information theory and psychology

I have read a good deal more about information theory and psychology than I can or care to remember. Much of it was a mere association of new terms with old and vague ideas. Presumably the hope was that a stirring in of new terms would clarify the old ideas by a sort of sympathetic magic.

From: John R. Piece’s 1961 An introduction to information theory: symbols, signals and noise. Plus ça change.

Pierce’s book is really quite wonderful and contains lots of chatty asides and examples, such as:

Gottlob Burmann, a German poet who lived from 1737 to 1805, wrote 130 poems, including a total of 20,000 words, without once using the letter R. Further, during the last seventeen years of his life, Burmann even omitted the letter from his daily conversation.

The two word games that trick almost everyone

270px-Cowicon.svgPlaying two classic schoolyard games can help us understand everything from sexism to the power of advertising.

There’s a word game we used to play at my school, or a sort of trick, and it works like this. You tell someone they have to answer some questions as quickly as possible, and then you rush at them the following:

“What’s one plus four?!”
“What’s five plus two?!”
“What’s seven take away three?!”
“Name a vegetable?!”

Nine times out of 10 people answer the last question with “Carrot”.

Now I don’t think the magic is in the maths questions. Probably they just warm your respondent up to answering questions rapidly. What is happening is that, for most people, most of the time, in all sorts of circumstances, carrot is simply the first vegetable that comes to mind.

This seemingly banal fact reveals something about how our minds organise information. There are dozens of vegetables, and depending on your love of fresh food you might recognise a good proportion. If you had to list them you’d probably forget a few you know, easily reaching a dozen and then slowing down. And when you’re pressured to name just one as quickly as possible, you forget even more and just reach for the most obvious vegetable you can think of – and often that’s a carrot.

In cognitive science, we say the carrot is “prototypical” – for our idea of a vegetable, it occupies the centre of the web of associations which defines the concept. You can test prototypicality directly by timing how long it takes someone to answer whether the object in question belongs to a particular category. We take longer to answer “yes” if asked “is a penguin a bird?” than if asked “is a robin a bird?”, for instance. Even when we know penguins are birds, the idea of penguins takes longer to connect to the category “bird” than more typical species.

So, something about our experience of school dinners, being told they’ll help us see in the dark, the 37 million tons of carrots the world consumes each year, and cartoon characters from Bugs Bunny to Olaf the Snowman, has helped carrots work their way into our minds as the prime example of a vegetable.

The benefit to this system of mental organisation is that the ideas which are most likely to be associated are also the ones which spring to mind when you need them. If I ask you to imagine a costumed superhero, you know they have a cape, can probably fly and there’s definitely a star-shaped bubble when they punch someone. Prototypes organise our experience of the world, telling us what to expect, whether it is a superhero or a job interview. Life would be impossible without them.

The drawback is that the things which connect together because of familiarity aren’t always the ones which should connect together because of logic. Another game we used to play proves this point. You ask someone to play along again and this time you ask them to say “Milk” 20 times as fast as they can. Then you challenge them to snap-respond to the question “What do cows drink?”. The fun is in seeing how many people answer “milk”. A surprising number do, allowing you to crow “Cows drink water, stupid!”. We drink milk, and the concept is closely connected to the idea of cows, so it is natural to accidentally pull out the answer “milk” when we’re fishing for the first thing that comes to mind in response to the ideas “drink” and “cow”.

Having a mind which supplies ready answers based on association is better than a mind which never supplies ready answers, but it can also produce blunders that are much more damaging than claiming cows drink milk. Every time we assume the doctor is a man and the nurse is woman, we’re falling victim to the ready answers of our mental prototypes of those professions. Such prototypes, however mistaken, may also underlie our readiness to assume a man will be a better CEO, or a philosophy professor won’t be a woman. If you let them guide how the world should be, rather than what it might be, you get into trouble pretty quickly.

Advertisers know the power of prototypes too, of course, which is why so much advertising appears to be style over substance. Their job isn’t to deliver a persuasive message, as such. They don’t want you to actively believe anything about their product being provably fun, tasty or healthy. Instead, they just want fun, taste or health to spring to mind when you think of their product (and the reverse). Worming their way into our mental associations is worth billions of dollars to the advertising industry, and it is based on a principle no more complicated than a childhood game which tries to trick you into saying “carrots”.

This is my BBC Future column from last week. The original is here. And, yes, I know that baby cows actually do drink milk.

The memory trap

CC Licensed Photo by Flickr user greeblie. Click for source.I had a piece in the Guardian on Saturday, ‘The way you’re revising may let you down in exams – and here’s why. In it I talk about a pervasive feature of our memories: that we tend to overestimate how much of a memory is ‘ours’, and how little is actually shared with other people, or the environment (see also the illusion of explanatory depth). This memory trap can combine with our instinct to make things easy for ourselves and result in us thinking we are learning when really we’re just flattering our feeling of familiarity with a topic.

