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

[Kevin Venzke]

Hi,

I didn't realize Chris' last message to me was posted to the list.

Here is my response to it:

--- En date de : Mar 17.6.08, Kevin Venzke <stepjak at yahoo.fr> a écrit :

> De: Kevin Venzke <stepjak at yahoo.fr>
> Objet: Re: [Election-Methods] Reducing 3-cand elections to 8 scenarios
> À: "Chris Benham" <cbenhamau at yahoo.com.au>
> Date: Mardi 17 Juin 2008, 13h01
> Hi Chris,
> 
> --- En date de : Mar 17.6.08, Chris Benham
> <cbenhamau at yahoo.com.au> a écrit :
> > De: Chris Benham <cbenhamau at yahoo.com.au>
> > Objet: Re: [Election-Methods] Reducing 3-cand
> elections to 8 scenarios
> > À: "EM"
> <election-methods at lists.electorama.com>
> > Date: Mardi 17 Juin 2008, 11h03
> > "A couple of drastic measures that appeal to me
> are
> > only accepting (and requiring) a first and a second
> > preference, 
> > and to the extent necessary, discarding ballots that
> > won't cooperate in voting for the top three
> candidates
> > (according 
> > to first preferences)."
>  
> > Kevin,
> > I have the same question I had the last time you
> proposed a
> > method focused on 3 candidates:
> > Instead of  "discarding ballots", why not
> apply
> > these methods to the ballots modified by eliminations
> > after all but 3 candidates have been IRV-style
> > one-at-a-time eliminated?
> 
> The motivation behind the suggestion is different.
> 
> When I proposed SPST I did not realize that IRV could be
> used to reduce the field to 3 candidates. I thought this
> would violate LNHarm. Simply extrapolating on the method to
> allow more than 3 candidates would have violated LNHarm,
> although if I had a way to do it, I don't think I would
> have been opposed to it.
> 
> 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.
> 
> > "Another measure occurred to me: Among the
> supporters
> > of each of the top three candidates, play "winner
> > takes all" 
> > for the second preference. In other words, all of the
> > second preferences from the "A-first" voters
> are
> > considered to 
> > be cast for whichever (of the other two candidates B
> and C)
> > received more. This has a consequence that not giving 
> > a second preference (if such were allowed) is never
> > optimal; your second preference is just determined by
> other
> > voters 
> > with the same first preference."
> 
> > With this weird  (but I suppose not in principle
> > unacceptable) feature, what is the point of 
> > "requiring a second preference"?
> 
> Two points.
> 1. It reduces the probability that the allocation of the
> second preferences will be determined based on a very small
> number of votes (i.e. because most people voting for some
> candidate bullet-voted). That could undermine the perceived
> legitimacy of the method.
> 2. It increases confidence that everyone will be voting a
> preference for two of the three candidates. If supporters
> of the two frontrunners (assuming we have two) are allowed
> to bullet vote en masse, I suspect that they won't care
> much about who the third candidate is. I want voters to be
> debating what ranking they're going to vote, not what
> candidate.
> 
> One of the big problems with trying to elect compromise
> choices, or third place in general, is that you have to get
> people to vote for them.
> 
> I'm not sold on the "winner takes all" system
> for second preferences being a necessary thing, but I think
> it's crucial to have voters believe that if they
> don't play along, they're wasting their votes.
> 
> The "winner takes all" thing is a necessary
> simplification for my method scheme, though.
> 
> I've managed to implement it in a computer program,
> complete with compromise, burial, and monotonicity
> checking. There are 6561 possible methods within the
> scheme, though only a bit over 2% satisfy my monotonicity
> property (i.e. a faction can't make their first
> preference win solely by sending some voters home), and
> only about a third of those offer some kind of strategy
> guarantee to at least one faction.
> 
> Maybe the monotonicity property can be weakened, but
> something is definitely necessary to avoid considering
> methods like "elect second place."
> 
> It is amazing how most of the "best" methods have
> been thoroughly discovered already. I searched for monotonic
> methods that had at least some number (3?) of strategy
> guarantees, and found six I believe, five of which have
> names: Schulze etc., Bucklin etc., FPP, IRV, VFA, and
> "elect B if he's the CW; else elect A."
> 
> I found four (very similar) non-monotonic methods that
> provide no compromise incentive to either the B or C
> factions. No other such methods though.
> 
> I'm currently looking into ways to search for
> strategies that are sometimes useful and never harmful when
> comparing two scenarios that are close enough to be called
> "adjacent" (exactly the same except that two
> factions are swapped in relative size). If a faction can
> predict that the scenario will be one of the two, and can
> assume that no one else will use strategy, they themselves
> are free to.
> 
> Kevin Venzke



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