Skewed noise

We study the attitude of decision makers to skewed noise. For a binary lottery that yields the better outcome with probability p, we identify noise around p with a compound lottery that induces a distribution over the exact value of the probability and has an average value p. We propose and characterize a new notion of skewed distributions, and use a recursive non-expected utility to provide conditions under which rejection of symmetric noise implies rejection of negatively skewed noise, yet does not preclude acceptance of some positively skewed noise, in agreement with recent experimental evidence. In the context of decision making under uncertainty, our model permits the co-existence of aversion to symmetric ambiguity (as in Ellsberg's paradox) and ambiguity seeking for low likelihood “good” events.