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

[Forest Simmons]

On Wed, 24 Oct 2001, Bart Ingles wrote:

 
> It seems to me that any time strategic (i.e. polling) information is
> potentially useful, the election can be manipulated by supplying
> inaccurate polling data.

True.

> Checking for a beatsall winner doesn't prevent this.

I would agree with this statement if you modified it to say,"Even checking
for a beats-all winner rarely prevents this completely." 

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?

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.

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