4 ms·
s/fairly difficult/impossible/ https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
by buzzdenver 10y ago
s/fairly difficult/impossible/
https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...
- agentgt 10y agoI was going to say impossible as the teacher even said that but I think for small numbers it is possible IIRC. There was some joke I think by Kenneth that the only fair voted government is a dictatorship.
- thaumasiotes 10y agoJoke? Non-dictatorship is one of the mutually impossible criteria of Arrow's impossibility theorem. "The only fair voted government is a dictatorship" is an accurate statement of the theorem, as far as it goes.
- soVeryTired 10y agoYes, but there's some equivocation there. The meaning of 'dictator' isn't quite what you might think it is.
- thaumasiotes 10y agoThe meaning of "dictator", as used in Arrow's theorem, is that the outcome of an election is exactly what the dictator says it should be. More technically, the election outcome considers only the dictator's vote, and is independent of the votes of everyone who is not the dictator. I don't see how that differs at all from the colloquial understanding. It's a perfect reflection of the principle of One Man, One Vote, as described for Ankh-Morpork ("The Patrician was the Man; he had the Vote").
- soVeryTired 10y agoBu then why does the theorem only hold with more than two candidates?
- deleted 10y ago[deleted]
- tunesmith 10y agoArrow's only proves you can't meet a certain set of criteria. It doesn't prove that set of voting criteria is necessary for a fair vote outcome. IIAC is particularly problematic.