[EM] immunity to burying

[Jameson Quinn]

2011/2/21 James Green-Armytage <armytage at econ.ucsb.edu>

>
> 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.
>

Yes, but my criterion is equivalent to yours for ranked methods, but the
natural extension is different for rated methods. Basically, it's a question
of whether you look at switching A>B for B>A as raising A, or lowering B,
when it comes to rated methods.


>
> 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?)
>

Thank you for the example. Unlike the "Bucklin" example which started out
this thread (which showed a pathology of ranked Bucklin which was not
pathological at all in the (rated) MCA case), this is indeed on-target. Not
only do I consider it to be a problem with Approval, I consider it to be the
most serious such problem, one which would probably occur in real life. I
like your analogy with a game of chicken; in fact, I've used it myself,
without knowing who thought of it first.

The undesirable strategic behavior here is one I'd termed "truncation", not
"burial", but I can understand how by your definition it's burial. I see how
your definition has precedence over mine, so that I need to come up with a
new term. Are you happy if I call burial lowering w "minimal burial", and
burial raising x "third-party burial"?

Actually, considering it further, that's not a particularly useful
distinction. As your example shows, even systems with immunity to
"third-party burial" can show undesirable burial pathologies. While the core
definition of MCA - that is, the "system" which may "elect" multiple or zero
winners for simultaneous or failed majorities - is in some sense immune to
these pathologies, I suspect you could construct a "minimal burial"
pathological example, where rational strategy risks electing C, for any
given MCA system.

The guarantee which some MCA systems (including Approval, which technically
falls under the MCA definition, although it's scarcely recognizable as such)
can give you is that there's no incentive for dishonest burial; in examples
like the above, you are never strategically forced to vote B below C.

I have to go, and I want to send this now. So, let me say, I'd like to find
a rigorous definition of burial, equivalent to yours in all ranked cases,
where only scenarios which risk electing a third party count. I haven't yet
found such a definition. Until I do, I accept your definition of "burial" as
the best existing definition; and unconditionally, I accept your right to
insist that I find a different name your definition has precedence, though I
trust that you'd be thoughtful about whether to insist on that right. This
discussion has helped my thinking, thank you.

Jameson
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