Is Ignorance Bliss?

<blockquote>``...where ignorance is bliss, 'tis folly to be wise.'' Thomas Gray</blockquote> <p>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</p> <ol> <li>A Bayesian agent with a proper, countably additive prior never maximizes utility by paying not to see cost-free data.</li> <li>The definition of ``cost-free'' is delicate, and requires explanation.</li> <li>A Bayesian agent with a finitely additive prior, or an improper prior, however, might pay not to see cost-free data.</li> <li>An agent following a gamma-minimax strategy might also do so.</li> <li>An agent following the strategies of E-admissibility recommended by Levi and of maximality recommended by Sen and Walley, might also do so.</li> </ol> <p>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.</p>