On the uniqueness of convexranged probabilities

Title:

On the uniqueness of convexranged probabilities

Author(s):

Amarante, Massimiliano

Date:

2003

Type:

Working papers

Department:

Economics

Permanent URL:

http://hdl.handle.net/10022/AC:P:504

Series:

Department of Economics Discussion Papers

Part Number:

020324

Publisher:

Department of Economics, Columbia University

Publisher Location:

New York

Abstract:

We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convexranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 < P(A∗) < 1 such that P(A∗) = P(B)=⇒ Q(A∗) = Q(B) whenever B∈Σ] is equivalent to the condition [∀A,B ∈ Σ P(A) > P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q.

Subject(s):

Economic theory
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