 Even though the likelihood ratios are numerically different, their posterior probabilities given the evidence are the same. Note that the prior odds of the three \(H_p\)’s in the table should be written in terms of \(\delta\). Following (Meester and Sjerps 2004), the prior odds of the first hypothesis in the table are \(\slashfrac{\delta}{(1-\delta)}\). The prior odds of the second hypothesis are \(\slashfrac{(\delta/2)}{(1-\delta)}\). The prior odds of the third hypothesis are \(\slashfrac{(\delta/2)}{(1-(\delta/2))}\). In each case, the posterior odds—the result of multiplying the prior odds by the likelihood ratio—are the same: \(R\times \slashfrac{\delta}{(2(1-\delta))}\). So despite differences in the likelihood ratio, the posterior odds of the different hypotheses are the same so long as the priors are appropriately related.