Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Ignorance Bliss?

Publication Date

March, 2007

Publication Type

Tech Report

Author(s)

Joseph B. Kadane, Mark Schervish, and Teddy Seidenfeld

Abstract

"...where ignorance is bliss, 'tis folly to be wise."
Thomas Gray

If ignorance were bliss, there is information you would pay not to have. Hence the question is whether a rationally-behaving agent would ever do such a thing. This paper demonstrates that

1. A Bayesian agent with a proper, countably additive prior never maximizes utility by paying not to see cost-free data.
2. The definition of "cost-free" is delicate, and requires explanation.
3. A Bayesian agent with a finitely additive prior, or an improper prior, however, might pay not to see cost-free data.
4. An agent following a gamma-minimax strategy might also do so.
5. An agent following the strategies of E-admissibility recommended by Levi and of maximality recommended by Sen and Walley, might also do so.

A discussion follows about how damaging to a decision theory intended to be rational it might be to pay not to receive cost-free information.

Areas of Research