Rob Lanphier's control letter

[Rob Lanphier]

Markus,

Thank you for providing an example we could sink our teeth into.  This
demonstrates a genuine effort to understand what has repeatedly been
discussed on this list for the past year or so, and I appreciate this
greatly.

I wish Donald would go through this exercise as well.

Now, to the meat of what you wrote :)

On Sun, 4 May 1997, Markus Schulze wrote:
> Here is an example to show why voters would truncate, if
> a Condorcet Criterion Method is used:
> 
> Case 1:
> 
> 47 voters vote ABC.
> 10 voters vote BAC.
>  8 voters vote BCA.
> 35 voters vote CBA.
> 
> A:B=47:53.
> A:C=57:43.
> B:C=65:35.
> 
> B wins against A and against C in the pairwise comparison. Thus B
> is the Condorcet winner.

Correct.

> 
> Case 2:
> 
> Now the 47 voters, who prefer A most, do truncate.
> 
> 47 voters vote A.
> 10 voters vote BAC.
>  8 voters vote BCA.
> 35 voters vote CBA.
> 
> A:B=47:53.
> A:C=57:43.
> B:C=18:35.
> 
> Now there is a tie between A, B, and C. Whether A is elected, 
> depends on the used tie breaker. 

True.
 
>But if Condorcet/Smith is
> used, then A is elected.

Wrong, given the version of Smith//Condorcet advocated by the Condorcet
camp on this list. The winner is still Candidate B. Neither A, B, nor C is
eliminated via Smith's method.

This situation is the result of a Condorcet tie-breaker. Notice there were
no candidates who won all pairwise elections. In a Condorcet tie-breaker,
the winning candidate is the one who has the least number of people that
explicitly vote against them in any pairwise election. Candidate B had the
fewest number of voters vote against him/her of any of the candidates in
his/her poorest showing (35 votes). 

Note that I just copied the paragraph above directly out of the Condorcet
calculator at:

http://www.eskimo.com/~robla/politics/condorcet-front.html

...using the following input:

All Candidates As Entered: 

1, Candidate A
2, Candidate B
3, Candidate C

All Votes as Entered:

47:1  # 47 voters vote ABC.
10:2>1>3  # 10 voters vote BAC.
8:2>3>1   #  8 voters vote BCA.
35:3>2>1  # 35 voters vote CBA.

We went through several iterations to get this program to match the method
preferred by the Condorcet advocates on this list.  The reason why this
particular flavor is preferred is because of its resilliance against
truncation.  It still is vulnerable to order reversal in rather limited
circumstances, but STV practically *forces* voters to resort to order
reversal.

> I believe, that to every tie breaker method it is possible to
> create an example, where truncation makes sense.

Ummm, the burden is still on you to prove that.

---
Rob Lanphier
robla at eskimo.com
http://www.eskimo.com/~robla