[EM] immunity to burying

[Jameson Quinn]

2011/2/20 James Green-Armytage <armytage at econ.ucsb.edu>

> Hi Jameson,
>
> A quick reply to your most recent post.
>
>  To me, the term "burial" implies burying under something. So, I'd propose:
>> If w is winner when votes are sincere, and voters who prefer q to w change
>> their ballots only by giving w an inferior ranking, or by improving the
>> rating of x, then the winner cannot change fro w to q.
>>
>
> First of all, if you'd like to define a new criterion, I urge you to give
> it a different name from existing criteria. I'm not just proposing these
> definitions of burying and compromising now; I've been using them for years
> -- see for example my 2004 Voting Matters paper. (I originally got the terms
> from Blake Cretney's condorcet.org web site, though this doesn't seem to
> be online anymore.) Having more than one criterion with the same name does
> happen, but when it does, it causes confusion, and signifies poor
> communication within the intellectual community. Take, for example, the
> endless muddle over the "independence of irrelevant alternatives" criterion.
> Another example I've recently discovered is 'local IIA', which has been
> defined one way on Wikipedia for years, but which had apparently been
> defined in a different way in the academic literature for several years
> before that.
>

Understood. But regrettably, many criteria are originally defined only for
ranked methods, which leaves their extension to rated methods ambiguous.
Without the link, I'm not sure if you included rated methods in your 2004
definition.

Furthermore, I believe that there is generally a "right way" to extend a
criterion from ranked to rated methods. The extension should of course be
naturally synonymous with the generally-accepted criterion in the ranked
case (since you can define ranked methods as being a subset of rated
methods, with a few simple assumptions). But it should be the
most-restrictive extension where failure is necessarily undesirable for some
consequentially-defined reason.

>
> Secondly, I find your statement of this new criterion somewhat confusing.
> Do you mean "*or* by improving..." or "*and* by improving..."?


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.

This is identical to your definition for ranked methods, because for such
methods lowering w must imply raising some x (and we can always find the
edge case where it only means raising one x). I claim that it is the "right
way" to extend your definition to rated methods, in that when a method
passes my definition and fails yours, that is not a good reason to avoid
that method; but that when it fails both, that is such a reason.


> To say that this is 'better' than the first definition seems like much too
> strong a statement. If anything, it's just a different criterion.
> If my preferences are A>B>C, I estimate that the sincere winner is B, and
> so I vote A>C>B in the hope of getting A elected, then this is unambiguously
> a form of insincerity, and yes, it risks getting C elected in some cases.


Exactly.


> Whether this is 'a priori wrong' seems like a question that is more
> abstract than necessary.
>

"a priori wrong" was shorthand for "could have socially undesirable
consequences", that is, elect C who is not an arguably-optimal winner. But
you're using a ranked example again. For rated cases, failing your
definition does not imply that rational strategies with such consequences
are possible. My definition, which is synonymous with yours for ranked
cases, works for rated cases, in that failure does have that implication.

Cheers,
Jameson
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