Converging and diverging views¶
I will just leave this here:
Suppose that two people, Mr A and Mr B have differing views (due to their differing prior information) about some issue, say the truth or falsity of some controversial proposition S. Now we give them both a number of new pieces of information or ’data’, D1,D2,…,Dn, some favorable to S, some unfavorable. As n increases, the totality of their information comes to be more nearly the same, therefore we might expect that their opinions about S will converge toward a common agreement. Indeed, some authors consider this so obvious that they see no need to demonstrate it explicitly, while Howson and Urbach (1989, p. 290) claim to have demonstrated it.
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Mr B’s opinion should be changed in the direction of Mr A’s. Likewise, if D had tended to refute S, one would expect that Mr B’s opinions are little changed by it, whereas Mr A’s will move in the direction of Mr B’s. From this we might conjecture that, whatever the new information D, it should tend to bring different people into closer agreement with each other, in the sense that
Although this can be verified in special cases, it is not true in general.
Is there some other measure of ‘closeness of agreement’ such as log[P(S|D Ia)∕P(S|D IB], for which this converging of opinions can be proved as a general theorem? Not even this is possible; the failure of probability theory to give this expected result tells us that convergence of views is not a general phenomenon. For robots and humans who reason according to the consistency desiderata of Chapter 1, something more subtle and sophisticated is at work.
Indeed, in practice we find that this convergence of opinions usually happens for small children; for adults it happens sometimes but not always. For example, new experimental evidence does cause scientists to come into closer agreement with each other about the explanation of a phenomenon.
Then it might be thought (and for some it is an article of faith in democracy) that open discussion of public issues would tend to bring about a general consensus on them. On the contrary, we observe repeatedly that when some controversial issue has been discussed vigorously for a few years, society becomes polarized into opposite extreme camps; it is almost impossible to find anyone who retains a moderate view.
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