[EM] Multiple Same Choices

[Steve Eppley]

Lucien Saumur wrote:
>          Whatever else Condorcet may have said in his
>life, we must recognize that the preferential ballot is the
>ballot which gives, to the voters, the option of expressing
>their will to the fullest. We must also recognize that the
>voters may not express their will to the fullest unless
>they are allowed to indicate equal preference between two
>or more candidates and unless they are allowed to rank as
>many or as few candidates as they wish.

And express disapproval of all of them.

To be fair, the rated ballot (example: -10 to +10) allows voters the
option of expressing their will more fully than the ranked ballot. 
But the argument against the rated ballot--that voters will exercise 
their option to vote tactically rather than express their true 
preferences--is a strong one.

>          I have developed a computer system which will
>allow the voters to produce printed ballots listing the
>candidates in order of preference. The ballots may also
>indicate the dividing line between the acceptable and the
>unacceptable candidates.

This is what I called Condorcet+NOTB.  The "dividing line" is 
inserted by ranking None Of The Below in the appropriate position.

>A ballot may indicate that no candidate is acceptable.

The voter ranks NOTB highest.

>It may also indicate that no candidate is ranked.

I'm unclear on this.  Do you mean some are equally approved and the 
rest are equally disapproved?
Examples:
  Some approved:  1=A,B,C   2=NOTB   3=D,E,F,G
  All approved:   1=A,B,C,D,E,F,G
  None approved:  1=NOTB

> My system is also designed to tally the ballots.
>When candidates are not ranked (indicating equal
>preference) the related counts for both candidates are
>updated with half (1/2) a vote.

I haven't thought about this, but my guess is that whether you should
score equally ranked choices as .5 and .5, or 1 and 1, or 0 and 0,
depends on the choice of tie-breaking algorithm you plan on using. 
It may not matter--is it possible to specify a sensible tie-breaking
method that doesn't care how the equal pairs are counted?

>          The tally system also maintains an acceptability
>count for each candidate. This count is independent of the
>pairwise counts.

I think you can simplify your code, and the ballot, by just letting
the voters rank NOTB.  "NOTB vs. each candidate" is just another set
of pairings to include in your array.

>          A candidate is not a winner solely because he is
>preferred to every other candidate but also because his
>acceptability count is equal to at least half the number of
>voters.

Disqualify any candidate beaten by NOTB.

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)