Reading Ron Chernow’s magisterial new biography of Ulysses Grant, I came across this very correct statistical inverse reasoning from the celebrated journalist Horace Greeley (whose role in the high school history curriculum has been reduced to the phrase, “Go West, young man” — that he denied having invented):
All Democrats are not horse thieves, but all horse thieves are Democrats.
This seems like an ironic bon mot, but after he became the Democratic candidate for president against Grant in 1872 he tried to use a milder version unironically as a defence of his new party colleagues:
I never said all Democrats were saloon keepers. What I said was all saloon keepers are Democrats.
Presumably he meant to add that if we knew the base rate of saloonkeeping (or horse thievery) in the population at large, we could calculate from the Democratic vote share the exact fraction of Democrats (and of Republicans) who are saloonkeepers (or horse thieves).
Common Infirmities 