Value and Unacceptable Risk: Temkin's Worries about Continuity Reconsidered

Consider a transitive value ordering of outcomes and lotteries on outcomes, which satisfies substitutivity of equivalents and obeys ‘continuity for easy cases’, i. e., allows compensating risks of small losses by chances of small improvements. Temkin (2001) has argued that such an ordering must also - rather counter-intuitively - allow chances of small improvements to compensate risks of huge losses. In this paper, we show that Temkin's argument is flawed but that a better proof is possible. However, it is more difficult to determine what conclusions should be drawn from this result. Contrary to what Temkin suggests, substitutivity of equivalents is a notoriously controversial principle. But even in the absence of substitutivity, the counter-intuitive conclusion is derivable from a strengthened version of continuity for easy cases. The best move, therefore, might be to question the latter principle, even in its original simple version: As we argue, continuity for easy cases gives rise to a sorites.