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

[Juho]

On Jan 23, 2010, at 1:55 PM, Kristofer Munsterhjelm wrote:

> Juho wrote:
>> On Jan 22, 2010, at 12:05 AM, Kristofer Munsterhjelm wrote:
>>> Jonathan Lundell wrote:
>>>> 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"?
>>>
>>> A very abstract concept of spoiler might be: denote f(X) the  
>>> minimal number of ballot changes/additions required to make X the  
>>> winner. Then a spoiler is a candidate with a high f-value relative  
>>> to the number of ballots (thus "hard to get to win"), who, by his  
>>> presence, still changes who wins.
>>>
>>> Determining f(x) for the various candidates would be very hard,  
>>> though, and one also runs into the question of what threshold to  
>>> say "above this f-value, spoiler, below it, not a spoiler".
>> Maybe one should add also the requirement that the spoiler makes  
>> the result worse from spoiler's or spoiler's supporters' point of  
>> view.
>
> Yes, although that cannot be mechanically tested. For some very  
> strange methods, it might be true that adding a candidate changes  
> the winner to someone who everybody who voted for the winner ranked  
> ahead of him, but that would be a very strange method indeed.

Yes. And there are also situations where some of the supporters of the  
spoiler are happy with the changes but some are not. A theoretical  
definition of the spoiler property might require all supporters to be  
unhappy (if simpler that way).

I was thinking also about methods like Borda where in 60: A>B, 40: B>A  
A wins but addition of B2 (=> 60: A>B>B2, 40: B>B2>A) means that B  
wins. B2 in a way spoils the election in general (and from A point of  
view) but from B point of view B2 "saves" the election. B and B2 are  
maybe from the same party but B2 is just worse. The B party may make  
the decision on if B2 will be nominated as a candidate (not the A  
party (that would spoil the election from their point of view if they  
did so)).

>
>> Another possible modification is not to require f(X) to be high.  
>> One would just see what would have happened with and without the  
>> spoiler. According to that definition also strong candidates (but  
>> not actual winners) could be spoilers. (Typically term spoiler  
>> refers to minor candidates since these discussions typically refer  
>> to a two-party set-up, but the corresponding scientific term might  
>> or might not be limited to minor candidates and/or this particular  
>> set-up.)
>
> Then a spoiler is just a candidate whose presence shows IIA failure,  
> subject to that this IIA failure must happen in first place (the  
> winner changes, not lower in the ranking). The definition of IIA  
> implies that the candidate ("spoiler") can't be the winner.

...plus the spoiling (not just changing) requirement.

Juho