[EM] Exact P.R. - Multiple Plurality Winners 21 June 2014

[Kristofer Munsterhjelm]

On 06/22/2014 06:12 AM, DNOW1 at aol.com wrote:
> A very simple P.R. method -- legislative body elections -- to get past
> the armies of math morons --- with their fixation with single member
> plurality / gerrymander AREA stuff.

This seems to be a combination of SNTV, IRV-type elimination, and 
representing voting weight explicitly instead of through numbers of 
votes. It's more or less the "IRV Sainte-Lague" thing we (me and 
Wahlberg) have been discussing earlier, but without the actual 
Sainte-Lague, instead preferring to represent each candidate by a direct 
weighting.

As such, I would refine it this way to clarify the loser elimination thing:

1. Starting with N candidates:
2. If N <= 5 (or whatever), then we're done.
3. Otherwise, eliminate the candidate with least votes, and transfer his 
votes to the first uneliminated candidate on his transfer ballot.
4. Go to 2.

This explicitly sidesteps the mutual dependency problem that might arise 
where loser A ranks B first and loser B ranks A first. However, this can 
lead to strategizing (analogous to Woodall vote management) by the 
candidates. If you don't want that, use something more complex, like 
some adaptation of Meek.

I would use a vote fraction limit instead of an N, though. Something 
like "as long as there's a candidate that has less than 1% of the vote, 
keep eliminating". That means that you can have more members when the 
people are divided than when they're nearly unanimous in opinion.

For some reason, no legislative bodies (that I know of) use weighted 
votes for representation. I'm not sure what the reason is, though, but 
what that reason is, it might also preclude using this method.

Also, because it's IRV style, it may eliminate minor candidates who 
would otherwise be centrists within their own view. Say you have a 
divided leftist group, and there's a Bush-Gore-Nader or Burlington 
situation among them. Then the wrong candidate will represent those 
leftists just as the wrong candidate represented the people.

-

Now that we know it's IRV-style, we could also make a more voter-centric 
method. Candidate vote transfers can encourage corruption - it seems to 
do so in certain places, at least. A voter-centric method would go like 
this:

1. Starting with N candidates and a bunch of ranked ballots:
2. If N <= 5 (or whatever), then we're done.
3. Count each candidate's number of votes, which is the number of votes 
where he is listed first.
4. Eliminate the candidate with the least number of votes from the 
ballots and the list of candidates.
5. Go to 2.

Finally, with the method being so close to IRV, I imagine you could have 
nonmonotonicity with either variant.

> ----
> Later - Condorcet Head to Head math using Number Votes with a YES/NO
> tiebreaker (for larger factions having sub-faction problems).
> e.g. some/all of the XYZ folks may be united enough to be 1 of the 5
> larger factions.
> ----------

I suppose you could use my CPO-SL logic here, since your method is very 
close to party list. It would require some mathematics to derive the 
method, though - something like taking the limit as the number of seats 
go to infinity.

> Longer term -- Each Elector/Voter has a direct or proxy vote in
> legislative bodies -- would require a 100 percent secure voting system.
> i.e. Agent legislators might only be giving speeches/data to each other
> -- with the voters doing the actual voting -- esp. on *major* stuff.

I wonder if one could make an internet system based on this to covertly 
introduce democracy in undemocratic countries. On the other hand, 
perhaps not; such a system would have to be encrypted so that the 
authorities couldn't just jail all the candidates ahead of time. But 
being encrypted, it would stand out against ordinary internet traffic 
and thus the users of it (the "voters") could come to attention of those 
in authority. And identifying individual voters in a way that their 
identities couldn't be cloned to do ballot stuffing would also be very 
tricky.