User talk:CRGreathouse/Arrow

I think this should be incorporated into the "Arrow's Theorem" page. mousomer 20:30, 25 August 2006 (UTC)

Please check!

I have several issues with this proto-section as I have written it so far. If someone would be so kind as to look over these points for me, I'd appreciate it.

1. I certainly don't think Taylor was the first to apply Arrow's theorem to settings other than SWFs, and even if he was he didn't do it for the first time in his book I cited. If you know of an earlier reference, please tell me.
2. I'm not sure I'm properly explaining Blau's result, but it's difficult for me to state. If you have a better wording, or advice on how to rephrase, I'd be interested. Also, if you think the wording is fine I'd like to know too.
3. The Tanaka result is odd to me. Can someone explain to me why monotonicity is a weakening of IIA rather than an independant condition, or why it would be considered as such, or how it relates to the standard definition of monotonicity? The paper is available, but for those not wanting to look through it I'll give the condition here:
   • If for a pair of alternatives x and y at some profile p:
     1. individuals in a group G prefer x to y,
     2. individuals in a group G' are indifferent between them,
     3. the other individuals prefer y to x,
   • and the society prefers x to y, then at another profile where individuals in G and G' prefer x to y, the society must prefer x to y.
4. Is the Igersheim result notable? It seems hardly relevant, since the condition affected can be removed anyway (in wilson's theorem) with similar change to the dictatorship condition. Is its relation to Sen's liberal paradox enough to make it worthwhile?
5. Campbell wasn't the first with that result, was he?

Thanks. CRGreathouse (t | c) 20:15, 2 September 2006 (UTC)