關於不可能定理 - 經濟

你好
因為曾修過公共選擇
所以也碰過Arrow's Impossibilty Theorem
可以和大家分享討論看看
(好像有些小部分和之前分享朋友不同...)
過去筆記簡單整理如下:

Arrow's Impossibilty Theorem

At least 3 persons,(1,2,3)
At least 3 choices,(x,y,z)

no mechanism can always aggregate personal preferences
to become a social preference,

which satisfies four conditions at the same time,

condition U : personal preferences and social preference are rational.
condition P : x,y belong to A , x>y in individual , x>y in society.
condition I : x,y belong to A ,
x and y's binary relation in individual is unchanged,
x and y's binary relation in society is unchangd.
condition D : non-dictatorship

Strategy of Proof :

if social preference satisfies condition U, P, and I,
it will not satisfy condition D.
we are sure to find a dictator.

----------------------------------------------------------------------
附註: 證明真的超難理解的....
也是看了好久再加上問老師才搞的好像有一點點懂....


--
多情而不牽戀
此情聖之風也
友善而又淡然
此君子之交也
----逐流

--