Here’s the start of the piece:

Even the most dedicated study plan can be undone by a failure to understand how human memory works. Only when you’re aware of the trap set for us by overconfidence, can you most effectively deploy the study skills you already know about.
… even the best [study] advice can be useless if you don’t realise why it works. Understanding one fundamental principle of human memory can help you avoid wasting time studying the wrong way.

I go on to give four evidence-based pieces of revision advice, all of which – I hope – use psychology to show that some of our intuitions about how to study can’t be trusted.

Link: The way you’re revising may let you down in exams – and here’s why

Previously at the Guardian by me:

The science of learning: five classic studies

Five secrets to revising that can improve your grades

The Devil’s Wager: when a wrong choice isn’t an error

Devil faceThe Devil looks you in the eyes and offers you a bet. Pick a number and if you successfully guess the total he’ll roll on two dice you get to keep your soul. If any other number comes up, you go to burn in eternal hellfire.

You call “7” and the Devil rolls the dice.

A two and a four, so the total is 6 — that’s bad news.

But let’s not dwell on the incandescent pain of your infinite and inescapable future, let’s think about your choice immediately before the dice were rolled.

Did you make a mistake? Was choosing “7” an error?

In one sense, obviously yes. You should have chosen 6.

But in another important sense you made the right choice. There are more combinations of dice outcomes that add to 7 than to any other number. The chances of winning if you bet 7 are higher than for any other single number.

The distinction is between a particular choice which happens to be wrong, and a choice strategy which is actually as good as you can do in the circumstances. If we replace the Devil’s Wager with the situations the world presents you, and your choice of number with your actions in response, then we have a handle on what psychologists mean when they talk about “cognitive error” or “bias”.

In psychology, the interesting errors are not decisions that just happen to turn out wrong. The interesting errors are decisions which people systematically get wrong, and get wrong in a particular way. As well as being predictable, these errors are interesting because they must be happening for a reason.

If you met a group of people who always bet “6” when gambling with the Devil, you’d be an incurious person if you assumed they were simply idiots. That judgement doesn’t lead anywhere. Instead, you’d want to find out what they believe that makes them think that’s the right choice strategy. Similarly, when psychologists find that people will pay more to keep something than they’d pay to obtain it or are influenced by irrelevant information in the judgements of risk, there’s no profit to labelling this “irrationality” and leaving it at that. The interesting question is why these choices seem common to so many people. What is it about our minds that disposes us to make these same errors, to have in common the same choice strategies?

You can get traction on the shape of possible answers from the Devil’s Wager example. In this scenario, why would you bet “6” rather than “7”? Here are three possible general reasons, and their explanations in the terms of the Devil’s Wager, and also a real example.


1. Strategy is optimised for a different environment

If you expected the Devil to role a single loaded die, rather than a fair pair of dice, then calling “6” would be the best strategy, rather than a sub-optimal one.
Analogously, you can understand a psychological bias by understanding which environment is it intended to match. If I love sugary foods so much it makes me fat, part of the explanation may be that my sugar cravings evolved at a point in human history when starvation was a bigger risk than obesity.


2. Strategy is designed for a bundle of choices

If you know you’ll only get to pick one number to cover multiple bets, your best strategy is to pick a number which works best over all bets. So if the Devil is going to give you best of ten, and most of the time he’ll roll a single loaded die, and only some times roll two fair dice, then “6” will give you the best total score, even though it is less likely to win for the two-fair-dice wager.

In general, what looks like a poor choice may be the result of strategy which treats a class of decisions as the same, and produces a good answer for that whole set. It is premature to call our decision making irrational if we look at a single choice, which is the focus of the psychologist’s experiment, and not the related set of choice of which it is part.

An example from the literature may be the Mere Exposure Effect, where we favour something we’ve seen before merely because we’ve seen it before. In experiments, this preference looks truly arbitrary, because the experiment decided which stimuli to expose us to and which to withhold, but in everyday life our familiarity with things tracks important variables such as how common, safe or sought out things are. The Mere Exposure Effect may result from a feature of our minds that assumes, all other things being equal, that familiar things are preferable, and that’s probably a good general strategy.


3. Strategy uses a different cost/benefit analysis

Obviously, we’re assuming everyone wants to save their soul and avoid damnation. If you felt like you didn’t deserve heaven, harps and angel wings, or that hellfire sounds comfortably warm, then you might avoid making the bet-winning optimal choice.

By extension, we should only call a choice irrational or suboptimal if we know what people are trying to optimise. For example, it looks like people systematically under-explore new ways of doing things when learning skills. Is this reliance on habit, similar to confirmation bias when exploring competing hypotheses, irrational? Well, in the sense that it slows your learning down, it isn’t optimal, but if it exists because exploration carries a risk (you might get the action catastrophically wrong, you might hurt yourself), or that the important thing is to minimise the cost of acting (and habitual movements require less energy), then it may in fact be better than reckless exploration.


