[EM] How to convert a set of CR ballots to a set of Approval ballots

[Kevin Venzke]

Forest,

 --- Forest Simmons <fsimmons at pcc.edu> a écrit : 
> Kevin, I think that the refined method can be slightly improved as
> outlined below.

I implemented the (original) refined method and it seems to be a great 
improvement, although I haven't done a side-by-side comparison.  (I was
judging based on how long I had to wait for a disagreement.  The display
is pretty slow and I'm not using an efficient sort method.)

[...]
> In our refined method we amalgamated adjacent slots with minimal combined
> viability.
> 
> A slightly simpler and (I believe) improved rule would be to amalgamate a
> slot of minimal viability with the less viable of its two neighbors (or
> with its only neighbor if it is one of the two extreme slots).

This should be easy to implement.  It seems to be a very slight modification
though.

> I would like to call this method Max Power Cardinal Ratings (MPCR) since
> its hueristic is to convert the CR ballot into an Approval ballot with the
> maximum likelihood of being positively pivotal, i.e. maximizing the voting
> power of the ballot.

So it's doing Joe Weinstein's strategy, right?  I sort of figured it must be
doing something like that, because when you amalgamate ratings based on
viability, you kind of make a mess of what those ratings were supposed to
stand for.

I wonder if anyone would object for this reason, since Weinstein's strategy
isn't the optimal Approval strategy.  (It only considers relative utility and
the odds.  It cares that you gain, but not by how much.)

> With that in mind, I wonder how three slot MPCR compares with three slot
> Condorcet, especially in the case of only three candidates.

It should be very easy for me to come up with some examples of disagreement.
I'll just do this latest revision, though, unless you're specifically curious
about something.

> Note that IRV judges viability by first place votes, and then eliminates
> the minimum viability candidate.  Perhaps it would do better to amalgamate
> rather than eliminate.  That might save the CW from early elimination.

I could stomach IRV if equal rankings were permitted.  You'd still have to
keep in mind that you can't transfer support to an eliminated candidate, but
it would be an improvement.

Kevin Venzke
stepjak at yahoo.fr


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