Jobst--
You wrote:
Still, SFC only refers to situations where "nobody reverses a
preference"
I reply:
SFC doesn't just stipulate that no one reverses a preference. It stipulates
that no one falsifies a preference. So if you have no preference between X
and the CW, and you vote X over the CW, you're not reversing a preference,
but you're falsifying one. And if you do, you're not part of an SFC
compliance-testing example.
You continued:
, so SFC doesn't help when people insincerely order-reverse.
I reply:
Condorcet's Criterion, when worded so that it actually works as intended,
only refers to situations where everyone votes sincerely. Criteria often
stipulate conditions. SFC's stipulated conditions are a lot less demanding
and a lot less unlikely than those of Condorcet's Criterion.
SDSC makes no such stipulation. That's why SFC can guarantee more than SDSC
does, provided that its no-falsification stipulation is met.
You can get more, but you only get it under specified conditions.
You continue:
I'd rather have pretty good strategy-proofness against order-reversal
I reply:
"Pretty good" doesn't reassure me much. Criteria are precise yes/no tests
that make it possible to say something definite about what a method will or
won't do. I like the definiteness of criteria. Because, if something can
happen, who can say how often it will happen? How about never. For sure.
You continue:
, which DMC provides better than wv-Condorcet as Forest showed, than
complete strategy-proofness against half-hearted strategies where the
strategizers don't order-reverse for some unknown reason...
I reply:
Here's a known reason: Offensive order-reversal, an attempt to steal the
election from a CW by order-reversing against him/her, can backfire badly in
wv Condorcet. All it takes is the possibility that some people will expect
the possibilityi of the order-reversal and use the simple counterstrategy of
defensive truncation. And with defensive truncation a good
reversal-deterrent, not ranking really disliked candidates, or not ranking
below the expected CW, will become common. The would-be reverer will have to
expect a good chance that his offensive strategy will backfire badly.
And organizing the order-reversal strategy would be easier said than done.
Beause order-reversal is something that won't come as natural as truncation.
So the deterrent counterstrategy is a lot more natural, more easily
spontaneous, and easier to ask for than the offensive strategy.
And how likely is it that one faction could organize a large-scale
order-reversal strategy without its intended victims hearing about it?
And, as I have pointed out, if the intended victims of the order-reversal
merely refuse to rank the perpetrators' candidate, that elects the
perpetrators' last choice. Offensive order-reversers can only steal an
election from someone who is trying to help them. Would that make you proud
of yourself when you use reversal strategy?
DMC probably meets SDSC, but so does MDDA.
With Condorcet wv, Approval, and RV, every situation (configuration of
candidates, voters, and voter preferences) with a CW has at least one Nash
equilibrium in which the CW wins and no one reverses a preference. That
can't be said of most other methods.
But actually maybe it can be said for DMC, because DMC probably meets WDSC,
and there's probably some relation between WDSC compliance and that property
in the previous paragraph. MDDA probably has that property too. And it
additionally meets SFC and FBC.
SFC requires that no one falsify, but, in actual elections, of course it's
only necessary that people don't falsify in sufficient numbers to change the
outcome.
If you don't like SFC's no (significant amount of) falsification
requirement, then I remind you of what you get with that requirement: That
majority is assured that, without any strategy on their part, they can beat
anyone over whom they vote the CW. That's a pretty nice guarantee. They
knonw that without even knowing who the CW is. That's why I say that SFC &
GSFC are the pinnacle of the promise of rank-balloting.
FBC is an absolute guarantee that doesn't ask for any conditions, and is
made individually to every voter.
MDDA meets SFC and FBC.
Mike Ossipoff
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