Notes on a simple thing about the world that we frequently do not think through even though it is, rhetorically speaking, a gigantic chunk of what we do in business and politics. It is not complex, but surprisingly hard to get an intuitive grip on. This is the basic-but-easy-to-confuse question, “what we mean when we say that X is Yer than Z when X and Y are both groups?”
If I claim that this apple is bigger than that orange, what I must mean is simple, and if we want to verify my claim, we can just measure the fruit in question if we have a reasonably reliable tape measure and a steady hand. This is not easy to misunderstand except in the most pathological of bone-headedness.
But imagine not that I am now talking about larger quantities of fruit. Like “the apples in this barrel are bigger than the oranges in that crate”. “The apples of the Pink Lady harvest in Australia in 2018 are bigger than the tangerines of Java in 2017.” “Clementines are smaller than pomellos.”
(Why do I care so much about fruits? Fruits are not my primary target here. This loose talk vexes me most of all when it is in statements about humans, or ecistential risk. We will get to those.)
See Figure 1 for example:
#par(mar = c(0, 1, 0, 1)) plot( #c( function(x) dnorm(x), # function(x) dnorm(x, 1) #), -2, 2, ) plot( #c( function(x) dnorm(x), # function(x) dnorm(x, 1) #), -2, 2, )
In the wild
- in any case these categories are porous
- Mention that this problem does not arise with Bernoulli RVs
Grimmett, Geoffrey, and David Stirzaker. 2001. Probability and Random Processes. 3rd ed. Oxford ; New York: Oxford University Press.