So if we see a perplexing behaviour, we might reach for one of these explanations to explain it: The behaviour is right for a different environment, a wider set of choices, or a different cost/benefit analysis. Only when we are confident that we understand the environment (either evolutionary, or of training) which drives the behaviour, and the general class of choices of which it is part, and that we know which cost-benefit function the people making the choices are using, should we confidently say a choice is an error. Even then it is pretty unprofitable to call such behaviour irrational – we’d want to know why people make the error. Are they unable to calculate the right response? Mis-perceiving the situation?

A seemingly irrational behaviour is a good place to start investigating the psychology of decision making, but labelling behaviour irrational is a terrible place to stop. The topic really starts to get interesting when we start to ask why particular behaviours exist, and try to understand their rationality.



Irrational? Decisions and decision making in context
My ebook: For argument’s sake: evidence that reason can change minds, which explores our over-enthusiasm for evidence that we’re irrational.

Irrational? Decisions and decision making in context

IMG_0034Nassim Nicholas Taleb, author of Fooled by Randomness:

Finally put my finger on what is wrong with the common belief in psychological findings that people “irrationally” overestimate tail probabilities, calling it a “bias”. Simply, these experimenters assume that people make a single decision in their lifetime! The entire field of psychology of decisions missed the point.

His argument seems to be that risks seem different if you view them from a lifetime perspective, where you might make choices about the same risk again and again, rather than consider as one-offs. What might be a mistake for a one-off risk could be a sensible strategy for the same risk repeated in a larger set.

He goes on to take a swipe at ‘Nudges’, the idea that you can base policies around various phenomena from the psychology of decision making. “Clearly”, he adds, “psychologists do not know how to use ‘probability'”.

This is maddeningly ignorant, but does have a grain of truth to it. The major part of the psychology of decision making is understanding why things that look like bias or error exist. If a phenomenon, such as overestimating low probability events, is pervasive, it must be for a reason. A choice that looks irrational when considered on its own might be the result of a sensible strategy when considered over a lifetime, or even over evolutionary time.

Some great research in decision making tries to go beyond simple bias phenomenon and ask what underlying choice is being optimised by our cognitive architecture. This approach gives us the Simple Heuristics Which Make Us Smart of Gerd Gigerenzer (which Taleb definitely knows about since he was a visiting fellow in Gigerenzer’s lab), as well as work which shows that people estimate risks differently if they experience the outcomes rather than being told about them, work which shows that our perceptual-motor system (which is often characterised as an optimal decision maker) has the same amount of bias as our more cognitive decisions; and work which shows that other animals, with less cognitive/representational capacity, make analogues of many classic decision making errors. This is where the interesting work in decision making is happening, and it all very much takes account of the wider context of individual decisions. So saying that the entire field missed the point seems…odd.

But the grain of truth the accusation is that the psychology of decision making has been popularised in a way that focusses on one-off decisions. The nudges of behavioural economics tend to be drammatic examples of small interventions which have large effects in one-off measures, such as giving people smaller plates makes them eat less. The problem with these interventions is that even if they work in the lab, they tend not to work long-term outside the lab. People are often doing what they do for a reason – and if you don’t affect the reasons you get the old behaviour reasserting itself as people simply adapt to any nudge you’ve introduced Although the British government is noted for introducing a ‘Nudge Unit‘ to apply behavioural science in government policies, less well known is a House of Lords Science and Technology Committee report ‘Behavioural Change’, which highlights the limitations of this approach (and is well worth reading to get an idea of the the importance of ideas beyond ‘nudging’ in behavioural change).

Taleb is right that we need to drop the idea that biases in decision making automatically attest to our irrationality. As often as not they reflect a deeper rationality in how our minds deal with risk, choice and reward. What’s sad is that he doesn’t recognise how much work on how to better understand bias already exists.

Why you forget what you came for when you enter the room

Forgetting why you entered a room is called the “Doorway Effect”, and it may reveal as much about the strengths of human memory, as it does the weaknesses, says psychologist Tom Stafford.

We’ve all done it. Run upstairs to get your keys, but forget that it is them you’re looking for once you get to the bedroom. Open the fridge door and reach for the middle shelf only to realise that we can’t remember why we opened the fridge in the first place. Or wait for a moment to interrupt a friend to find that the burning issue that made us want to interrupt has now vanished from our minds just as we come to speak: “What did I want to say again?” we ask a confused audience, who all think “how should we know?!”

Although these errors can be embarrassing, they are also common. It’s known as the “Doorway Effect”, and it reveals some important features of how our minds are organised. Understanding this might help us appreciate those temporary moments of forgetfulness as more than just an annoyance (although they will still be annoying).

