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

[Kristofer Munsterhjelm]

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.

> 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.