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
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