"The log used to determine number of bits should..."

Imagine what happens when the oyster is blue\. $H$ predicted blueness with $\\frac{1}{8}$ of its probability mass, while $\\lnot H$ predicted blueness with $\\frac{1}{4}$ of its probability mass\. Thus, $\\lnot H$ did better than $H,$ and goes up in probability\. Previously, we've been combining both $\\mathbb P(e \\mid H)$ and $\\mathbb P(e \\mid \\lnot H)$ into unified likelihood ratios, like $\\left(\\frac{1}{8} : \\frac{1}{4}\\right)$ $\=$ $(1 : 2),$ which says that the 'blue' observation carries 1 bit of evidence $H.$ However, we can also take the logs first, and combine second\.

The log used to determine number of bits should probably be consistent throughout or clarified each time. Here, the log 2 scale is used, when elsewhere there is usage of the log 10 scale.