 To cover evidence streams (or subsequences of evidence streams) consisting entirely of experiments or observations on which \(h_j\) is fully outcome-compatible with hypothesis \(h_i\) we will first need to identify a useful way to measure the degree to which hypotheses are empirically distinct from one another on such evidence. Consider some particular sequence of outcomes \(e^n\) that results from observations \(c^n\). The likelihood ratio \(P[e^n \pmid h_{j}\cdot b\cdot c^{n}] / P[e^n \pmid h_{i}\cdot b\cdot c^{n}]\) itself measures the extent to which the outcome sequence distinguishes between \(h_i\) and \(h_j\). But as a measure of the power of evidence to distinguish among hypotheses, raw likelihood ratios provide a rather lopsided scale, a scale that ranges from 0 to infinity with the midpoint, where \(e^n\) doesn’t distinguish at all between \(h_i\) and \(h_j\), at 1. So, rather than using raw likelihood ratios to measure the ability of \(e^n\) to distinguish between hypotheses, it proves more useful to employ a symmetric measure. The logarithm of the likelihood ratio provides such a measure.