[EM] I need an example of Condorcet method being subjected to the spoiler effect if any

[Juho]

On Jan 21, 2010, at 5:33 PM, Jonathan Lundell wrote:

> On Jan 21, 2010, at 1:03 AM, Juho wrote:
>
>> What is good in all the common Condorcet methods is that their  
>> vulnerabilities to strategies (and their differences in general)  
>> may very well be so small in typical real elections (large, public,  
>> with independent voter decision making, with changing opinions and  
>> less than perfect poll information) that strategic voting will not  
>> be a problem. Also their differences with sincere votes (e.g.  
>> spoiler related problems) are quite small in real life elections.
>>
>> Here's one simple spoiler related example as a response to Kathy  
>> Dopp's request.
>>
>> 35: A>B>C
>> 33: B>C>A
>> 32: C>A>B
>>
>> I this example there are three candidates in a top level cycle. If  
>> any of the candidates would not run that would mean that there is a  
>> Condorcet winner, and that winner would be different in each case.  
>> Let's say that the method we use will pick A as the winner. If B  
>> would not run then the votes would be 35: A>C, 33: C>A, 32: C>A and  
>> C would win. B is thus a spoiler from C's point of view.
>>
>> I note however that these spoiler cases in Condorcet are not as  
>> common as in many of the other methods. In practice it may be that  
>> there is no need to worry about these cases. Maybe Kathy Dopp's  
>> comparisons will reveal something about how problematic the spoiler  
>> effect is or is not in Condorcet. Not also that in the example  
>> above B was not a minor party candidate (often term spoiler refers  
>> to minor candidates) but a pretty strong candidate.
>
> In that case it might be a good starting point to define "spoiler",  
> so we know what we've found when we find it.
>
> What's an example of an IRV spoiler who's not a "pretty strong  
> candidate"?

In Plurality a typical spoiler scenario is one where the spoiler is a  
minor candidate (e.g. Nader in the US presidential elections). In IRV  
the spoilers are typically stronger.

Here's one IRV example where the centrist candidate (C) wins.

30: R>C>L
35: C>L>R
35: L>C>R

Then we add one more candidate (C2, spoiler) that the R and L  
supporters strongly dislike.

30: R>C>L>C2
15: C>C2>L>R
20: C2>C>L>R
35: L>C>R>C2

As a result C will be eliminated first, R next, and since C2 is not a  
strong candidate L will win. C2 thus was a spoiler from C's point of  
view.

C2 is not fully a minor candidate. Although C2 has no chances to win  
C2 has more first preference votes than C. In IRV this kind of chains  
of influence could be also longer (5 candidates, 6 candidates etc.),  
and as a result the spoilers could be more and more minor. But on the  
other hand the probability of such minor candidates spoiling the  
election is very low. So, in theory also very minor spoilers are  
possible but they don't seem probable in practice.

This is related to the observation that while Plurality may be in  
trouble already when there are only two major candidates, main  
problems of IRV (and Approval and Range) seem to appear only when  
there are at least three credible candidates.

Juho