[EM] Is there a Good Clone Independent Election Method Based on VFA Style Ballots?

[Forest Simmons]

Like the taxi cab metric it is asymmetrical ... the democrqtic cost of
convering finish order FO into its opposite FO' Will in general be greater
in onf the two directions ... just li like the cost of traveling from A to
B may be greater in time or dollqrs than that of the return trip.

There is a classic monograph on this tópic by a Soviet Mathematician
entités "What Is Distance?"

The Kendall-tau metric is insensitive to direction ... so is of no use to
us ... besides its defective clone dependence.

Using the top and bottom counts to de-clone Kendall-tau gave us the bonus
of directional sesitivity.

The simplest example is

60 A>B
40 B>A

The two possible finish orders are the two faction orders A>B and B>A.

The swap cost of converting A>B to B>A is the a×b' ... the For count of A
times the Against count of B ... i.e. 60×60.

The democratic cost of reversing B>A is b×a'  the For count of B times
theAgainst countvof A ...b40×40.

Since 60^2 > 40^2 the democratically preferred order is A>B ... the one
that is the most costlybor democratic difficult to reverse.

Over the last dozen years I have given various uses for this swap cost
metric ... and always  the proof of its clone independence.  Then I had
better vision ... much easier to type these messages.

I'll just give you the algebraic identity that is the essence of proof:
(Sum a_k)(Sum b'_j) is equal to
DoubleSum [(a_k) (b'_j)]

This is in the context where candidates A and B are replaced by respective
clone sets {A_k} and {B_j} and
a=Sum a_k and b'=Sum b'_j

Search theM archive under Swap Cost for more applications.

There is no guarantee that this VFA application will prove useful ... I'm
just giving you the opportunity to get in on the experiment if you want to.

I'm 76 years old ...my memory and eyesight are fading ... I hope the EM
Archives can survive the degeneration of civilization that seems almost
inexorable in some ways.

-fws

On Fri, Feb 2, 2024, 1:34 PM Joshua Boehme <joshua.p.boehme at gmail.com>
wrote:

>
> Two questions came to mind...
>
> 1. The cost function isn't symmetric. How do you translate it into a
> distance between two orderings, then? For example, if A is 70% for/30%
> against and B is 60%/40%, then the cost of going from A>B to B>A is 28% and
> vice versa is 18%.
>
> 2. Once you narrow it down to the two most-distant orderings, how do you
> pick the final one? Yes, it's probably "obvious" to a human, but you can't
> write a law or program that way. Once we have a rule to formalize that,
> though, why wouldn't we just directly use it to create a "better than"
> relationship for all the orderings instead of relying on a two-step process?
>
>
> On 2/1/24 17:18, Forest Simmons wrote:
> > VFA abbreviates "Vote For and
> > Against"
> >
> > More than a decade ago I thought of using VFA syle ballot information to
> > declone Borda, Copeland, and Kememy-Young ..but none of them was suitable
> > for public proposal.
> >
> > For example, VFA information allows us to construct a clone independent
> > "Swap Cost Mettic" that can replace the clone dependents Kendall-tau
> > metric, thereby resulting in a clone free version of Kemeny-Young ...
> > which, in turn transforms it into an election method with acceptable
> > properties ... but only  ncorporatimg the VFA information to create the
> > clone independent metric without being able to dispense with the voter
> > rankings ... a gasoline/ electric hybrid that cannot exist as a
> standalone
> > power source, so to speak.
> >
> > However, last night it occurred to me that we can use the soap cost
> metric
> > on the space of possible candidate finish orders to make a comceptually
> > simple (vsry  simple in comparison with Kememy-Young) standalone election
> > method:
> >
> > Choose the finish order most distant from its opposite.
> >
> > This makes simse when you realize that the cost of a single trasposition
> of
> > a pair of candidates in the finish order is a measure of the combined
> > mental anguish that would result from reversing their first and last
> place
> > prferemces.
> >
> > To be precise, the seap cost of reversing a single preference of X>Y
> to.Y>X
> > in the finish order is the number of nallots that voted for X times the
> > number that voted against Y.
> >
> > If you were toouble the number of voters that voted for X or the number
> > that voted against Y,, you would double the total number of voters
> > disappoimted by the seap of the positions (in the finish order) of the
> > respective candidates A and B ... so the "cost" in seap cost is measured
> in
> > voter disappoiment.
> >
> > In our context the greater the voter disappointment cost of reversing a
> > proposed finish order FO o its opposite FO', the better FO is in contrast
> > to FO' ... which is why we chopse the finish order that would result in
> the
> > most disappointment if it were replaced by its opposite..
> >
> > An app that uses this method for making group decisions based solely on
> > first and last choices might catch on at the grass roots level. If so, it
> > would work even better in large groups where statistical laws would
> enhance
> > performance.
> >
> > What do you think?
> >
> > Is there a VFA organization somewhere in need of revitalization?
> >
> > -fws
> >
> >
> > ----
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> info
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>
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