James G-A here, replying to Jameson Quinn, on the topic of what the
'burying strategy' means.
Understood. But regrettably, many criteria are originally defined only for
ranked methods, which leaves their extension to rated methods ambiguous.
Oh... I see. I've never thought that the definitions of compromising
and burying were at all ambiguous in their application to non-ranked
methods, but at least now I know what you're talking about. My view is
that the definition extends quite naturally: For ranked methods, it
means giving w a worse-than-sincere ranking, and for ratings methods,
it means giving w a worse-than-sincere rating. I see no ambiguity there.
Anyway, to give this some focus, maybe you can tell me a method that
is not immune to burying (as I've been defining it for years), but
which you feel 'ought' to be considered immune to burying.
Approval voting, perhaps? If so, I completely disagree. If you bury w
in approval, there's no need to improve any candidate x in the
process. So perhaps it is immune to burying in your proposed revised
definition? (If so, please don't call it immunity to burying, because
it really is another criterion. Maybe you could call it immunity to
burying-reversal-necessity, or something like that.)
Here's an example of why I disagree, even using your own axioms. You
wanted the criterion to be linked to the socially undesirable
consequences of risking the election of a candidate who couldn't win
given sincere voting, and that's easy to provide.
28 voters: A>B>>C
2 voters: A>>B>C
24 voters: B>A>>C
1 voter: B>>A>C
45 voters: C>>A>B
Suppose that these are sincere preferences, with >> representing
sincere approval cutoffs. The intuition is that A and B are members of
one party, and C is a member of another... sort of like an Obama,
Clinton, McCain situation, if you like. The sincere approval scores
are 54 for A, 53 for B, and 45 for C. However, B voters have an
incentive to bury A (i.e. only approve B, thus lowering their rating
of A from the sincere 1 to the insincere 0), and if they do, A voters
have an incentive to bury B (i.e. only approve A). The risk of
electing C is clear. I described this situation in 2003 or 2004, I
believe, as a game of chicken between A and B supporters, in which
approving the other candidate is analogous to swerving, disapproving
them is analogous to going straight, and electing C is analogous to
the car crash. (Remember the dark talk toward the end of the primary
of Clinton supporters not voting for Obama in the general election?
How much worse might that have been with no time interval separation,
creating a true game of chicken?)
Without the link, I'm not sure if you included rated methods in your 2004
definition.
I'm sorry; here it is.
http://www.votingmatters.org.uk/ISSUE19/I19P2.PDF
Actually, the paper is about a ratings-based method.
OK, let me be more precise and restrictive:
If w is winner when votes are sincere, and voters who prefer q to w and x
change
their ballots only as much as necessary for improving x, q cannot thereby
win.
The wording here still seems quite ambiguous to me.
my best,
James
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