[EM] Re: "sprucing up"

[Kevin Venzke]

Forest,

I certainly think this is an impressive, interesting idea, even if I don't
have a lot of comments on it. But:

 --- Forest Simmons <simmonfo at up.edu> a écrit : 
> In particular, Spruced Up River, Spruced Up Ranked Pairs, Spruced Up Short 
> Ranked Pairs, Spruced Up MinMax, Spruced Up SSD, Spruced Up PC, etc. are 
> all equivalent as long as they all go with the same choice for measuring 
> defeat strength (wv, margins, cardinal pairwise, approval, etc.).

I raise an eyebrow upon reading this, since if all you have done is 
eliminate clones, how can River, RP, and Schulze produce different winners
when they haven't been "spruced up"? All of those methods are supposed to
be clone-proof.

> Consequently, we can subsume all of these methods under the title of 
> "Spruced Up Condorcet," which might come in handy at public proposal time.
> 
> Also Spruced Up Bucklin and Spruced Up Weighted Median Approval (Chris' 
> version) are equivalent.
> 
> Spruced Up Black is equivalent to Spruced Up Borda.
> 
> How about Spruced Up IRV ?

Sprucing up Bucklin and IRV seem particularly interesting. But I doubt it
is able to do anything helpful with the 49 A, 24 B, 27 C>B scenario.

> I have heard that Craig (of Polytopes and Politicians) has a good three 
> candidate method.  If so, then its spruced up version should be a good 
> public election method.

It's not so, though. I believe he immediately eliminates any candidate
with fewer than 1/3 of the first preferences. He has diagrams to justify
this, but unfortunately I can't understand them.

> With little or no loss in generality we can assume that x+y+z=100%.  This 
> equation determines a triangle with corners at (100%,0,0), (0,100%,0), and 
> (0,0,100%) in the first octant of a three dimensional coordinate system. 
> The inequalities max(y,z) < x, and x < y+z narrow down to a subset R of 
> this triangle.  Each partition of R into three subsets (winning regions 
> for A, B, and C, respectively) determines a (deterministic) method.
> 
> In other words, design of election methods (of this type) amounts to 
> shading in subsets of a triangle. How about that for a "Geometry of 
> Voting"? [This is more like what I was hoping for when I read Saari's book 
> by that title.]

Yes, that would be extremely interesting.

It would be nice, in general, if key differences in the behavior of
methods could be shown in diagrams. I don't know how to do such a thing,
though.

Kevin Venzke



	

	
		
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