Is Ignorance Bliss?
``...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
- A Bayesian agent with a proper, countably additive prior never maximizes utility by paying not to see cost-free data.
- The definition of ``cost-free'' is delicate, and requires explanation.
- A Bayesian agent with a finitely additive prior, or an improper prior, however, might pay not to see cost-free data.
- An agent following a gamma-minimax strategy might also do so.
- 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.