05 November 2008

The notion of "typical" doesn't behave nicely

Matt Yglesias makes an interesting point. The "typical" American is white, in that more than half of all Americans are white. The "typical" American is Christian, in that more than half of all Americans are Christian. But does this mean that the "typical" American is a white Christian, in that more than half of all Americans are white Christians? Not necessarily; I don't have the numbers.

Moreover, the "typical" white Christian votes Republican. Thus typical people vote Republican, so the Republicans should have won last night. But they didn't.

The point is that most people are "typical" in some ways, but few people are "typical" in all ways. And a party that is based around just people who are "typical" in all ways (note that I'm not saying this describes the Republican party) is doomed to fail, because most people are unusual along some dimension. I don't think this deserves the name of "paradox", but it's just something worth keeping in mind about How Statistics Work.

4 comments:

unapologetic said...

see also: Most-Wanted Song.

Although, truth be told, I find it sort of catchy. Not nearly the hit that "Most Unwanted Song" is, though.

D. said...

This reminds me of an article I read by Steven Brams in his book "Mathematics and Democracy" (maybe this one: http://ideas.repec.org/a/spr/sochwe/v15y1998i2p211-236.html) which talked about a California election with a large number of propositions in which nobody cast a 'winning ballot' (ie nobody agreed with the majority on every proposition)

Nathan said...

"The Census report, like most such surveys, had cost an awful lot of money and didn't tell anybody anything they didn't already know--except that every single person in the Galaxy had 2.4 legs and owned a hyena." (So Long, and Thanks for All the Fish)

Paul Soldera said...

This is a tragic twist of statistical reporting that has plagued the Marketing world for decades. Your 'average' customer is never your 'average' customer.