[EM] Multiple Same Choices

[Lucien Saumur]

In an article, DEMOREP1 at aol.com writes:


>Does Mr. Condorcet say that a voter cannot have 2 or more equal first (or
>later) choices ? If so, Mr. Condorcet is anti-freedom of choice.

          I do not know if Condorcet said that a voter
cannot have 2 or more equal choices. What I know that he
did say is that, from a group of ballots listing ranked
candidates, it is possible to develop pairwise tallies and
that one of the candidate may be a winner against all other
candidates. Condorcet also imagined the possibility of a
paradoxical result because of circular winners (A is
preferred to B who is preferred to C who is preferred to
A.)

          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.

          Although Condorcet may or may not have imagined
that some or all of the candidates may be unacceptable, we
must now recognize that the voters will not express their
will to the fullest unless they are allowed to indicate the
acceptability of the candidates. We must also recognize
that the possibility of ranking the candidates and of
indicating their acceptability are not mutually exclusive
and the voters must not be denied the right to rank
unacceptable candidates.

          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. A ballot may indicate that no
candidate is acceptable. It may also indicate that no
candidate is ranked. A ballot may also indicate these two
options at once. Such ballots would not be redundant
because they may affect the outcome of the tally as, I will
explain further on.

          My system does not allow equal ranking except for
unranked candidates which are logically ranked as equal. I
plan to redesign the system to incorporate this feature, at
a later date.

>C. The test winner, test loser and test other losers terminology is the same
>as what the Condorcet method does in making pair comparisons- one of the pair
>is a test winner, one is a test loser. The first choice votes for each of the
>pair and the votes transferred from the other first choice candidates (test
>other losers) for one of the pair determines which of the pair is a relative
>winner. Saying that the Condorcet method compares the votes each of two
>candidates receives as if there were only those two candidates may be good
>enough for speaking to folks but not for math examples on paper and election
>computer programmers.



          My system is also designed to tally the ballots.
To do so, it is necessary to enter the content of the
ballots as was done when the ballots were produced. This
process will serve to update a matrix of counts where every
candidate is compared to every other candidate. The update
will consist in adding one (1) vote to the related pairwise
count of a candidate who is preferred to another candidate.
When candidates are not ranked (indicating equal
preference) the related counts for both candidates are
updated with half (1/2) a vote. The consequence of this
process is that the sum of all related pairwise counts are
always equal to the number of voters.

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

          The system will flag those candidates who have
obtained a vote count equal to at least half the number of
voters. If more than one candidate is flagged in this
manner, then the result is paradoxical.
          
          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. It is in this respect that we may see that even a
ballot where no candidate is indicated as preferred to
another may affect the election results. This ballot may
either help or prejudice the acceptability count of a
candidate depending on whether or not the voter has
indicated that all the candidates are unacceptable.

__________________________________________
          aa447 at FreeNet.Carleton.CA
          http://www.igs.net/~lsaumur/