[EM] proportional constraints - help needed

[Kristofer Munsterhjelm]

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.