[EM] Maybe my suspicion can be justified somewhat
mikeo2106 at msn.com
Fri Jun 29 18:02:23 PDT 2007
I said that I suspect that no nonprobabilistic method can be more
strategy-free than wv Condorcet and its close relatives that trade one of
its criterion-compliances for another. I don' have a proof. It's only a
suspicion. It was suggested by my brief look at DSV and Nash Equilibrium
Selection. I can also say a few very un-rigorous words about why that
suspicion makes sense:
First it's necessary to say what I mean by strategy-freeness. A majority is
a group who can get their way. It's just a question of what they need to do
to get their way. If they all want the same candidate to win, then, with
pretty much any method but Borda, that's easy. More demanding is if they
want to keep Y from winning, by voting X over him/her. To complicate things,
maybe they like Z even less than Y, and want to similarly vote Y over Z for
the same reason. Can they do that against Y while still voting Y over Z?
They may not know who their best attainable compromise is. Maybe, for all
they know might be Y, but that doesn't mean they don't want to defeat Y if
they can do better.
So the question is: If a majority prefer X to Y, what need they do to make Y
lose? That's the demanding strategy question, and that's what my majority
defensive strategy criteria are about.
And that's how I'd measure strategy-freeness.
No method can distinguish sincere pairewise votes from falsified ones. If
each of the 3 candidates has a majority against him/her, no method can say
which is sincere and which is strategically falsified.
So evidently no method that looks at pairwise majorities (as the most
strategy-reducing methods must) can avoid vulnerability to offensive
If something has to be done by voters to thwart offensive order-reversal,
what could be a more mild and minimal defense than mere truncation?
So far, then, it's looking as if wv can't be beat.
As I was saying before, it would be nice to say that if a majority prefer X
to Y and vote sincerely, Y can't win, period. That would be too much to ask
for, due to indeciveness. Order-reversers might make everyone have a
majority against them. So then say there's no falisification and no majority
sincerely prefer someone to X, as would be the case if X is CW. Then Y's
majority defeat can't be nullified by being in a cycle of such defeats.
Intuitively it seems that one shouldn't expect more than a guarantee that Y,
with a majority against him, can't win under those conditions. Again, what
wv guarantees looks like the best that we could ask for.
As I said, it isn't rigorous at all. But it has some convincingness, and it
gives some confirmation to what my brief look at DSV & Nash Equilibriium
Selection (NES) seemed to suggest.
By the way, someone objectes to NES on the grounds that the number of Nash
equilibria could be greater than or less than one. No problem. There could
be a rule to deal with such situations.
NES and DSV has something in common. They both simulate voters getting the
best they can. NES has rankings as input and DSV uses ratings. DSV uses
strategies more involved than NES's simple question "Can anyone improve on
this?". NES, then, has more simplicity appeal than DSV does.
NES & DSV are probably too involved, too elaborate procedurally to be as
winnable as SSD or MDDA.
But they (and maybe especially NES) have a simple, natural moral
justification that's otherwise difficult to get with rank methods.
I'm not proposing NES, but it's an interesting possibility. Maybe under some
circumstances it could be a good proposal, but not likely under present
conditions. It's interesting that NES seemed to duplicate wv's properties,
and that DSV likewise didn't seem to improve on wv.
Add-on enhancements like ARLO help by automatically doing strategy so that
the voter won't have to. In previous years I've discussed, here,
enhancements more automatic than ARLO. ARLO could be helpful with all sorts
of methods, not even limited to rank methods. I don't propose it with a
first proposal of a good single-winner method, because its added
complication would hurt the proposal.
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