Condorcet Truncation Example

[Rob Lanphier]

On Sun, 4 May 1997, Markus Schulze wrote:
> I want to show a way, how it is possible to vote
> strategically if a Condorcet Criterion
> method is used:

No argument here, it is *possible* to vote strategically.

> Example:
>   
>   There are one right-wing candidate A, one moderate left-wing
>   candidate B and one radical left-wing candidate C.
> 
>   The opinions of the voters are as follows:
> 
>   40 voters prefer ABC.
>   25 voters prefer BAC.
>   10 voters prefer BCA.
>   25 voters prefer CBA.
>   
>   Then B is the Condorcet winner.
> 
>   Now suppose the 40 right-wing voters use the above mentioned
>   strategy. Then:
> 
>   40 voters vote ACB.
>   25 voters vote BAC.
>   10 voters vote BCA.
>   25 voters vote CBA.  
> 
>   Now A, B, and C are in a tie. And if you use
>   Smith//Condorcet [EM], then A wins.


The problem is that this strategy could go disasterously wrong for the "A"
supporters, and is a longshot at best.

In order to coordinate their vote so tightly, they'd have to pretty much
advertise that they were going to resort to this strategy.  This would
mean that the "B" supporters might catch wind of this, and perhaps this
would actually cause a small number of "B" supporters (say 6%) to drop
their secondary support for "A", so that the vote becomes:

    40 voters vote ACB.
    19 voters vote BAC.
    16 voters vote BCA.
    25 voters vote CBA.  

So, now candidate "C" wins in a squeeker, where "C" is presumably on the
far opposite extreme from "A".

The fact of the matter is that the "A" voters are relying on a lot of
support from the "B" voters in order to make the order reversal tactic
work in their favor.  I would have a hard time believing that "B" voters
wouldn't engage in the defensive tactic of ranking "C" above "A".

Given the danger of reprisal, I doubt that the party leaders responsible
for the "A" candidacy would advocate this, and because of this, I doubt
that the "A" supporters would *unanimously* choose order reversal.

Furthermore, let's say that the "B" supporters voted as they had in your
example, and that a handful of "A" voters (say, 6% again), out of bitter
hatred for "C" (or their genuine preference of "B" over "C") can not stand
to rank *anyone* higher than "C": 

     6 voters vote ABC.
    34 voters vote ACB.
    25 voters vote BAC.
    10 voters vote BCA.
    25 voters vote CBA.  

Now, "B" still beats "A".

Given the risk associated with order reversal and the relatively low odds
of payoff, I really don't see a large constituancy like you mention
actually attempting it. 

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