 Olsson defines truth conduciveness in the standard fashion. His impossibility theorem is based on the following alternative proof strategy (Olsson 2005, appendix B): Consider a situation of two witnesses both reporting that \(A\), represented by \(S = \langle A, A\rangle\). Take a measure \(C\) of coherence that is informative with respect to \(S\), in the sense that it does not assign the same degree of coherence to \(S\) regardless of which probability assignment is used. This means that the measure is non-trivial in the situation in question. Take two assignments \(P\) and \(P'\) of probabilities to the propositions in \(S\) that give rise to different coherence values. Olsson shows that a counter example to the truth conduciveness of \(C\) can be constructed through a strategic choice of the probability of reliability. If \(P\) makes \(S\) more coherent than does \(P'\) according to \(C\), we fix the probability of reliability in such a way that \(S\) comes out as more probable on \(P'\) than on \(P\). If, on the other hand, \(P'\) makes \(S\) more coherent, then we choose a value for the probability of reliability so that \(P\) makes \(S\) more probable. It follows that no coherence measure is both truth conducive and informative.