[EM] proportional constraints - help needed
Kristofer Munsterhjelm
km_elmet at lavabit.com
Tue Feb 12 10:07:15 PST 2013
On 02/12/2013 04:59 PM, Kristofer Munsterhjelm wrote:
> On 02/12/2013 12:24 AM, Jameson Quinn wrote:
>>
>> What does monotone even mean for PR? You can make something that's
>> sequentially monotone, but it's (I think) impossible to avoid situations
>> where AB were winning but changing C>A>B to A>B>C causes B to lose (or
>> variants of this kind of problem). That's still technically "monotone",
>> but from a voters perspective, it's not usefully so.
>
> I was thinking of a one-candidate generalization to monotonicity, yes.
> That is, say that X is on the council. Then if some voters raise X on
> their ballots, that should not kick X off the council.
>
> But wouldn't this imply the more strict monotonicity you're talking
> about? Say A and B are in the council. Then you raise B, changing C>A>B
> into C>B>A and then into B>C>A. By monotonicity, B shouldn't stop
> winning. Now you raise A by changing B>C>A into B>A>C and finally into
> A>B>C. Again, by monotonicity, A shouldn't stop winning.
I think I see now. The problem is that raising B may kick A off the
council. So we could define a strong and weak mono-raise. The strong
mono-raise says that if you raise any subset of candidates in the
council (not necessarily all by the same amount), none of those should
be kicked off the council by your actions. The weak monotonicity is just
that for a single candidate.
However, strong monotonicity may be too strong because you could imagine
saying the set is the set of all the initial winners, and then you raise
only one of them first. For the criterion to change, the outcome must
not change at all. So the strong criterion might easily mean "if you
raise a winner, the outcome shouldn't change", and managing that would
be impressive indeed.
I can't off-hand say it's incompatible with Droop, though. Perhaps
impossibility can be shown by making use of Schulze's vote management
proofs. Schulze did qualify Schulze STV by saying it would be
susceptible to vote management where resisting it would mean breaking
Droop proportionality, thus implying that full resistance to vote
management is incompatible with Droop proportionality. Yet I'm not sure
it's entirely the same situation.
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