[EM] disappointment vs. regret

[Forest Simmons]

Here's a method that I consider to be good in its own right, not only as a
starting point for "Minimum Disappointment Covering Enhancement."

Assume ranked preference ballots with equal ranking and truncation allowed.
Also assume access to a "random favorite" probability distribution, whether
from a separate poll or by inference from the ballot set itself.

A ballot B is said to "like" candidate X if a random favorite is less
likely to be ranked ahead of (i.e. above) X than not on ballot B.

The method elects the candidate liked by the greatest number of ballots.

This method is monotone whether or not the random favorite distribution is
computed on the fly.

It also satisfies clone winner and clone loser the same way that range
voting does, i.e. as long as the clone sets are ranked (or truncated)
together.





On Tue, Feb 18, 2020 at 1:51 PM Forest Simmons <fsimmons at pcc.edu> wrote:

> Warren Smith reminds us from time to time that range voting minimizes in
> some sense something called "Bayesian Regret" which is the difference
> between the social utility of the "best candidate" and the one elected by
> sincere ballots.
>
> A related but different concept is what I call "ballot disappointment,"
> which tries to quantify the disappointment for one voter in one step of a
> sequential elimination method.
>
> Suppose that an elimination step replaces candidate X with candidate Y, as
> the new "champion."  How much disappointment does that incur for the
> sincere voter of a ranked preference ballot B?
>
> For example if the method must eliminate candidate X in favor of some
> candidate Y that covers X, it would be nice if Y were the candidate (among
> those covering X) that incurred the least total disappointment for this
> transition.
>
> Here's my proposal.  For each candidate Z let f(Z) be the first place
> (that is random favorite) probability for candidate Z over the entire set
> of ballots.
>
> Then on ballot B the disappointment in going from candidate X to candidate
> Y  is ...
>
> ....zero if Y is ranked ahead of or equal to X
> else the sum (over all candidates Z ranked ahead of Y) of f(Z).
>
> So if Y is ranked higher than X on ballot B, then the voter of ballot B
> has little cause for complaint, otherwise the disappointment is the
> probability that a better Y would have been chosen by random ballot.
>
> This is the foundation of my new Landau method based on ranked preference
> ballots with out the need for approval cutoffs.
>
> Ordinarily my proposal for the initial candidate in the sequence would be
> a candidate chosen by random ballot or else the approval winner, but I'm
> studiously avoiding requiring the voters to make approval judgments, and I
> want to have a deterministic version of the method, as well. So in the next
> message I have a deterministicsolution that does not require voter to make
> approval judgments..
>
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