requested domonst

[Mike Ossipoff]

In recent posts, I've sent precise definitions of criteria, and 
have demonstrated that Condorcet's method meets those criteria.
Because I talked about different possibilities for the Generalized
Majority Criterion, I should state it here in the form that I'm
using:

A method meets the Generalized Majority Criterion if & only if
it will never elect an alternative over which another alternative
is ranked by a full majority of all the voters, unless every
alternative in the Smith set has an alternative ranked over it
by a full majority of all the voters.

***

A very simple & briefly stated criterion. It's obvious from
Condorcet's method's scoring rule that Condorcet meets that
criterion.

***

There was another criterion that I'd previously called 
"Generalized Majority Criterion", and then changed its name
to "Defensive Strategy Criterion". But before I wrote it, I'd
been wording the same property in terms of "Lesser-of-2-evils
guarantees". It might be better to use the 2 simple lesser-of-2-
evils guarantees rather than the Defensive Strategy Criterion,
which combines them into 1 criterion. And, to fit into the
way of putting things that Bruce as requesting, I'll put those
guarantees in the form of criteria. I'll first state them,
and then demonstrate that Condorcet meets them:

Lesser-of-2-evils criteria:

A method meets Lesser-of-2-Evils Criterion #1 if a full majority
of the voters who vote A over B always have a way that they
can vote that will ensure that B won't win, without any of
those voters having to vote a less-liked alternative equal to
or over a more-liked one.

A method meets Lesser-of-2-Evils Criterion #2 if, when a full
majority of all the voters vote A over B, that automatically
ensures that B won't win, if there's a Condorcet winner, and
if order-reversal isn't used on a sufficient scale to affect
the election's result.

***

Why does Condorcet meet these criteria?

It meets  LO2E Criterion #2 because B has a majority against it,
and a Condorcet winner can't have a majority against it unless
order-reversal is used. Therefore B can't possibly win, according
to Condorcet's method's scoring rule.

Condorcet's method meets LO2E Criterion #1, for all practical purposes,
because, again, B has a majority against it. That majority of voters
who voted A over B, because they're a majority, have the power
to prevent any alternative from having a majority against it.
In other words, they have the power to prevent any alternative
from having another alternative ranked over it by a majority.
In particular, by merely not including B in their rankings, they
ensure that nothing will have B ranked over it by a majority.

If they refuse to rank B, the only way that B could possibly win
is if alternatives other than B were in a circular tie with
eachother, in which every one of those other alternatives have
another alternative ranked over it by a majority.




--