Unbounded expectations and the Shooting Room

Abstract

Several treatments of the Shooting Room Paradox have failed to recognize the crucial role played by its involving a number of players unbounded in expectation. We indicate Reflection violations and other vulnerabilities in extant proposals, then show that the paradox does not arise when the expected number of participants is finite; the Shooting Room thus takes its place in the growing list of puzzles that have been shown to require infinite expectation. Recognizing this fact, we conclude that prospects for a ``straight solution" are dim.

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