Praesidium

Monday, April 28, 2008

Transitivity and Footballers, Old and Young

I've recently been thinking again about transitivity (you can find another example, also concerning football, here), due to writing a presentation for G A Cohen's Contemporary Political Philosophy course, focusing on this paper.

I was interested, therefore, to observe an intransitivity in the PFA player of the year awards: Ronaldo was voted player of the year, and Fabregas young player of the year, although Ronaldo was also eligible for that one! How can Ronaldo be the best out of all players but not best out of the young ones? (A subset of which he is a member). This seems to violate the Independence of Irrelevant Alternatives axiom - and that, presumably, is what happened - people who voted for David James, Adebayor or Gerrard for the main award (letting Ronaldo beat Fabregas) chose to back Fabregas rather than Ronaldo.

It's possible, therefore, that no individual has intransitive preferences. Then again, some footballers aren't too bright. Micah Richards reveals, in his BBC column, that he voted for both Ronaldo and Fabregas, rather than working out which was best and voting twice for him: that would have been complicated, since he's also quoted as saying "Liverpool's Steven Gerrard is the best player I have ever seen" (although, in fairness, that may not mean this year).

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