[EM] Defeat Strength

[Forest Simmons]

I'm happy that this thread has excited so much interest ... and astute
comments ... obviously the result of careful and thoughtful study and
experimentation.

"Equity" was not the apt word. There are many kinds of fairness, as the
subject of fair division makes clear , what I try to aim for is the kind
of fairness that minimizes reasonable people thinking that the rules were
stacked against them from the start ... an admittedly  nebulous concept.

What is the best tweak of Borda that restores some semblance of clone
independence?

 I once suggested something called "ranked rankings" that (like Borda)
removes the burden of numerical quantification from the voter .. who is
only required to supply a rough relative strength preference between
alternatives:

A=B>C>D>>>E>>F=G, for example.

A and B would both get 100% approval whileF and G would each get zero.
The separation between B and C, and C and D would both be X, while the
separation between D and E would be 3x, and between E and F would be 2x.

The total number of chevrons (the ">" symbols) is seven, so we must have
 7X=100, which means x is 14 + 2/7 or approximately 14.3

The voter doesn't have to do any of this arithmetic, which allows the
"ranked rankings" to be turned into ratings.

If all of the rankings are of equal strength (one chevron each, say), then
the resulting ratings will agree with the normalized Borda scores. In other
words, this way of counting "ranked rankings" style ballots is a precise
generalization of Borda that satisfies clone independence (for all
practical purposes).

In particular, there is no need to indicate strength of preference if they
are all roughly equal in strength.

Does any version of this idea have any potential as a basis for a public
proposal?

-Forest


On Sun, Sep 4, 2022, 1:01 PM Kevin Venzke <stepjak at yahoo.fr> wrote:

> Hi,
>
> I'm afraid that defeat strength is such a tangible concept that it
> inclines us to view it as
> a finished product that we can now simply customize as we please. Or
> worse: That we are
> duty-bound to measure it "accurately." We maximize some desired property,
> readily identified
> within a single pairwise contest, and then apply the minmax algorithm to
> this ranking, and
> expect it to result in a method whose properties have some kind of
> relationship to the
> property we were maximizing, or properties that will at least be as good
> as the defeat
> strength metric sounded.
>
> I couldn't count how many times I had a nice idea, tried to use minmax or
> River with it,
> and discovered some horrible basic flaw. Or just mediocre results.
>
> I see Forest wants to lock a 1%:0% victory first because there is no one
> around to object
> to that particular point. Only the local question is considered, not
> whether "hard feelings"
> might come from some other factor than this. That's the key issue. What
> can we say about the
> overall method that results from applying this logic? We have no real
> idea, without
> checking.
>
> The question then of why anything would "represent defeat strength better
> than margins" is
> strange to me. Defeat strength is just a possible tool to get to the
> winner. There's no
> need for it to represent anything with fidelity to any principle. It might
> be a marketing
> concern, I admit. But when evaluating method properties you only need to
> know who wins when;
> you won't talk about the underlying algorithm and indeed you don't even
> need to know what
> it is.
>
> I don't know what to make of the term "equity" below. Can reducing
> strategic incentives
> cause inequity? How can I tell whether a method is equitable? (Of course
> then I mean its
> *results* being equitable, rather than its method of calculation.)
>
> Usually there's a simple approach to reducing strategy: If a lot of people
> want something,
> such that they could lie on the ballot in order to get it, then just let
> them have it. Then
> that's a complaint of inequity you can avoid, if they were to not get what
> they want. Maybe
> there are other types of inequity, but I'm not sure what, staying within a
> majoritarian
> perspective.
>
> Kevin
> votingmethods.net
>
>
>
> Le samedi 3 septembre 2022 à 20:31:14 UTC−5, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
> >
> > It has more to do with strategy than equity.
> >
> > I prefer minimizing opposition to the defeat, because that relieves
> tension, resentment, and
> > polarization. Perhaps it is possible to win without alienating the
> opposition, i.e. without
> > all of the bad feelings.
> >
> > Notice in the three examples, there was zero opposition against the
> victory of A over B, so
> > no hard feelings if A beats B.
> >
> > On the other hand, the C beats D defeat is highly polarized ... 4999
> angry losers.
> >
> > But my question which of the three claims is most defensible
> statistically ... i.e. which one
> > is least likely to be reversed by a random fluctuation in the weather on
> election day in a parallel
> > universe.
> >
> > It seems to me that the margins result (F defeating G) is the most
> stable in this case. Is
> > that always true?
> >
> >
> > On Sat, Sep 3, 2022, 5:33 PM robert bristow-johnson <
> rbj at audioimagination.com> wrote:
> > >
> > >
> > >
> > > I never really groked why WV (or LV) would represent defeat strength
> better than margins.
> > >
> > > I just don't get it.  WV, that is.
> > >
> > > - robert
> > >
> > > Powered by Cricket Wireless
> > >
> > > ------ Original message------
> > > From: Forest Simmons
> > > Date: Sat, Sep 3, 2022 8:19 PM
> > > To: EM;Richard Lung;robert bristow-johnson;
> > > Cc:
> > > Subject:Defeat Strength
> > >
> > > Suppose there are ten thousand voters, and ...
> > > A defeats B, 100 to 0, (9900 abstentions)
> > > C defeats E, 5001 to 4999, and
> > > F defeats G, 1000 to 500 (8500 abstentions)
> > >
> > > Which pair should have defeat strength priority?
> > >
> > > Under wv, the (C, E) pair has priority.
> > > Under margins (F, G) has priority, and
> > > under losing votes (A, B) has priority.
> > >
> > > But which defeat should be considered most secure statistically?
> > >
> > > -Forest
> > >
> >
>
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