Jameson,
Sorry to be so tardy in replying.
"That is not a bad suggestion; I like both systems. Yours gives less of a
motivation for
honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0."
No, mine gives more motivation for honest rating (in the sense that it gives
less incentive
for dishonest rating). If A, B, C are the three Smith-set members then
it makes both
A100, B99, C0 and A100, B51, C0 equivalent to A100, B100, C0.
"I guess you'd give exactly half an approval if B were at exactly 50?"
Yes.
49: A100, B0, C0
24: B100, A0, C0
27: C100, B80, A0
More than half the voters vote A not above equal-bottom and below B, and yet
A wins.
"True. Yet B could win if the C voters rated B 99, which would still be
Condorcet-honest."
That isn't really in principle relevant because your suggested method doesn't
guarantee to a
section of the voters comprising more than half who rate/rank A bottom that
they can ensure
that A loses while still expressing all their sincere pairwise preferences.
4999: A100, B0, C0
2500: B100, A0, C0
2501: C100, B99, A0
B>A 5001- 4999, A>C, C>B.
In this modified version of my demonstration that your suggested method fails
Minimal Defense,
the majority that prefer B to A cannot ensure that B loses and still be
"Condorcet-honest".
"Anyway, the main motivations for a DSV-type proposal like this is to make it
really rare for voters
to have enough information to strategize without it backfiring. I think that
including full range information
(that is, my proposal as opposed to yours) makes the voter's analysis harder,
and so makes the system
more resistant to strategy."
I don't think the type of examples I've given would be "really rare", and in
them I don't think the C
supporters have to very well-informed or clever to work out that their
candidate can't beat A and
so they have incentive to falsely vote B (at least) equal to their favourite.
"Favorite Betrayal in this case means, honest ABC voters who know that A's
losing and that C>B>>A
and A>>C>B votes are both relatively common, can vote BAC to cause a Condorcet
tie and perhaps
get B to win ..."
Not necessarily, no. You seem to be assuming that Favourite Betrayal strategy
is only about falsely creating
a "Condorcet tie" when one's favourite isn't the (presumed to be) sincere
Condorcet winner. It can
also be the case that the strategist fears that if she votes sincerely there
will be no Condorcet winner,
so she order-reverse compromises to try to make her compromise the voted
Condorcet winner.
Chris Benham
________________________________
Jameson Quinn wrote (26 June 2009) :
This Condorcet-Range hybrid you suggest seems to me to inherit a couple of
>the problems with Range Voting.
Fair enough.
>
>It fails the Minimal Defense criterion.
>
>49: A100, B0, C0
>24: B100, A0, C0
>27: C100, B80, A0
>
>More than half the voters vote A not above equal-bottom and below B, and yet
>A wins.
True. Yet B could win if the C voters rated B 99, which would still be
Condorcet-honest.
>
>Also I don't like the fact that the result can be affected just by varying the
>resolution
>of ratings ballots used, an arbitrary feature.
>
>I think it would be better if the method derived approval from the ballots,
>approving all
>candidates the voter rates above the voter's average rating of the Smith set
>members.
That is not a bad suggestion; I like both systems. Yours gives less of a
motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent to
A100 B51 C0. I guess you'd give exactly half an approval if B were at exactly
50?
Anyway, the main motivations for a DSV-type proposal like this is to make it
really rare for voters to have enough information to strategize without it
backfiring. I think that including full range information (that is, my proposal
as opposed to yours) makes the voter's analysis harder, and so makes the system
more resistant to strategy. Under honest range votes, it also helps improve
the utility.
>
>
>"For strategies which don't change the content
>of the Smith set, it does very well on other criteria, fulfilling
>Participation, Consistency, and "Local IIA". "
Sorry, I wasn't clear. If the content of the smith set DOES change, this method
fails all those criteria. See below for argument of why that's not too bad.
>
>"And because it uses Range ballots as an input but encourages
>more honest voting than Range,.."
>
>That is more true of the "automated approval" version I suggested, and also it
>isn't
>completely clear-cut because Range meets Favourite Betrayal which is
>incompatible
>with Condorcet.
Favorite Betrayal in this case means, honest ABC voters who know that A's
losing and that C>B>>A and A>>C>B votes are both relatively common, can vote
BAC to cause a Condorcet tie and perhaps get B to win (if A would win that tie,
then A would be winning already, so they can't get their favorite through
betrayal. In other words, at least it's monotonic.). But if they bring on the
Condorcet tie, they are also risking C winning if there are more C>>B>A votes
than C>B>>A votes. (Of course they're also risking having been wrong and
throwing away an A win, though that's the nature of favorite betrayal and
scarcely bears mentioning.) If they are even considering favorite betrayal,
they probably feel A>B>>C, so even a small risk of C should be a strong
deterrent.
In other words, the whole point of this system is that honesty is the safest
strategy. If voters are even moderately risk-averse and information is anything
less than perfect, the system (and your alternate version proposal) is, I
believe, unparallelled for its strategy resistence. If voters are risk-seekers
and enjoy attempting strategy, then it's no worse than min(condorcet,
approval), which is both IMO implausible and really not too bad anyway.
Jameson
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