(with Franz Dietrich). Mind 122(487), 655-685, 2013. Preprint PDF.
It is often claimed that opinions are more likely to be correct if they are formed by processing many other independent opinions. But what does it mean to have independent opinions? To clarify this condition, we distinguish four notions of probabilistic opinion independence. Which notion applies depends on environmental factors such as commonly perceived evidence, and, more generally, on the causal network in which people interact and form their opinions. In a general theorem, we identify conditions on this network which guarantee opinion independence in each sense. Our results have implications for `wisdom of crowds' arguments, as we illustrate by providing old and new jury theorems.