a Condorcet winner.

The important elections are the ones where there's a Condorcet
winner. But even when there isn't one, it can be said that
an alternative with something ranked over it by a majority can't
win if there's something that _doesn't_ have anything ranked
over it by a majority.

In Bruce's example, the truncation works because only 26/101
of the voters have bothered to rank C over B. In that case,
who should we blame that B won? Apparently very few people
oppose B enough to vote anything over it.

So it doesn't seem to me that this example shows anything wrong
with Condorcet's result. And the only reason C wins in Regular-
Champion is because it has a 1st choice plurality. Anything could
have won in Regular-Champion. 

Of course even if a majority had ranked C over B, order-reversal
could have still won for B, since the C voters didn't use defensive
truncation strategy--they helped make A be beaten by a majority,
by some of them ranking B over A. Otherwise it wouldn't have been
possible to muster a majority against A, and it would therefore
have been impossible for B, with a majority against it, to win.

But that defensive truncation would only be needed if large-scale
order-reversal was likely. Otherwise no strategy whatsoever is
needed. And Copeland, including Regular-Champion, needs not
just strategy, but drastic defensive strategy, under common
conditions, without order-reversal. And order-reversal can
make Copeland (incl. Regular-Champion) need the especially
drastic defensive strategy of ranking a less-liked alternative
_over_ a more-liked one. With mere truncation, Copeland would
only require the drastic defensive strategy of ranking a
less-liked alternative _equal to_ a more-liked one. But
either way, Copeland, in all its versions, doesn't come
close to Condorcet when it comes to getting rid of the 
lesser-of-2-evils problem or eliminating the need for
defensive strategy.


Mike




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