Felix Salmon smackdown watch, misperceptions edition

By Felix Salmon
January 9, 2012
dismissing their science out of hand on my Tumblr: they really are careful and sophisticated researchers, and Sides is well within his rights to give me a good slap.

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Apologies to John Sides and Jack Citrin for dismissing their science out of hand on my Tumblr: they really are careful and sophisticated researchers, and Sides is well within his rights to give me a good slap.

On the other hand, when Sides talks about “the substance of my remarks about innumeracy”, he doesn’t get me exactly right — which is hardly surprising, given that he was going on just two throwaway sentences.

My point about innumeracy was not that people will always guess wrong when asked to estimate something. In fact, there are some things — especially very salient variables like gas prices — which people know to within a high degree of accuracy. But that doesn’t make them numerate.

Instead, I had in mind two broader points. Firstly, everybody is bad at estimating small or large numbers: the difference between a millionth and a billionth, for instance, or the difference between a billion and a trillion, is much smaller, in the human mind, than the difference between 1 and 1,000. So when you ask people to estimate things which are small in reality but high in perceived salience, like the percentage of the US budget going on foreign aid or the proportion of immigrants in the population as a whole, then you’re always going to end up with an overestimate.

And more generally, numeracy is about much more than estimating proportions and percentages. It’s about comfort with numbers and number lines, and having an intuitive feel for how they work. If I ask you what two thirds of three quarters is, do you have to work it out, or do you pretty much know that it’s one half without having to think about it? In my experience there are two kinds of people in the world: the ones who have to think about it and will probably get it wrong, and the ones who don’t have to think about it and will probably get it right. That’s what I mean by numeracy.

And what about my second point, that “generally you can’t argue people out of positions that they weren’t argued into”? I still think that’s true. Sides gives a couple of carefully-chosen counterexamples, which show that in certain circumstances it can be possible to influence some people’s opinions on certain subjects, at least for a limited period of time, if you provide them with clear information about those subjects first. (This is a well-known fact in political circles, and has given rise to the phenomenon of “push-polling”.)

And in other research Brendan Nyhan has shown that if you present information in graphical form, it’s more effective than if you just present it verbally. Again, this comes as little surprise.

But the big picture base case is still unchanged — indeed, Nyhan says that his results “underscore the challenges faced by those who hope to reduce misperceptions among the public”. The general public doesn’t want its mind changed, and any changes which do happen are always going to happen slowly. Which is why presidential debates are almost never about who won the argument on any particular point, much as people like myself would love it if they were. The goal in such debates isn’t to win some kind of intellectual argument: it’s to make as many people as possible think that you think the same thing that they think. People will vote for the person they agree with — not the person with the sharpest wit or the cleverest arguments or the most apposite facts.

Wouldn’t you agree?


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political “science” is no science, and calling it that is an insult to real scientists. People who study that field may fancy themselves to be scientists, but since they can’t prove or disprove any of their theories, it’s not a science. Being able to express their research in numbers does not make it science any more than summarizing the gambling results at a casino.

Posted by KenG_CA | Report as abusive

No! But only because you should have said: “People will vote for the person they think agrees with them…”

(Which also happens to be what I think you really meant!)

Posted by djseattle | Report as abusive

From my College Rhetoric Teacher: “You can’t change anyone’s mind, but you can convince them they believed something all along.”

Posted by DonthelibertDem | Report as abusive

“the difference between a billion and a trillion, is much smaller, in the human mind, than the difference between 1 and 1,000″

Who is having the number problem here is the question…the difference between a billion and a trillion is by magnitude a trillion is a thousnd times bigger than a billion just like 1000 is a thousand times bigger than one. Have to wonder what human mind you are referencing.

Posted by Irving13 | Report as abusive

@Irving13 – you and Felix are both right. You, on the fact that both 1-to-1,000 and billion-to-trillion are three orders of magnitude.

Felix, on the fact that on the scale that the human mind can reasonably comprehend, one versus a thousand are quite different things and people appreciate the relativeness of that difference, while a billion and trillion are both just “a lot” and the difference between those two large numbers is also “lots”. The former can be perceived as a larger difference than the latter.

Posted by SteveHamlin | Report as abusive

KenG_CA, you are absolutely correct.

Can’t state it better than this:

http://www.youtube.com/watch?v=HtMX_0jDs rw&feature=related

Posted by Danny_Black | Report as abusive

“Wouldn’t you agree?”
How many people ever ask themselves why they believe what they believe?
It isn’t what we don’t know that gives us trouble, it’s what we know that ain’t so.
Will Rogers

Posted by fresnodan | Report as abusive

Way back when I did social psychology research, I focused on Festinger’s theory of cognitive dissonance, which in one form noted that if you changed behavior so that it no longer reflected belief, the belief would change to be in conformance with the behavior. Arguments rarely work, but if you could incentivize different behavior, you could change the belief.

I had used this principle come up with a reasonably good mathematical model that predicted behavior in a gaming situation, based on changing behavior using rewards offered in the game.

Posted by Curmudgeon | Report as abusive

“That’s what I mean by numeracy.”

OK, I write subject to correction by knowledgeable types like Curmudgeon, but I think you have this backwards. Everyone has a gut reaction answer to numerical problems, but the thing about number problems is that you have to think about them to get them right. A numerate person isn’t someone who gets the right answer without thinking, it’s someone who’s good at thinking about number problems instead of using his gut.

So for instance, your example is easy because 2/3 of 3 is 2, and 2/4 is 1/2. That is why most people can answer “what’s 2/3 of 3/4″ quickly – the answer comes up directly. But “what’s 3/4 of 2/3″ is harder, even though it’s mathematically equivalent. A numerate person would perceive this and mentally invert the question into the easier format. Numeracy is the combination of being willing to think about what the right numerical answer really is together with a grab-bag of little tricks for making such thinking easier. The latter trait is developed by the former.

Posted by Greycap | Report as abusive

@Greycap, I’m currently reading Daniel Kahneman’s “Thinking, Fast and Slow”, which proposes two systems of thought. Within the instinctive “fast” system, he notes instinct based on expertise, and instinct based on heuristics. Either one could account for what you describe here. He also notes that we can revert to “slow” thinking when presented with a numeric problem of greater complexity, and that slow thinking is usually more accurate than fast (but often not timely enough).

Kahneman is a psychologist who received the Nobel in economics for his work in discrediting the notion that people think and behave rationally (that is a greatly simplistic description, of course).

Posted by Curmudgeon | Report as abusive

@Curmudgeon: And here he is speaking at the London School of Economics:
http://www2.lse.ac.uk/newsAndMedia/video AndAudio/channels/publicLecturesAndEvent s/player.aspx?id=1251

Posted by engineer27 | Report as abusive