[EM] Classifying 3-cand scenarios. LNHarm methods again.

[Dave Ketchum]

Why IRV?  Have we not buried that deep enough?  Why not Condorcet  
which does better with about the same voting?

Why TTR?  Shouldn't that be avoided if trying for a good method?  TTR  
requires smart deciding as to which candidates to vote on.

Will not Condorcet attend to clones with minimum pain?  Voters can  
rank them together (with equal or adjacent ranks).

Does not Condorcet properly attend to "symmetric" with a voted cycle?

Dave Ketchum

On Apr 17, 2010, at 7:07 PM, Kevin Venzke wrote:
> Hi,
>
> This post is going to ramble a bit but I thought I'd get something  
> out.
> There are no big conclusions; I'm just explaining where I am at in my
> mind currently.
>
> Here are classifications of three-candidate scenarios as they exist in
> my head:
>
> .'. symmetric - you need a second axis in issue space (beyond left/ 
> right)
> to explain the location of at least one candidate.
>
> ... centrist - the third candidate is between the other two.
>
> :. clone - the third candidate is a clone of one of the other two.
>
> These labels would apply to sincere preferences rather than cast votes
> (e.g., I could interpret the 49/24/27 scenario as resulting from any  
> of
> these).
>
> The situation I'd like to arrive at is .'. (assuming the candidates  
> aren't
> staying quite far from the median for some reason). If we can get good
> preformance arriving at ... then that's pretty good also, but seems  
> like
> a bit of a waste that we only use one axis. The :. scenario is least
> promising but good performance there would still be nice if it's the  
> best
> we can accomplish.
>
> As always, I like simple methods and don't really care if they can't
> realistically support more than three viable candidates. (Unless those
> candidates aren't going to be good.)
>
> The first method I look at fondly is SPST (strongest pair with single
> transfer). In this method we compare the strongest candidate (in terms
> of first preferences) with the strongest pair of candidates (in  
> terms of
> a solid coalition of first/second preferences). If the strongest  
> candidate
> is also a member of the pair, or has more first preferences than  
> there are
> votes in the pair's solid coalition, this candidate wins. Otherwise we
> elim the strongest candidate and transfer his voters' second  
> preferences
> to one of the pair (if possible). The one of the pair holding the most
> votes then wins.
>
> Alternatively you can just have a second round of voting, and not  
> collect
> second preferences. In that case the original ballot could be a  
> "vote for
> one and against one" ballot, probably requiring a majority of against
> votes to eliminate the strongest candidate and then assuming that the
> strongest pair were the 2nd and 3rd place candidates. (I have doubts  
> about
> nomination strategy going this route. But you could add incentives to
> stop it from getting out of control.)
>
> This is a LNHarm method. I also think that VFA is if it isn't  
> mandatory
> to vote against a candidate. (VFA is similar to SPST but there is no
> transfer: If the strongest candidate is disqualified, the second-place
> candidate is elected. A majority of votes against is required to
> disqualify. Also incidentally I'm warming to the name "Venzke
> disqualification plurality" that Warren came up with, which would  
> leave
> the term "VFA" to describe the ballot format.)
>
> [Clarification after writing the whole post: If VFA requires you to
> vote against a candidate, then the voter who doesn't want to do this
> has to randomly vote against someone, and it is possible that this  
> results
> in something better than if he picks someone deliberately. I *believe*
> this is why I didn't in the past claim that VFA satisfied LNHarm.]
>
> Also, continuing to digress, I think an iterative, LNHarm-satisfying
> version of SPST is possible. I'm a little rusty so no promises on that
> yet. But it would work like this:
>
> 1. voters submit a rank ballot truncating wherever they like.
> 2. compare the frontrunner with the strongest pair as usual in SPST.
> (So: check that the pair doesn't include the frontrunner, and includes
> more voters than are currently voting for the frontrunner, and also
> that some voters are actually still ranking 2+ of the remaining
> candidates.)
> 3. if SPST would elect the current leader, "ISPST" does also, and the
> method is over.
> 4. otherwise transfer the current leader's preferences to any  
> remaining
> candidates (eliminating him) and go back to step 2.
>
> It's not completely clear whether the proper complaint is that this  
> favors
> or disfavors the current leader. Maybe the proper complaint is that  
> the
> reasoning behind this method isn't very clear. It makes most sense  
> when
> you really do only have three candidates. In that case IRV and ISPST  
> will
> both pick a winner from the pair, but ISPST will let the supporters of
> the strongest candidate transfer their votes to the one of the pair  
> that
> they like better.
>
> [Having written all that I'm feeling doubts that this satisfies  
> LNHarm.
> It seems like it could be the case that adding a preference creates a
> strongest pair that is not resolved in your candidate's favor, whereas
> perhaps your preferred candidate would've won if that pair had been
> weaker. I won't delete the above though.]
>
> There's a tricky thing with elimination methods. We want to  
> eliminate the
> candidates who can't possibly win and also reveal the votes that we
> think we want to see. If candidates are bunched together in the  
> center,
> chances are the first round leader is leading because he sits on the
> outside and dominates a huge chunk of issue space. If that's true then
> it's clear we don't want to elect that guy and would rather see who  
> his
> supporters' lower preferences are (as opposed to letting him stick  
> around
> to the end, when it's too late for those preferences to move if the  
> guy
> ends up losing). However, eliminating someone because he has a lot of
> votes is clearly not going to end well with monotonicity.
>
> Back to SPST: I think it's good for the :. and ... (clone and  
> centrist)
> scenarios. There are a couple problems. One is minor I think.
>
> 1. If it's a clone scenario and the non-clone candidate can't even  
> manage
> to place first in first preferences, then his supporters do not get to
> transfer their preferences. If one of the clones is more of a  
> centrist, I
> would bet that he doesn't win. I don't see how to fix this, but the
> situation involved seems unusual.
>
> 2. If we approach a .'. (symmetric) scenario then SPST will  
> disappoint.
> If it's not clear that there will be a majority against one of two
> known candidates, then there will be FPP-style pressure to have one of
> the three candidates drop out. In this scenario I'd rather use IRV  
> since
> IRV's center-squeeze problem wouldn't come into play. It's too bad I  
> can't
> flick a switch based on the scenario.
>
> 3. Even though this is a LNHarm but *not* LNHelp method, it could be  
> that
> expecting people to list second preferences isn't reliable. That would
> to me suggest that we should use "against votes" more often.  
> Mechanisms
> like antiplurality are powerful centralizers if you can get control of
> the clone problem.
>
> One thing I don't have a clue about is how you create incentive to
> produce .'. symmetric scenarios. I think that top-two runoff with  
> certain
> incentives (some nomination disincentive namely) might be the best  
> bet,
> but it seems to me that TTR has an appalling lack of centralizing
> incentives in the first round. One has to carve out a fiefdom of  
> voters in
> the first round and then hope you're median enough to win in the  
> second
> round.
>
> It's quite possible that sacrificing LNHarm can produce a solution. I
> haven't been focusing on that possibility since keeping LNHarm while
> sacrificing LNHelp seems like the best way to approximate "votes  
> against"
> without having one on the ballot explicitly.
>
> So that's roughly what I've been thinking about.
>
> Kevin Venzke