Definitely maybe and possibly even probably: efficient communication of higher-order uncertainty

Possibility and probability expressions, like possibly or probably, are frequently assumed to communicate that the probability of a proposition is above a certain threshold. Most previous empirical research on these expressions has focused on cases of known objective chance: if the true objective probability is given, would a speaker use possibly, probably or one of their kin? Here, we investigate the use of probability expressions when speakers have subjective uncertainty about objective chance, i.e., higher-order uncertainty. Experimental data suggest that speakers’ choices of a probability expression is a complex function of their state of higher-order uncertainty. We formulate a computational probabilistic model of pragmatic speaker behavior that explains the experimental data.