Example with contrary half preference votes

[Mike Ossipoff]

Say we were using Condorcet's method, with the added provision,
recently proposed, that if a ballot ranks X & Y equally, below
everything else in the Smith set, then that ballot is counted
as casting half a vote for X over Y, & half a vote for Y over
X.

Sincere rankings:

46%: Dole, Clinton, Nader
20%: Clinton
34%: Nader, Clinton, Dole

Dole voters truncate:

46%: Dole
20%: Clinton
34%: Nader, Clinton

With the compulsory contrary half preferences provision,
Dole wins. Without it, Clinton wins. Clinton is the Condorcet
winner, & Dole is the only candidate over whom a majority
has ranked someone else. GMC, Trunation-Resistance, &
LO2E-1 are violated if the contrary half preferences provision
is applied.

But, if the contrary preference votes are _optional_, and
if those criteria are re-stated, replacing "order-reversal"
with "voting of a false preference", and if using the
contrary half prefernces option is regarded as voting a
false preference, then those re-defined criteris would then
be met. TRC, for instance, would be met because it would
no longer be just truncation that's giving the election to
Dole; it would be truncation & false preference voting.
GMC would be met if we regard the person using that option
as ranking Nader over Dole--as he is in fact doing with
half of a preference vote. So Condorcet with that contrary

unvoted half preference votes provision could meet reasonably
re-written versions of those criteria. But the contrary half
preference votes should be optional.

***

Immediately after this note, I'm going to post the "What Condorcet
Offers" letter that I said I'd post. It defines GMC, LO2E-1
& LO2E-2. I'd hesitated to post it, because I've recently discussed
those things on the list. But the letter combines the discussion
in one message, and states it more briefly.

***

Earlier, I defined 3 versions of LO2E-1 & GMC. For brevity, I've
only included one version of each in "What Condorcet Offers".

I should emphasize that, in that letter, the LO2E-1 & GMC criteria
are about particular single choice rules, as opposed to overall
compound methods such as Smith//Condorcet. But though those
particular criterion versions in that letter are only about the
Condorcet part of Smith//Condorcet, since they aren't for
compound methods, it's still obvious that Smith//Condorcet fully
benefits from the fact that the Condorcet choice rule meets
those versions of those criteria.

For GMC & LO2E-1 versions that apply to entire overall compound
methods, the words "the Smith set" should be subsituted for
the words "the set of alternatives from which that choice
rule [or that method] is to choose". With that wording change,
those 2 criteria apply to overall compound methods, so that
it's meaningful to say that a compound method meets or doesn't
meet the criteria.

 With the "the set of alternatives from which that choice rule
is to choose" wording, Smith//Condorcet qualifies in the sense that the
choice rule that it uses to choose from the Smith set meets
the criteria. With the "the Smith set" wording, Smith//Condorcet
qualifies because it, as an entire overall method, meets the
criteria, which now can be meaninfully said to be met or
failed by overall compound methods.

Sorry about all this extra discussion, but I like to try to
not leave things unsaid.

"What Condorcet Offers" will be posted immediately. It only covers
the 2 LO2E criteria & GMC, because those are the criteria that
distinguish plain Condorcet & Smith Condorcet from all other methods.
(Truncation resistance is for comparing pairswise methods, and
IME is worded for comparison of pairwise methods, though IME
could be re-worded for more generality).


Mike



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