[EM] CR/Approval

[Adam Tarr]

Interesting idea Forest.  This method basically simulates a two-stage 
repeated approval balloting, with one significant difference - that the 
winner of the first round gets partial votes in the second round.

This effect actually creates some problems.  If I prefer the first round 
winner to his closest competitor, then I have an incentive to insincerely 
rank the (expected) first round winner at 100%, so that I cast the full 
mark for him in the second round.  This of course forces me to rank 
everyone I like more at 100% as well.  Conversely, if I prefer the closest 
competitor to the first round winner, I have an incentive to rank the 
expected first round winner at 0%, which forces me to do the same for 
everyone I like less.

The way to avoid this seems to be to incorporate some approval strategy in 
the way the second round votes are done.  I'd suggest using the generally 
accepted strategy for good information:  "approve all candidates I prefer 
to the current first-placer; also approve the first-placer if I prefer him 
to the second-placer."  This means every candidate gets either 100% 
approval or 0% approval in the second vote.  This removes the incentive to 
stack all the rankings toward the top or bottom.

The advantage of this approach is that it basically allows all the voters 
in an approval election to make fairly intelligent votes without having to 
think about it.  The disadvantage is that, by getting rid of the partial 
votes for the cutoff candidate, we have lost the most direct link to utility.

I assume the strategy in this method involves manipulating which candidates 
finish top two in round one, which determines the cutoffs in round two.

-Adam

At 12:47 PM 7/2/2003 -0700, you wrote:

>Here's another method that makes use of CR ballots to enhance Approval:
>
>Each voter rates each candidate on some scale, say zero to 100%.
>
>The ballots are counted in two stages:
>
>In the first stage the approval cutoff for each ballot is a rating of 50%.
>
>In the second stage the approval cutoff on a ballot is the rating of the
>first stage winner on that ballot.
>
>In each stage on each ballot each candidate above the cutoff (for that
>stage) gets 100% approval, while each candidate below the cutoff gets zero
>approval, and each candidate precisely at the cutoff rating gets a
>percentage of approval equal to the cutoff rating.
>
>The winner of the second stage is the method winner.
>
>[end of description of method]
>
>The idea is that if you knew the sincere approval winner, you would
>probably want to use that candidate as your approval cutoff if you had a
>second chance.
>
>The question is should you approve the cutoff candidate C?
>
>This method says that you should give this cutoff candidate C more or less
>approval according to how high you rate C.
>
>If you rate C 100%, then you should give C 100% approval.
>
>If you rate C zero, then you should give C no approval.
>
>If you rate C 50%, then you should give C half approval.
>
>In other words, the cutoff candidate gets approval equal to his rating
>while all other candidates get full approval or no approval according to
>their ballot rating relative to the cutoff.
>
>Forest