The Interface of Information with State Likelihood

One intuits that if the state likelihoods were only slightly skewed, say, the ortho product was 1.10 times more likely than meta, there would be only slightly less information than 1 bit available. If instead, the ortho/meta likelihoods were dramatically 

An imbalance factor F (= 1.10,10, 10 ) is readily converted to a pair of fractions, 

The results then approximate the fraction of times—the likelihood—the particular state will be realized in experiments. For the aforementioned three cases, one has 

A more formal connection between the fractional likelihoods and probabilities is reserved for Section 2.4. For now, it is sufficient to note that formulae analogous to Equations (2.8) and (2.9) extend beyond aromatic substitution. The generality is conveyed by labeling the likelihood fractions by subscripts 1 and 2 /j and/2. Then, if one considers the fractions as logarithm arguments and multiplies the results by -1, one arrives at  

This leads to Table 2.2. Included is the case of the equal-likelihood venues of Section 2.1 where/i =/2 = 0.5000. The purpose of Table 2.2 is to demonstrate that the two rightmost columns move in opposite directions. The term 

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