[EM] Nanson

[Adam H Tarr]

Steph wrote:

>This amazes me.
>You are not the first to tell me Borda and Condorcet are "equivalent".
>It could be the case in term of determining the winner when there is a
>Condorcet winner.

Nanson is a Borda-elimination method (read: NOT the classic Borda count) and is 
Condorcet compliant.  The classic Borda count is NOT Condorcet compliant.

>However, Borda is not cloneproof and I always believed Condorcet methods were.

Well, the good Condorcet methods (like Ranked Pairs and SSD/Beatpath) are.  But 
not all Condorcet-compliant methods are.

Consider this super-simple Condorcet method:

1)  Compute a pairwise matrix from ranked ballots.
2)  AT RANDOM, draw two candidates out and compare them pairwise.  Eliminate the 
losing candidate.
3)  Repeat step 2 until only one candidate remains.  Declare this candidate the 
winner

It is trivial to see that this is not clone independent.  For example, say 
A>B>C>A is a three way tie.  Normally, this method gives each candidate a 1/3 
chance of winning.  Now, add 10 clones of A and 10 clones of B to the election.  
One of the A clones now wins the election roughly 99.9% of the time.

So, clone-independence is not a feature of all Condorcet methods - only the best 
ones.