Too Odd (Not) to Be True? A Reply to Olsson

In ‘Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ascribes to L. Jonathan Cohen the claims that if two witnesses provide us with the same information, then the less probable the information is, the more confident we may be that the information is true (C), and the stronger the information is corroborated (C*). We question whether Cohen intends anything like claims (C) and (C*). Furthermore, he discusses the concurrence of witness reports within a context of independent witnesses, whereas the witnesses in Olsson’s model are not independent in the standard sense. We argue that there is much more than, in Olsson’s words, ‘a grain of truth’ to claim (C), both on his own characterization as well as on Cohen’s characterization of the witnesses. We present an analysis for independent witnesses in the contexts of decisionmaking under risk and decision-making under uncertainty and generalize the model for n witnesses. As to claim (C*), Olsson’s argument is contingent on the choice of a particular measure of corroboration and is not robust in the face of alternative measures. Finally, we delimit the set of cases to which Olsson’s model is applicable. 1 Claim (C) examined for Olsson’s characterization of the relationship between the witnesses 2 Claim (C) examined for two or more independent witnesses 3 Robustness and multiple measures of corroboration 4 Discussion In ‘Corroborating Testimony, Probability and Surprise’, Erik J. Olsson ([2002]) takes L. Jonathan Cohen to be making the following claims in The Probable and the Provable ([1977], p. 98): (C) The smaller the prior probability of the proposition that two court witnesses agree upon, the greater our degree of confidencewill be that their testimony is true. (C*) The smaller the prior probability of the proposition that two court witnesses agree upon, the stronger it is corroborated by their testimony. Brit. J. Phil. Sci. 53 (2002), 539–563 &British Society for the Philosophy of Science 2002 1 It would be more fitting for Cohen and Olsson to talk about the strength of confirmation, since ‘corroboration’ carries with it the vestiges of Popper’s program which turns its back on inductive approaches to investigate the relationship between hypothesis and evidence. Olsson constructs a clever and elegant model to assess under what conditions these claims are true. The upshot of his argument is that there is only ‘a grain of truth’ in claim (C): the claim is not ‘correct as it stands [ . . . ], not even under a charitable rendering’. Claim (C*) purportedly holds only if we make certain special assumptions about our epistemic status with respect to the reliability of the witnesses. The first question that concerns us is whether Cohen really intends to be making claims like (C) and (C*). Let us look at the pages preceding the ones from which Olsson draws his quotes. Cohen is trying to give an account of the fact that concurring reports (i.e. reports with the same content) from independent witnesses corroborate what is being reported to a greater extent than a single report does. He discusses Boole’s account of this fact, which originated in Jakob Bernoulli’s Ars conjectandi. Either the two witnesses whose reports concur are truth-tellers or they are liars. Let the chance that they are truth-tellers be p and q for the respective witnesses. If the witnesses have a choice between reporting one of two options, then their reports will concur if and only if they are both telling the truth or they are both lying. Hence, the chance that they are both truth-tellers given that their reports concur is: PðTruth-TellersjConcurrenceÞ 1⁄4 PðTruth-Tellers & ConcurrenceÞ PðConcurrenceÞ 1⁄4 PðTruth-Tellers) PðTruth-Tellers or LiarsÞ 1⁄4 pq pqþ ð1 pÞð1 qÞ Notice, however, that the chance that we are dealing with truth-tellers goes up as the number of reports increases from one to two if and only if p, q > 0:50 on Boole’s formula. Cohen objects to this result. He envisions two independent witnesses who are rather unreliable, i.e. p, q < 0:50. If their reports are concurring, then ‘Boole’s formula produces a lower probability for their joint veracity, whereas normal juries would assign a higher one’ (ibid., p. 96). Indeed, if p 1⁄4 q 1⁄4 0:20, then it is easy to verify that the chance that two witness reports rather than one witness report is true goes down from 0.20 to approximately 0.06 on Boole’s formula. The reason that the formula fails is that there are not just two options in a typical case of witness reports in court, but ‘so many different things can be said instead of the truth’ (ibid., p. 97). Hence, the chance that two liars will produce concurring reports is no longer ð1 pÞð1 qÞ, but much lower. It is in this context that we should assess the claim of Cohen quoted by Olsson: ‘Where agreement is relatively improbable (because so many different things might be said), what is agreed is more probably true’ (ibid., p. 98). The 540 L. Bovens, B. Fitelson, S. Hartmann and J. Snyder