[EM] Approval Stable Winner

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[EM] Approval Stable Winner

Forest Simmons
This can be thought of as a much less ambitious approach (compared to what Kris and Kevin have been discussing) to formulating a relatively unmanipulable method.

It is based on the following question in the context of an approval based election:  If you believed that candidate X was the clear frontrunner in a single winner race, would you approve candidate Y ?

Let's assume for simplicity's

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Re: [EM] Approval Stable Winner

Forest Simmons
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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