[EM] Is there a PR voting method obeying "participation" criterion?

[Abd ul-Rahman Lomax]

At 01:08 PM 11/17/2009, Warren Smith wrote:
>This seems to be an open question at present.  But it might be pretty
>easy to prove or disprove.
>
>A multiwinner voting method "obeys participation" if an extra voter,
>by voting honestly, cannot make the election result worse (in her
>view) than if she had not voted.

Might be a small point, but "voted" should be defined. Under Robert's 
Rules, if a voter writes something on a ballot, the voter has voted, 
and the vote is counted in the basis for majority, and analogous for 
PR would be that the voter has possibly increased the quota.

But we can also look at what happens if the voter votes for an 
irrelevant candidate. If we are going to be able to properly analyze 
the systems in a fair way, I think we have to assume that the voter 
votes for someone who is at least eligible, and that if it's Asset, 
the candidate actually is available to recast the vote and fairly 
functions as an effective representative of the voter in further 
process. No voting method can protect a voter from being dissatisfied 
with the candidate they voted for!

Asset, then, could only change the outcome negatively for the voter 
by causing some effect due to increasing the quota. How could that happen?

 From the voter voting, the quota increased by a fraction. For 
accuracy of vote transfers later on, I recommend that exact quotas be 
used. In the first round, the fractional vote is irrelevant, but it 
would be considered when determining excess votes available for 
transfer. In any case, an increase in quota could cause a failure to 
immediately elect, or could prevent a later election.

But the candidate holding this voters' vote could overcome this, 
still effectively casting the voter's vote to improve the outcome, 
should an initial election that would improve the outcome fail by one 
vote, being a fractional vote short.

I think Asset, properly implemented, satisfies a reasonable 
interpretation of participation. There is no harm caused by the 
voter's participation that cannot be remedied by a proper recasting 
of the voter's vote.

Ah! The voter's vote can affect more than one election. But if 
fractional vote transfers can be made (which I recommend) then the 
voter's "proxy" can fix the problem by spreading that vote among the 
affected candidates. If fractional vote transfers can't be made, 
then, sure, there is a technical failure which is basically roundoff 
error. That's silly, an example of voting criteria gone mad, 
separated from practical reality.

>It is "fair" if symmetric under permuting the candidates and voters.
>
>Conjecture: there does not exist a fair multiwinner proportional 
>representation
>voting method obeying participation.

I don't know how to apply "fair." Can you give an example of a system 
which is not fair by this definition? That would help.