[EM] CR/Approval

Forest Simmons fsimmons at pcc.edu
Thu Jul 3 12:39:02 PDT 2003

Good points in the critique below.

Here's another way to get around the problem of deciding whether or not to
approve a candidate whose rating precisely matches the approval cutoff:

Use an even number CR resolution, so the max value is odd, for example CR
values from zero to three.  Then the first stage approval cutoff is an
half integer value (in this case 1.5), a value occupied by no candidate.

In the second stage use for a cutoff value the average of the old cutoff
value and the CR of the first stage winner.

In the zero thru three example this value will be of the form (n/2) + .75,
so it will not be the CR of any candidate.

This method gives equal weight to the first stage winner CR and the zero
info cutoff value in determining the second stage cutoff value.

If the voter wanted to, she could award only the extreme CR values.  That
would be equivalent to casting an approval ballot.

But it seems to me that there would be some advantage in using the two
middle levels as well.

In the case of eight levels (zero thru seven) it might be good to have
four stages, because that is how many stages it would take before the
cutoff could possibly distinguish between zero and one, or between six and

At the fourth stage the cutoff level would be (r1+r2+r3+3.5)/4, where the
ratings r1 thru r3 are the CR values for the stage one thru three winners.

None of the cutoffs at any of the stages could be a whole number, since
the average of a set of integers with a non-integer (in this case 3.5)
cannot be a whole number.

I like this zero thru seven method because of the "seven plus or minus"
psychology, and the fact that the most common Condorcet cycles are cycles
of three candidates.

I'll post some examples next week if someone doesn't beat me to it.


On Wed, 2 Jul 2003, Adam Tarr wrote:

> 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
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