[EM] Condorcet Flavored PR Methods

[Forest Simmons]

Is there a sequential version?  Yes, as a matter of fact I discovered the
sequential version first and then worked backwards to see what the form of
the simultaneous version would have to be.

To derive the sequential version from the simultaneous, just start with
the winner w1 of Ranked Pairs, say, and compare all two candidate subsets
of the form  {w1,x}.

Say the winning pair is  {w1,w2}, then compare all three candidate subsets
of the form  {w1,w2,x},  etc.

The sequential version is computationally feasible for large races.

A hybrid would be to do three simultaneous for starters, and then continue
in the sequential fashion for the rest.

I'll answer your other (longer) question later.

Forest


On Thu, 7 Nov 2002, Adam Tarr wrote:

> 2 more questions about Condorcet-PR:
>
> - is there any sequential version of this?  I can't figure one, since the
> placement of the cutoffs depends on the total number of candidates being
> elected.
>
> - I will admit this is the first election method I've dealt with where I
> have trouble manipulating small examples.  Here's a very small example that
> was gibing me trouble: say we are electing two candidates out of four.  My
> ballot is: A(>B=C=D).  The pairwise matrix will be 6x6 (with 6 empty
> slots).  With respect to my ballot, every comparison is equivalent to one
> of the following:
>
> AB vs. CD
> (k1 + j2 = 1 + 1 = 2?  k2 + j1 = 0 + .5 = .5?)
>
> or
>
> AB vs. BD
> (k1 + j2 = .5 + 1 = 1.5?  k2 + j1 = 0 + 1 = 1?)
>
> or
>
> AB vs. AC
>
> (k1 + j2 = k2 + j1 = 1.5 + .5 = 2)
>
> Do the summations I wrote make sense?  The results (except the trivial last
> one) seem a bit odd.  I was toying with this example to try and measure how
> equivalent your Condorcet-PR method is to PAV in situations where the
> voters vote in an approval-like fashion.
>
>
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