[EM] Approval Stable Winner

Forest Simmons fsimmons at pcc.edu
Wed Mar 4 10:44:04 PST 2020

```I don't know why that message got sent prematurely, but let's try again..

It is based on the following question in the context of score based
election:  If you believed that candidate X was the clear frontrunner which
candidates would you approve (i.e. give max support to)?

Let's assume for simplicity's sake that if you like Y better than X, you
would approve Y, and that if you liked X better than Y, you would not
approve Y.  In other words you would approve down to X but not below X.

That leaves us with the decision about X itself.  Would you approve X or
not?

Again let's assume that if you ranked X equal top, then you would approve
X, and that you would never approve a candidate that was not ranked above
at least one other candidate.

Since we don't have any information about whether the runner-up is
someone you like better than X or not, let's make the further assumption
(again for simplicity's sake) that you would give X the same rating that
you would give X in a zero information context.

On the basis of these simplifying assumptions we can make  various DSV
(Designated Voting Strategy) methods that have some immunity to
manipulation. These methods will differ mainly (if not soley) on their
estimate of support for X itself in the zero information case.

Suppose that S(X) is the total estimated support for X over all ballots in
the zero iinformation case, and that MPO(X) is the max pairwise opposition
against X, then the ratio S(X)/MPO(X) is a gauge of how well X could hold
up if put on a pedestal as a target in their cross hairs of all the voters.

Accordingly, we will call the candidate X with the greatest ratio
S(X)/MPO(X) the "Stable Approval Winner."

In my next message I will suggest some ways to estimate the zero info
support S(X) based on various kinds of ballots and other considerations.

Thanks!
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