[EM] Participation Criterion

[Richard Moore]

Forest Simmons wrote:

> Richard! Where have you been?

I've been lurking on the list a bit but haven't found the time to post 
on it.

> Perhaps we should do three tests for each ballot: one with all ballots of
> that type removed, another with the one percent replication added, and
> then the normal ballot set (which would be the same for all ballots, so it
> would only need to be done once).
> 
> If the best result were the one without any copies of B, and the worst
> were the one with the most copies of B, then it would seem reasonable to
> remove all copies of B.
> 
> Of course this doesn't guarantee a better result for the B voter, but it
> seems like it would be an improvement more often than not.

I suppose that if a participation violation has already occurred, 
adding 1% probably will not necessarily trigger another one, so the 
benefit will be lost. I would expect that as ballots of type B are 
increased from 0% on up there might be multiple trigger points. Some 
of these will cause the B faction to get hurt, and others will benefit 
the B faction. When the B faction gets to 100% (or exceeds 50%, if the 
method complies to the first-place majority criterion) that faction 
has won, so the last trigger point is a positive one. I don't expect 
the trigger points to be grouped closely together as a rule.

So a better test would be to see if a small negative delta (of the 
magnitude of your 1% or sqrt(N)) makes matters better for the B 
voters. If so, make that negative adjustment.

Additionally, I'm not sure how (or even if) you should group similar 
ballots for such a test; should you coalesce A>B>C>D>E ballots with 
A>B>C>E>D? What about with A>B>D>E>C ballots, and so on? Not 
coalescing similar ballots might mean that some participation 
violation effects could go unnoticed. Coalescing ballots that are only 
superficially similar (such as A>B>C>D>E and A>E>B>C>D) might appear 
arbitrary.

>>Couple that with the computational problem when the number of ballots
>>runs in the thousands or millions, and it seems better to use a
>>participation-compliant method in the first place, or else ignore the
>>criterion.
>>
> 
> 
> It's hard to ignore a defect that discourages participation when one of
> the goals of election  reform is to encourage additional voter
> participation.

I agree it shouldn't be ignored, but patching participation violations 
this way may have unintended consequences as bad as the original 
problem. Keeping the adjustments small might reduce the possibility of 
interaction when multiple groups are scaled back, but it also reduces 
the likelihood that a participation violation will be caught and 
corrected. So my real preference is to use a participation-compliant 
method to begin with.

  -- Richard