Here is a little puzzle, inspired by a brief visit to the UK Supreme Court yesterday.
Suppose that an appeal, which turns purely on questions of law rather than on questions of fact, comes to a supreme court. (That is important - we are to assume that this hearing is the end of the line, so if something goes wrong, there is no further appeal procedure to put it right.) And suppose that 9 justices hear the appeal, and decide who wins by a simple majority.
5 justices would allow the appeal, and 4 would dismiss it, so the appeal succeeds. But the 5 are split 3-2. 3 of them reach their conclusion by using argument-3, and make clear their view that another argument, argument-2, would be not merely inadequate but mistaken. The other 2 rely on argument-2, and make clear their view that argument-3 would be mistaken.
The 4 who would dismiss the appeal all rely on exactly the same argument, argument-4.
Given that we expect legal decisions to be made for good reasons, should we worry that the court's decision is opposite to the decision which would be supported by the argument that attracts more support than any other argument?