LSAT Kung Fu Blog / Quick Hit: Proportion Confusion

Quick Hit: Proportion Confusion

Categories: 
Quick Hit: Proportion Confusion

69.1.20

Hey, you remember how last time we were here (i.e., yesterday), I told you that the causal flaw was, by my count, the single most commonly-committed error in reasoning on the LSAT?

Did that—even for a moment—make you think that most of the arguments in the Logical Reasoning exhibited that flaw?

Of course not, because you are awesome, and thoughtful, and furthermore, equipped with strong evidence to the contrary.

In exactly the same way that if I told you that October 5th was the most common birthday in the US (which it evidently is, if I am to believe the interwebs), you wouldn't take that to mean that most of the people in the US were born on October 5th. That would be stupid; only about 1 million people, or roughly one-third of one percent of Americans, were born on that date. 

So it's clear that just because something is most common does not mean that it's a majority.

To confuse those two concepts is to commit an error of reasoning I like to call Proportion Confusion. It's to conflate a proportion (the most common birthdate) with a real number (the birthdate of a majority of people).

Now, let's see this shizz in action on an LSAT question.

In Q 20 here, the medical reporter tells us that heart disease is one of the most common forms of disease, and then claims that preventing it would therefore help most people. AND THIS IS THE SAME THING WE WERE JUST TALKING ABOUT!

Just because it's the most common by proportion doesn't mean heart disease afflicts a majority; maybe it afflicts just 0.3% of people, but maybe every other disease involves even fewer people than that.

So the big idea, here, again is to sidestep the analysis by means of recognition. Whenever you see mention of any kind of proportion, you ought to ask yourself, "Hey, man; how are they using this proportion to try (vainly) to trick me?".

And check out answer choice (B)—if you bring up the possibility that even if a disease is most common, it still doesn't mean most people have it—then you point out the flaw of the argument, by pointing out that its assumption (that a proportion does tell you about a real number) is false.

And that, as the fellow said, is that.

Tags: