[EM] Hybrid Beats-All/Approval v. Straight Approval

[Bart Ingles]

Forest Simmons wrote:
>
> Consider the case of a beats-all check followed by your random ballot
> suggestion:
> 
> Voters are to submit ranked ballots with truncations allowed internally as
> well as at the extremes (i.e. where there is no preference equal ranks are
> allowed).
> 
> Suppose that the winner of the election is to be the beats-all candidate
> if there is one, and otherwise the highest ranked candidate on a randomly
> drawn ballot.
> 
> How would polling information make any difference in the way anybody
> voted?

I'm not sure how we defined "beats-all", so I'm taking it to mean "sole
Condorcet winner".

If the polling data shows your candidate to be drawing 35% of first
preferences, you can expect your candidate to have a 35% chance of
winning the random completion method.  If you view the likely beats-all
candidate's utility as .30, then your best strategy is to vote in such a
way as to prevent the ballots from showing any beats-all winner (try to
force a cycle, in other words), assuming you can't otherwise make your
own candidate the beats-all winner.

If, on the other hand, false polling data convinces you that your
candidate is only drawing 25% of the first-choice vote, you would want
to help the beats-all candidate as much as possible.


> After the election, no matter who the winner turned out to be, and no
> matter how all of the other voters actually voted, how could any sincere
> voter regret his/her voted ballot?
>
> So beats-all with random completion is strategy free and non-manipulable.

The sincere voter would regret voting sincerely if the .30 beats-all
candidate won, but the results showed that the voter's first choice
would have had > 35% chance of winning the random drawing.


I don't think I agree with claims in the rest of this message either,
but they seem to be based on the earlier arguments, so I think I'll stop
here until I'm sure I've understood correctly so far.

Bart


> If some other completion is used, then the election can be manipulated to
> some degree, depending on the completion method.
> 
> It seems to me that the beats-all check on the front end of the method
> can soften the effect of strategy mistakes on the back end "completion" as
> long as the completion method isn't too blatantly prone to order reversal
> strategy like Borda.
>
> Suppose that Approval is the completion method, for example.  It takes
> polling information for voters to make a good choice of approval cutoff,
> but no polling information to decide on the order of the candidates.
>
> If the polling information is totally wrong, the approval cutoff choices
> may be bad, but with a little bit of luck, the election is decided before
> the approval stage.
> 
> To minimize the potential for manipulation, Condorcet with Approval
> Completion would be carried out with two trips to the polls.
> 
> If there is a CW, only one trip is necessary.
> 
> If not, then the results of the first trip reliably inform the choices for
> the second (Approval) trip to the polls.
> 
> Of course (as Demorep is sure to point out) this method is too complicated
> and inconvenient for public consumption, but it may have private
> application in situations where it is important to minimize the potential
> for manipulation.
> 
> More importantly, as far as I'm concerned, it helps us see the practical
> limitations of strategy free methods.
> 
> Forest