[Election-Methods] Reducing 3-cand elections to 8 scenarios

[Kevin Venzke]

Hi Chris,

I didn't notice you replied on EM. I've forwarded my previous message.

This reply is on-list because I don't think you said anything that you might not want posted. Apologies in advance if that is wrong.

--- En date de : Mar 17.6.08, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> Kevin,
> I'm a bit surprised  that you apparently didn't
> copy this response
> to EM.  It hasn't shown up in the Electorama EM
> archive.
> 
> "At this time, though, my approach is to try to deliberately
> create the nomination disincentive that would prevent there
> from ever being uncertainty as to who the top 3 candidates
> are. I'm reading from FPP's playbook."
> 
> Strong nomination disincentive (as in FPP) is a great evil,

I am trying to look at the big picture, at the desired results. The election method doesn't exist in a vacuum. The most strategy-free (wrt voting and nomination) method with the greatest degree of expression permitted, while great in principle, is still a failure if it doesn't provide the desired results.

FPP's nomination disincentive creates mistakes. I think it would make far fewer if it permitted three candidates, with the same "positioning" incentives it already offers two candidates.

I also don't think (and am not too sure I ever thought) that it's part of the job of an election method to reveal support for candidates that could scarcely win under any method.

I think it's largely a question of at what point in the process voters are asked for their input. With FPP, the major players have already whittled the possible decisions down to two, understandably making many voters feel they can't vote for what they want. With high-magnitude PR in a parliamentary system, voters can vote directly for what they want, but the actual decision (as to policy and the composition of the government) is left to the negotiations of the leaders of the elected parties.

A more complicated method like Schulze(wv), or a method like I want to make which just tries to expand on the best part of FPP, just ask for the voters' input at a different stage of the process of finding a group decision. What I am suspecting is that it won't work very well to ask voters to consolidate the options on election day, using their complicated vote expressions. I think whichever parties consolidate in advance will probably still win. There may be other good options, but they need support and attention prior to election day or they won't get enough votes. (This could explain candidates playing for second under TTR.)

> as is wilfully and avoidably wasting votes.

It would be important to frame the rule so that it doesn't sound like that. For example, you don't hear of FPP having an explicit rule to "throw away all the ballots that don't vote for first place."

The fundamental problem is that I need voters to rank the three major candidates. I can ask the voter to kindly identify just those three and rank them (two of them, that is), or I can force everybody to rank all the candidates. I think the latter is worse for everybody, except for people who just want their vote for fourth place to be noted.

Candidates "playing for third" at the voting stage is not supposed to be possible.

> An intermediate version that might frustrate your purpose
> less would be to Contingent Vote-style eiliminate at once 
> all but the FP top 3.

The method might not even use elimination in its core rules, though. So any kind of preference transfer seems like a lot of work just to satisfy voters who basically cast protest votes (which is less understandable when they're theoretically being given three viable choices). Plus I believe it would still substantially undermine what I'm trying to do, in that the voters would be less focused on the big three.

> "That could undermine the perceived legitimacy of the method"
> I have been assuming that this is a bizzare academic
> exercise on your part,
> and not some serious reform proposal that might have any
> "perceived legitimacy".

The three-faction "winner-takes-all second preferences" part is an academic exercise. But "winner-takes-all" would solve the problem of voters insisting on ranking only one of the three viable candidates.

> With your set-up "3-candidate, 3-faction, full strict
> ranking" scenario many weird and wonderful methods are
> possible.
> You might get some ideas from  the "3-small
> elections" part of  Woodall's draft paper.  
> Maybe even Black wouldn't be bad?  Or whichever is
> Borda-superior of  the winners of methods A and B (and C?)
> ?

I haven't looked at the draft paper for this purpose yet, but some of the ones I remember (and also Borda) can't be performed under the framework because in e.g. Borda it isn't possible to find the winner knowing only the relative sizes of the factions.

Also, there are only 9 Condorcet-efficient methods under the framework, and only three of them are "monotonic." They differ only in the cycles, and correspond to e.g. Schulze, Bucklin, and VFA Runoff.

I would like to consider expanding the framework, but it's hard to introduce anything without causing the number of possible scenarios to balloon. If I allowed all six strictly ranked ballot types, there would be I think 720 ways to order the factions, allowing 3^720 methods to be defined. Most of those would be garbage, or have silly inconsistencies; in addition you couldn't even represent a method like Schulze because you'd have to be able to compare sums of factions' sizes.

Kevin Venzke


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