[EM] Multiple Same Choices

Lucien Saumur aa447 at freenet.carleton.ca
Fri Mar 1 19:27:34 PST 1996

In an article, seppley at alumni.caltech.edu ("Steve Eppley") writes:

>Lucien Saumur wrote:
>>Steve Eppley writes:
>>>Lucien wrote:
>>          Or NOTR for None of the Rest.
>Or NOTB for None of these Bums...  
>I don't care which term is used.
>>>>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?
>>          I mean that ballots would be produced indicating:
>>                    NO CANDIDATE IS RANKED
>>                    NO CANDIDATE IS ACCEPTABLE
> That's what is meant by simply voting:  1=NOTB
>>          Such ballots would be tallied by adding .5 vote
>>to every count of the matrix and by adding zero to the
>>acceptability count of every candidate.
>Like I said, you can produce the same result by treating NOTB as just
>another candidate in the matrix, simplifying the algorithm.  You
>don't need a separate data structure for approval counts.  This is
>just an implementation detail, though; what matters is what the
>voters see.

          Yes, what matters is what the voters see. The
voting process must appear clear, simple and attractive to
the man in the street who will have to use it. The man in
the street will vote but he will not do the tally although
he will see the tally results.

          My computer system attempts to simplify the
voting aspect by asking the voters to use a computer mouse
and to rank the candidates by clicking on a list of
candidates on a computer monitor screen. As the voter
clicks on the name of a candidate, the name is transferred
to another list of "ranked" candidates on the same screen.
When the voter is satisfied with his selection, he may then
click on a button to produce a printed ballot.

          It is important to keep the number of buttons to
its minimum and the complexity of the system to its least.
My system has a button to restart the ranking process to
correct a mistake. It has a button to end the ranking
process prematurely and another button to mark when the
rest of the candidates are unacceptable.

          I am now considering the addition of a button to
allow equal ranking and I am concerned that the system
would be made too complicated for most voters. However, I
think that it is possible to train people to use a more
complicated system, as was done with banking machine.
However, for demonstration purpose and to sell the idea, we
should not include all the bells and whistles that may
eventually have to be incorporated to the system.

          The voters do no need to know the precise
tallying procedure. The tally must be done by electoral
officials who may be expected to understand more of the
process than the ordinary voters. In my system, the ballots
are tallied in two stages. In the first stage, the
electoral official reenters the data on the ballot by
repeating the voting process. The data, as it is entered,
is retained on a computer file. The second stage will
process this file to produce the matrix of pairwise counts
which may then be explained to the voters. (My
demonstration version of the system does create a computer
file but produce the matrices immediately. There are two
matrices: one for the current ballot and another for all of
the ballots processed to-date.)

          It think that the voters will better understand a
separate acceptability count than they would understand
that NOTB has become one of the candidates.

>>>>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?
>>          A tie means a tie and it may be broken most
>>fairly by flipping a coin.
>I meant a "Condorcet circular tie", in which no candidate beat all
>the rest in the pairwise matchups.  We're not yet in a coin-flipping
>The tie-breaking should probably look at how badly each candidate is
>beaten overall.  If a voter ranks two choices equal, does that mean
>each is unbeat or half-beat?  Using .5 means you think each is
>half-beat.  (There was a message several days ago, from Rob or Mike
>I think, on this question.  I'll have to go back and reread it.) 

          A Condorcet circular tie does not necessarily
involves all of the candidates. Inasmuch as it does not
involve the winners, then it is irrelevant. Inasmuch as it
does, then all the candidates who are not involved may be
considered eliminated leaving only the candidates involved
in the circular tie to be considered as potential winners.

          I do not think that it makes any sense to speak
of a candidate as being "beaten overall." The point is
that, in a circular tie, each candidate has beaten another
candidate and may therefore consider himself cheated if
that candidate is declared elected. I suppose that circular
tie mean that the voters have no great preference between
the candidates involved and that the winner should be
decided most fairly PURELY by chance (by flipping a coin).

          I am ready to look at an actual situation and to
test if my hunch is correct. To prove that it is correct,
we should have a runoff election which would ask the voters
to indicate if it is, or is not, true that they have no
great preference between the candidates involved in the
circular tie.

          aa447 at FreeNet.Carleton.CA

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