[EM] "Total Vote Runoff"
Forest Simmons
forest.simmons21 at gmail.com
Fri Jan 20 23:40:22 PST 2023
A Condorcet Candidate will never have the lowest Borda Count ... not even
below average ... so you could speed this up by eliminating at each step
all candidates with below average "total votes."
But the method is clone dependent ... unlike a similar but simpler
Condorcet Compliant method that Benham calls "Gross Loser Elimination"
(GLE) which (at each step) eliminates the candidate with the smallest
single pairwise vote instead of eliminating the candidate with the smallest
sum of pairwise votes.
In my opinion GLE is the simplest elimination method worth supporting.
Operationally you start by constructing the same precinct summable pairwise
matrix that you would use for Borda Elimination.
But instead of eliminating (at each step) the remaining candidate with the
smallest row sum, you eliminate (at each step) the remaining candidate with
the smallest row min ... the Gross Loser.
The margins versions of these two related methods are slightly more
transparent, as well as precisely equivalent in the case of complete
rankings.. The pairwise margins matrix is obtained from the pairwise vote
matrix by subtracting is transpose from it.
In a margins matrix every negative entry in the row of a candidate
represents a pairwise loss for that candidate.
The row of a Condorcet candidate will have no negative entry, but every
other row will. In particular the margins row of the Gross Loser must have
a negative entry ... so the Gross Loser cannot be a Condorcet Candidate ...
therefore eliminating the Gross Loser (or any other candidate with a
negative entry) cannot eliminate a Condorcet candidate.
The average of all of the rows in the margins matrix is a row of zeros ...
and therefore has a zero row summ. But the row of a Condorcet candidate
has a positive row sum ... therefore above average.
So you no longer have to take on blind faith the veracity of these
assertions about the Condorcet efficiency of Borda Elimination and GLE....
you can see for yourself the complete rationale!
Next time you see Maskin ... alert him to the existence of GLE ... so he
can break out of his rut of supporting clone depend methods ... like
Copeland, Borda, Black, Nanson, Baldwin, etc.
At least he hasn't yet recommended Kemeny-Young! ... (as far as I am aware)
I have to believe that if he knew better, he would do better!
-Forest
On Fri, Jan 20, 2023, 7:54 PM robert bristow-johnson <
rbj at audioimagination.com> wrote:
>
>
> > On 01/20/2023 10:31 PM EST Bob Richard (lists) <
> lists001 at robertjrichard.com> wrote:
> >
> >
> > If Robert (or anyone else) can demonstrate that this is not Condorcet,
> > they should let Foley know pronto. He is a Condorcet enthusiast.
> >
>
> I am that. But I, also, am not trained in social choice theory or
> psephology. I am trained in the mathematics surrounding digital signal
> processing and my experience is DSP of audio and music signals (stuff like
> guitar effects and music synthesis).
>
> I have trouble reading some of the math in other papers coming from the
> likes of Maskin or Tideman or Schulze. Sometimes it's just the way it's
> setup, but I am not as good at discrete mathematics as I am into the kinda
> math that engineers and meatball physicists use (that comes outa calculus
> and diff eq and linear system theory)
>
> > The method appears to be to eliminate the current Borda loser in each
> > round, until one remaining candidate has a majority. Or something very
> > close to that. Foley is a lawyer, not a social choice theorist, and his
> > explanations are a little hard to follow.
>
> He got Maskin on his side. I almost got Maskin and Tideman to appear (via
> Zoom) before the Vermont Senate Government Operations committee last April
> but the chair of the committee *snubbed* them. Unbelievable.
>
> I am reading (or skimming) Foley's paper now and will probably send him an
> email. His email address appears to be foley.33 at osu.edu . I would hope
> that folks here better than me might pipe in. It appears that Foley is
> unaware of Burlington 2009 and of Minneapolis 2021 (which had a cycle).
> And since Maskin was certainly aware of Burlington 2009 (because of my
> conversations with him), I am surprized that there is all this talk in the
> paper of Alaska 2022 but none of Burlington 2009.
>
>
> --
>
> r b-j . _ . _ . _ . _ rbj at audioimagination.com
>
> "Imagination is more important than knowledge."
>
> .
> .
> .
> ----
> Election-Methods mailing list - see https://electorama.com/em for list
> info
>
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