LO2E criteria. Demonstration of compliance.

[Mike Ossipoff]

About a day ago I posted precise & simple definitions of a number
of criteria, and demonstrated that Condorcet meets them.

You had a question about a lesser-of-2-evils criterion. I sent
you 2 such criteria. Let me list them both here:

If there's a set, M, of the voters in an election, consisting of
a full majority of all the voters, all rank the alternative(s)
in set S1 over the alternative(s) in set S2, then the method
by which the winner is chosen meets Criterion LO2E1 if it
meets the requirement in paragraph a) below, and it meets
Criterion LO2E2 if it meets the requirement in paragraph b)
below:

a) The winner can't come from set S2 unless every alternative
in the Smith set has another alternative preferred to it by
a majority or order-reversal strategy is used on a scale
sufficient to change the election result.

b) The voters in M have a way that they can vote that will ensure
that the winner won't come from S2, and this doesn't require
any of those voters to vote a less-liked alternative equal to or
over a more-liked one.

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Those are my Lesser-of-2-Evils Criteria (LO2E critria).

***

LO2E is met by Condorcet for the same reason that the Truncation-
Resitance Criterion is met by Condorcet:

Since the M voters rank the S1 alternatives over the S2 alternatives,
the S2 alternatives each have at least 1 alternative ranked over
it by a majority. If not every alternative in the Smith set
has another alternative ranked over it by a majority, and if
false orderings haven't been voted on a sufficient scale to change
the outcome, then there's at least 1 alternative not in S2
that doesn't have another alternative raned over it by a majority.
So, by Condorcet's method's rule, the winner can't come from S2.

***

Condorcet strictly meets LO2E2 when the "subcycle rule" is used,
and otherwise it meets that criterion for all practical purposes.
I'll show why that is in a posting that will immediately
follow this one.

***

Mike







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