[EM] Five Slots and Cranor

Forest Simmons fsimmons at pcc.edu
Thu Apr 26 11:08:59 PDT 2001

You're right, Martin, just like Bush winning when Gore got the popular

I think that it would be extremely rare that the two winners would be
different; grading pass/fail probably wouldn't change who graduates at
the top of the class.  The law of large numbers works for discrete random
variables as well as continuous ones.

But suppose that the two winners are different. Why not go with the one
preferred by the majority?

You might say that would tend to distort the CR expressive ballots. But
since the pairwise comparison is only based on order of preference,
inflation or deflation of grades won't change the result, unless you
collapse a preference, which just nullifies your influence in the outcome.

Here's an entirely different way of using CR ballots that would preserve
expressivity: forget Cranor, forget Condorcet, forget Approval, forget
Average Ratings ...

Give the win to the candidate with the highest median score, i.e. the
candidate whose list of scores has the highest median.

[A candidate's list of scores is a list of numbers. The median of
a list of numbers is the middle number (or the average of the two
middle numbers) when the list is sorted in numerical order.]

If several candidates have the exact same median score (which is quite
possible in the case of low resolution CR ballots) give the win to the
candidate with the greatest difference between the number of votes above
and below the common median.

[This is equivalent to considering the common median to be the Approval
cutoff, and declaring the Approval winner to be victor.]

The median is not sensitive to the extremes, so there is no strategic
advantage of rating your compromise candidate (Gore) as high as your
favorite (Nader) or your bad front runner (Bush) as low as your most
despised (Buchanan). 

On Thu, 26 Apr 2001, Martin Harper wrote:

> Forest Simmons wrote:
> > In any case, if Cranor's method were used in public elections, there
> > should be a little check box on the ballot that asks if you want your
> > ballot Cranor optimized or not.  If you check yes, then your ballot is
> > supplemented with the Cranor optimized ballot. The original is used for
> > expression, while the optimized is used for instrumentality. Otherwise
> > (with the option declined), the original serves both purposes. 
> The danger is that the 'expression' votes will occasionally elect a 
> different winner to the 'instrumental' votes. In which case whoever was 
> the 'expression' winner will probably raise merry hell...

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