Condorcet without Circular Ties?? - well, maybe!!

Blake Cretney bcretney at postmark.net
Sun Feb 21 22:36:01 PST 1999


Donald E Davison wrote: 

> 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. 

The Condorcet winner is a candidate who has a pair-wise victory over
each other candidate.  When there is no Condorcet winner, this is
sometimes referred to as a circular tie.  All Condorcet-type methods
pick the Condorcet winner, based on expressed preferences, when one
exists.  They also provide winners when there is a circular tie,
although they may differ in how they do this,. 

It is not true, therefore, to say that one ranked method, such as
IRV, has fewer circular ties than another, like Schwartz.  The
presence or absence of circular ties has nothing to do with how you
tabulate the ballots. 

The only way to avoid circular ties in the ranked ballots is to not
have ranked ballots at all.  Of course, circular ties and Condorcet
winners will still exist in the sincere preferences of voters, just
not on their ballots.  Perhaps you will explain what you mean by the
statement that circular ties are a problem with Condorcet.

All Condorcet-type methods are based on the belief that the majority
is more likely to be right, on any given question.  Of course, few
Condorcet advocates would claim that the majority was always right on
every question. 

So, for example, if of the people expressing a preference, a majority
rank A over B, we are led to suspect that A is in fact a better
alternative than B.  If A is majority preferred to every other
candidate, we view A as most likely the best alternative of all.  If
there is a circular tie, what this means is that majority opinions are
in conflict.  But no one said the majority was always right.  We try
to find a sensible winner anyway. 

The particular Condorcet-type method I advocate, I call Path Voting
(which I hope is catchier than marginal Schwartz or LCM as I
previously called it).  If you want to read a more thorough
justification of this method, and Condorcet methods in general, check
out: 

http://www.fortunecity.com/meltingpot/harrow/124/path 

--- 

Blake 
  



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