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 data.
2. A Bayesian agent with a finitely additive prior, or an improper prior, however, might do so.
3. An agent following a gamma-minimax strategy might do so.
4. An agent following the strategies of E-admissibility recommended by Levi and of maximality recommended by Sen and Walley, might do so.
A discussion follows about how damaging to a decision theory intended to be rational it might be to pay to not receive information.