LSAT Kung Fu Blog / Quick Hit: Proportion Confusion and The World's Deadliest Peanut
Quick Hit: Proportion Confusion and The World's Deadliest Peanut
Last time we spoke, we talked about a typical flaw in LSAT Logical Reasoning, and I enjoyed myself so much that I've decided to KEEP THAT BALL ROLLING. We're talking about—you guessed it,
without me even telling you with me just having told you one sentence ago!—another kind of error that's typical on the test. This is one of my favorite flaws (but really, how can I pick a favorite? That's like asking me which of my children I love most.* It's Sophie's Choice, is what it is!†).
Proportion Confusion is the name I've given to what happens when an arguer confuses a proportion (e.g., a ratio or a percentage) with a raw number. In this question, we've got an example of just such an error; the columnist gives us raw numbers for pedestrian deaths, then uses those numbers as the basis for a conclusion about the frequency of such deaths.
This is almost exactly the same argument as if you said "More people die from peanut allergies every year than from shark bites. So contrary to popular belief, peanuts are actually the world's deadliest predator." It's problematic because it has ignored the fact that 200 million people come into contact with peanuts every day, while, like, 7 people come into contact with sharks (these figures are approximate). Yes, in terms of raw numbers, peanuts kill more often, but when seen as a proportion, they are actually much less bloodthirsty than sharks.
And so it is with this argument; just because more people are killed crossing with the light doesn't tell us anything without context. What if 32 people die with the light, and 30 die against it, but 2,000,000 people cross with the light, while only 2,000 cross against? In other words, what proportion of people crossing in each manner end up getting killed? That's what we'd need to know.
So, we've answered the question; the flaw in the argument is that this columnist has confused the number of deaths as indicating a proportion (deaths relative to crossing frequency).
Now, a quick refresh on our Four-Fold Path For Increasing Your Velocity®:
- The question asks us to articulate what's wrong with the argument.
- The right answer will identify an assumption made by the arguer.
- If it's a typical assumption (AS IT IS HERE. WHEEE) we can expect language describing that error in general terms.
- We're likely to see at least one wrong choice that correctly identifies a common error, but one that wasn't committed within this argument.
Notice the very general, rule-like wording of these answer choices; basically all of them identify real errors of reasoning. Of course, only one of them is an error manifest in this case.
For those of you keeping score at home, here's what they're saying:
(A) Sampling error (possibly also a whiff of Ad Hominem)
(B) Causal Flaw
(C) Causal Flaw redux
(D) Sampling error redux
(E) Proportion Confusion
YAY FOR FLAW TYPES.
Hope that helps you out some. Let me know if you'd like to discuss it further.
Now, I'm going to go have a PB+J. Y'know. FOR REVENGE.
*No, it really isn't.
†Nope. Not even close, really.