The Conservatives, as being by the law of their existence the stupidest party…Mill later clarified his statement like so:
I never meant to say that the Conservatives are generally stupid. I meant to say that stupid people are generally Conservative.As a matter of strict logic, these are distinct claims; S --> C does not entail C --> S. However, if what Mill says is correct, then we should be able to make a probabilistic judgment about the intelligence of conservatives. Suppose that stupid people constitute 60% of the population (a generously low number). Suppose that smart people split 50-50 between conservatism and liberalism. And suppose that stupid people split 80-20 between conservatism and liberalism, consistent with Mill’s claim. Now, say you meet a random person who turns out to be conservative, and you know nothing else about him. How likely is he to be stupid? A quick application of Bayes’ Rule tells us
P(stupid | conservative) = [(0.8)(0.6)] / [(0.8)(0.6) + (0.5)(0.4)] = 0.71And thus we may conclude that a random conservative person – that is, a randomly chosen person who turns out to be conservative – is more than 70% likely to be stupid.
More generally, if s = the fraction of the public that is stupid, a = the fraction of stupid people who are conservative, and b = the fraction of smart people who are conservative, then the probability a randomly chosen person is stupid given that he is conservative is
P(stupid | conservative) = as / [as + b(1 – s)]Just plug in the numbers you think appropriate. Of course, it’s worth noting that the meaning of ‘conservative’ has changed substantially since Mill’s time. And being neither a conservative nor a liberal (in the modern American sense of that word), I have no dog in this hunt. Stupidity seems well represented in both parties. My interest here is purely mathematical!