However, I think a weakness in the argument is that it assumes the probabilities exist and are constant throughout, but they arenât defined by assumption in the Ellsberg paradox. In particular, looking at the figure for case 1, the argument assumes p is the same when you start at the first random node as it is looking forward when youâre at one of the two choice nodes, 1 or 2. In some sense, this is true, since the colours of the balls donât change between, but you donât have a subjective estimate of p by assumption and âunknown probabilityâ is a contradiction in terms for a Bayesian. (These are notes I took when I read the paper a while ago, so I hope they make sense! :P.)
Another weakness is that I think these kinds of sequential lotteries are usually only relevant in choices where an agent is working against you or trying to get something from you (e.g. money for their charity!), which also happen to be the cases where ambiguity aversion is most useful. You canât set up such a sequential lottery for something like the degree of insect consciousness, P vs NP, or whether the sun will rise tomorrow.
This might also be of interest:
The Sequential Dominance Argument for the Independence Axiom of Expected Utility Theory by Johan E. Gustafsson, which argues for the Independence Axiom with stochastic dominance, a minimal rationality requirement, and also against the Allais paradox and Ellsberg paradox (ambiguity aversion).
However, I think a weakness in the argument is that it assumes the probabilities exist and are constant throughout, but they arenât defined by assumption in the Ellsberg paradox. In particular, looking at the figure for case 1, the argument assumes p is the same when you start at the first random node as it is looking forward when youâre at one of the two choice nodes, 1 or 2. In some sense, this is true, since the colours of the balls donât change between, but you donât have a subjective estimate of p by assumption and âunknown probabilityâ is a contradiction in terms for a Bayesian. (These are notes I took when I read the paper a while ago, so I hope they make sense! :P.)
Another weakness is that I think these kinds of sequential lotteries are usually only relevant in choices where an agent is working against you or trying to get something from you (e.g. money for their charity!), which also happen to be the cases where ambiguity aversion is most useful. You canât set up such a sequential lottery for something like the degree of insect consciousness, P vs NP, or whether the sun will rise tomorrow.
See my discussion with Owen Cotton-Barratt.