 As we have seen, in preference aggregation, the ‘boundary’ between possibility and impossibility results is easy to draw: when there are only two decision alternatives, all of the desiderata on a preference aggregation rule reviewed above can be satisfied (and majority rule does the job); when there are three or more alternatives, there are impossibility results. In judgment aggregation, by contrast, the picture is more complicated. What matters is not the number of propositions in \(X\) but the nature of the logical interconnections between them.