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.
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