Condorcet(x( ))

[Steve Eppley]

>>Because, in each pairwise comparison in which X is beaten,
>>Condorcet's circular-tie-breaker counts only the votes for the 
>>other candidate over X, I call that "votes-against".

Lucien wrote:
>          Did Condorcet propose this tie-breaking scheme?
>
>          I find this scheme artificial. While circular
>ties are logically possible, I am not sure that they are
>probable 

The probability increases with the number of candidates, with the
number of voters, and with the number of issue spectra, other
considerations being equal.

The possibility of circular ties is known as Condorcet's Paradox. 
Condorcet's Paradox is a natural phenomenon in group voting.  Each
voter may be assumed to have transitive preferences (A>B and B>C
implies A>C) but when these preferences are tallied there can be a
circular tie.  Strange but true.

Condorcet's Paradox can be exploited (and probably has many times)
in groups which vote sequentially between pairs of proposals: C vs
winner(A vs B), like a single-elimination tournament where C gets a
"bye".  If the clever chairperson who controls the order of votes
knows there is a circular tie, s/he may arrange the agenda so that
the "bye" is given to his/her favorite (C).  If the voters are
clever and also know about the circular tie, they may misrepresent
their true preferences during the A vs B vote so they can later 
defeat C with their favorite or with a compromise which they think 
is better than C.

>         nor do I know what they would mean.  I am inclined
>to think that they would mean that the voters have no great
>preference between the candidates involved in the tie. If
>my assumption is correct, then the winner may more simply
>and reasonably be decided by drawing lots.

I suspect most people would be unhappy with a voting method that
depends on luck.  There's enough info in the votes that we can do
better than random selection.  If there's a majority against one of
the tied candidates and only a minority against another one, why
draw lots?

Also, since voters are able to misrepresent their preferences when
voting they may be able to engineer a circular tie, probably robbing
the candidate who would have beaten all others pairwise of a
rightful victory if luck breaks the tie.  (Take another look at 
the Dole/Clinton/Nader example where the Dole voters, instead of
voting{Dole>Clinton>Nader}, truncate to their ballots to {Dole}.)
Condorcet's method makes it very hard for the rightful winner to be
robbed.  Luck would make it very easy, and thereby create strategy
opportunities and dilemmas for the voters.

* *

Lucien, your webpage says it implements Condorcet's method and you've 
written in the ER list that Condorcet's method in single-winner 
districts is the best way to elect legislatures.  What do you think 
now?  

When I looked at your webpage a couple months ago it didn't support
equal rankings (except maybe for the unranked; I don't recall).  How
does your program tally the equally unranked, and how will it tally
the equally ranked when you implement equal rankings?  Are you
adding .5 to each of the tied pair or leaving their counters alone?

--Steve