Condorcet without Circular Ties?? - well, maybe!!
Donald E Davison
donald at mich.com
Sun Feb 21 10:24:55 PST 1999
Greetings,
It would be nice if Condorcet did not have those circular ties. Maybe
something can be done to eliminate them. Hear me out.
In my studies of circular ties I have observed that it only takes a
small percentage in the shifting of votes in order for Condorcet to go in
and out of the circular tie zone. I have also observed that it is possible
to go in and out of the zone by changing only the lower vote totals.
It seems that if the total of the lower choices is increased, we face
the possibility of going into the circular tie zone. If the total is
decreased, we slip out of the zone.
I want to suggest that we decrease the total of the lower choices for
every election, in the hope that this will take us out of the zone of
circular ties.
Current Condorcet and Approval Voting are both extreme cases of a form
of Borda Count. Approval Voting is one of two special cases of Borda Count.
It is the case in which the lower choices are equal to the same value as
the first choices.
Plurality Voting is the second extreme case of Borda Count. Its lower
choices are equal to zero.
Current Condoret is one of two extreme cases of what I call Borda
Count Condorcet(BCC). It is the case in which the lower choices are equal
to the same value as the first choices. And, it is the case in which we get
circular ties. Plurality Voting is the second extreme case. Its lower
choices are equal to zero, but we never have a circular tie in the second
cases. I suggest that BCC would be better to use than the current Condorcet
because BCC is between the two extreme cases of Condorcet and maybe we can
find a spot that is outside the circular tie zone.
I know of three ways in which we can reduce the total of the lower
choices for both Approval Voting and Condorcet.
1). Use the reducing scale of Borda Count.
2). Make the lower choices netural.
3). Use Cumulative Voting before Condorcet.(my favorite)
If we used a reducing scale, like 4-3-2-1 for a four candidate
election, this would reduce the totals of the lower choices. But, this
theory need testing to prove we can get out of the circular tie zone.
About a year ago, Demorep ran a program on Condorcet in which he was
able to tell us how many circular ties we could expect. If Demorep could
run that program again, but this time using a Borda Count scale for the
lower choices, he may be able to tell us if the scale will take us out of
the circular tie zone.
I have worked a few examples, but a few examples do not make a proof.
It would be nice if someone, that had a program, would run a number of
examples.
If this theory proves to be true, then the gain for the pairwise
people would be great - no circular ties..
The second way to reduce lower choices: If we made the lower choices
mathematically netural, this would also reduce the totals of the lower
choices. The first choices are netural because every candidate has the same
mathematical possibility of receiving 0 to 100 percent of the votes. The
lower choices are not netural because every candidate does not have the
mathematical possibility of receiving the same percent of the lower
choices. For example, consider: 40 A 30 B 20 C 10 D
Candidate D has the mathematical possibility of receiving 0 to 90
percent of the second choices, while candidate A has the mathematical
possibility of receiving only 0 to 60 percent of the second choices.
If we used factors to adjust the second choices, we can make them
netural, and we will also be reducing the totals of the second choices.
Each vote of the second choices is to be rreduced by the following factors:
The factor to reduce the votes of candidate A will be 1.000 (60.60).
The factor to reduce the votes of candidate B will be 0.857 (60/70).
The factor to reduce the votes of candidate C will be 0.750 (60/80).
The factor to reduce the votes of candidate D will be 0.667 (60/90).
This will give every candidate the same mathematical possibility, but
this may not be the best way to go, because this math will have to be
repeated anew for more sets of choices when we have more than three
candidates.
Cumulative Voting Condorcet(CVC): I like this means the best for
reducing the lower choice counts because it will be the voters that decide
how much value to give to each choice.
CVC would work as follows: The voter will be allowed a number of votes
equal to the number of candidates times two. The voter must give at least
one vote to all but one candidate. The voter is free to vote the balance of
his votes like Cumulative Voting.
The following is an example:
100 A 40 B 80 B 30 A 50 C 20 A
75 A 30 C 50 B 10 C 30 C 15 B
---------- ---------- ---------
175 A 130 B 80 C
Pairs >>> A --- B A --- C B --- C
175 130 175 80 130 80
20 15 30 10 40 30
--- --- --- --- --- ---
195 > 145 205 > 90 170 > 110
Again, I will say that this theory of reducing the lower choice count
to avoid the circular tie zone, needs testing to prove it right or wrong. I
will also say that those of you who favor Condorcet should do the lion
share of the testing, because if this theory proves to be correct, you will
have eliminated the biggest flaw of Condorcet.
Regards,
Donald
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| Q U O T A T I O N |
| "Democracy is a beautiful thing, |
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