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Ellen Peters, of the University of Oregon (and also an NFP policy advising company) came to speak about "Numeracy and Decision-Making". She describes numeracy as the ability to understand and use quantitative tools, such as probability and statistics.

It is suggested that perhaps about half of Americans today are innumerate - that is, they have a weak grasp of quantitative thinking. (Having no grasp would be unusual because it seems to be inborn - to a certain degree. There are variations, of course.) Dr Peters's hypothesis was that numeracy aids decision-making; innumeracy harms decision making. This is because of the role of affect (emotional state, more or less) in making decisions. When we're presented with a decision, we typically analyze it in a deliberate way - but we also weigh the emotional implications of our choice with respect to past experience. And those parallel processes, the experiential and the deliberative, can be thought to output some conclusion which can then be further modulated or modified by immediate affect - your mood at the time you're making the decision. If you hate the weather, you just got married, you're hungry, your feet hurt, those things are going to affect how you make your choice, even though they're irrelevant.

Affect is, basically, a filter for perceptual information as well as a source of information itself. Keep that in mind.

Dr Peters's hypothesis suggested that high numeracy would be associated with better decision-making. And in fact, some prior work supported that. If you described a risk to people in terms of frequency (1 out of 100) or in terms of probability (1% out of 100), highly numerate people assess this risk equivalence more accurately than the general population and poorly numerate people assess this risk equivalence less accurately than the general population. 1% is kind of abstract, kind of rare, right? If 1% of 100 people exposed to nuclear waste develop cancer, that's no big deal. If 1 out of 100 people exposed to nuclear waste develop cancer, that's a terrible tragedy, because one person is a whole individual. You see, the percent sign is an abstraction away from humanity, and that really does affect people's feelings about the matter.

But here's where it gets even weirder than that.

Peters took a population of undergraduate students at UO and assessed their numeracy, and then split them into two groups - highly numerate and poorly numerate. Then she split these two groups in half and to one half gave a 9:27 chance of winning $9 (the other 27 chances had no effect), and to the other half gave both the same 9:27 chance to win $9 but also a 27:9 chance of losing five cents. So there were four groups: numerate and winning only, numerate and win/lose, innumerate and winning only, and innumerate and win/lose. Got it? You can draw it on a grid, a 2x2 array, if it helps.

Okay now. Here's the fun bit. Peters asked the people in the groups to give a 1-20 assessment of how good the bet was, and asked them to rate (1-3) their feelings about whatever winnings they might get. She assumed that the highly numerate population would assess the win/lose bet as worse, and rate the cash from the win only condition as better because it was won by outsmarting the house. Makes sense? Too bad it's wrong.

Yeah, that's what I said. The innumerate group rated both bets as more or less the same, but the highly numerate group rated the worse bet (win or lose) as better, and said they would feel better about the cash won from it. Now, I ask you, does that make sense? And the answer is: yes, it does, if you factor in affect. Too often we don't think about the role emotion plays in our decisions. But if you give people the chance to lose money as well as to win it, you make winnings seem more of a big deal. Here, affect overrides analysis.

So, you might say, college students are silly callow youth. Surely the experts would perform better? To assess this, let's do as Peters did, and ask a bunch of actuaries. You know, the grim-faced men and women who compile data and assess risks for insurance companies. Guess what: they do even worse than highly numerate college students. And when this is pointed out, they get mad.

And then we were back to the original hypothesis. If you have a big bowl of a thousand jellybeans, and make sure there are ninety red ones; and a small bowl of a hundred jellybeans, and make sure there are ten red ones; and you tell your high- and low-numerate groups to choose which bowl to pick a jellybean out of, and if they get a red one, they win some cash - low-numerate people frequently choose from the larger bowl (with 9% probability) while high-numerate people frequently choose from the smaller bowl (with 10% probability). This lasts even if you take the percent red jellybeans in the big bowl down to 5%.

Crazy, isn't it? This kind of thing makes me want to jump up and down and laugh at our hubris. We really don't understand ourselves so well as we thought, and we really aren't so rational as we thought either. We're starting to open up the mystery of the human mind, and it is awesome.

Incidentally, I work in a field called behavioral neuroscience for a reason - I love to try and figure out how things work. With a lot of stuff you can find out just by unscrewing the back or cutting the cover away, but you really can't do that with brains. A turbine engine will run if you take off the shell, and a computer will run if you take off its case, but brains react badly to having their cases pulled away. And you can take a computer, or a turbine, apart to see how it works and then put it back together and make it work, but you can't do that with a brain. So basically, I'm in the field you could call psychology for engineers.