A pragmatic argument against equal weighting

Abstract

We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” (and, more generally, in the “Linear Pooling” view) regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ , assigns an equal or higher weight to another agent, $$\hbox {j}$$ , (i.e. if $$\hbox {i}$$ takes $$\hbox {j}$$ to be as epistemically competent as him or epistemically superior to him), he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely rational and sympathetic $$\hbox {j}$$ choose for him whether to accept a bet with positive expected utility. If $$\hbox {i}$$ assigns a lower weight to $$\hbox {j}$$ than to himself, he must not be willing to pay any positive price for letting $$\hbox {j}$$ choose for him. Respecting the constraint entails, we show, that the impact of disagreement on one’s degree of belief is not independent of what the disagreement is discovered to be (i.e. not independent of j’s degree of belief).