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Is Ignorance Bliss?

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journal contribution
posted on 01.01.2007, 00:00 by Joseph B. Kadane, Mark J. Schervish, Teddy Seidenfeld
``...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.




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