These features of our minds are perhaps best illustrated by a story about a woman who meets three builders on their lunch break. “What are you doing today?” she asks the first. “I’m putting brick after sodding brick on top of another,” sighs the first. “What are you doing today?” she asks the second. “I’m building a wall,” is the simple reply. But the third builder swells with pride when asked, and replies: “I’m building a cathedral!”

Maybe you heard that story as encouragement to think of the big picture, but to the psychologist in you the important moral is that any action has to be thought of at multiple levels if you are going to carry it out successfully. The third builder might have the most inspiring view of their day-job, but nobody can build a cathedral without figuring out how to successfully put one brick on top of another like the first builder.

As we move through our days our attention shifts between these levels – from our goals and ambitions, to plans and strategies, and to the lowest levels, our concrete actions. When things are going well, often in familiar situations, we keep our attention on what we want and how we do it seems to take care of itself. If you’re a skilled driver then you manage the gears, indicators and wheel automatically, and your attention is probably caught up in the less routine business of navigating the traffic or talking to your passengers. When things are less routine we have to shift our attention to the details of what we’re doing, taking our minds off the bigger picture for a moment. Hence the pause in conversation as the driver gets to a tricky junction, or the engine starts to make a funny sound.

The way our attention moves up and down the hierarchy of action is what allows us to carry out complex behaviours, stitching together a coherent plan over multiple moments, in multiple places or requiring multiple actions.

The Doorway Effect occurs when our attention moves between levels, and it reflects the reliance of our memories – even memories for what we were about to do – on the environment we’re in.

Imagine that we’re going upstairs to get our keys and forget that it is the keys we came for as soon as we enter the bedroom. Psychologically, what has happened is that the plan (“Keys!”) has been forgotten even in the middle of implementing a necessary part of the strategy (“Go to bedroom!”). Probably the plan itself is part of a larger plan (“Get ready to leave the house!”), which is part of plans on a wider and wider scale (“Go to work!”, “Keep my job!”, “Be a productive and responsible citizen”, or whatever). Each scale requires attention at some point. Somewhere in navigating this complex hierarchy the need for keys popped into mind, and like a circus performer setting plates spinning on poles, your attention focussed on it long enough to construct a plan, but then moved on to the next plate (this time, either walking to the bedroom, or wondering who left their clothes on the stairs again, or what you’re going to do when you get to work or one of a million other things that it takes to build a life).

And sometimes spinning plates fall. Our memories, even for our goals, are embedded in webs of associations. That can be the physical environment in which we form them, which is why revisiting our childhood home can bring back a flood of previously forgotten memories, or it can be the mental environment – the set of things we were just thinking about when that thing popped into mind.

The Doorway Effect occurs because we change both the physical and mental environments, moving to a different room and thinking about different things. That hastily thought up goal, which was probably only one plate among the many we’re trying to spin, gets forgotten when the context changes.

It’s a window into how we manage to coordinate complex actions, matching plans with actions in a way that – most of the time – allows us to put the right bricks in the right place to build the cathedral of our lives.

This is my BBC Future column from Tuesday. The original is here

3 salvoes in the reproducibility crisis

cannonThe reproducibility crisis in Psychology rumbles on. For the uninitiated, this is the general brouhaha we’re having over how reliable published psychological research is. I wrote a piece on this in 2013, which now sounds a little complacent, and unnecessarily focussed on just one area of psychology, given the extent of the problems since uncovered in the way research is manufactured (or maybe not, see below). Anyway, in the last week or so there have been three interesting developments


Michael Inzlicht blogged his ruminations on the state of the field of social psychology, and they’re not rosy : “We erred, and we erred badly“, he writes. It is a profound testament to the depth of the current concerns about the reliability of psychology when such a senior scientist begins to doubt the reality of some of the phenomenon upon which he has built his career investigating.

As someone who has been doing research for nearly twenty years, I now can’t help but wonder if the topics I chose to study are in fact real and robust. Have I been chasing puffs of smoke for all these years?

Don’t panic!

But not everyone is worried. A team of Harvard A-listers, including Timothy Wilson and Daniel Gilbert, have released press release announcing a commentary on the “Reproducibility Project: Psychology”. This was an attempt to estimate the reliability of a large sample of phenomena from the psychology literature (Short introduction in Nature here). The paper from this project was picked as one of the most important of 2015 by the journal Science.

There project is a huge effort, which is open to multiple interpretations. The Harvard team’s press release is headlined “No evidence of a replicability crisis in psychological science” and claimed “reproducibility of psychological science is indistinguishable from 100%”, as well as calling from the project to put effort into repairing the damage done to the reputation of psychological research. I’d link to the press release, but it looks like between me learning of it yesterday and coming to write about it today this material has been pulled from the internet. The commentary announced was due to be released on March the 4th, so we wait with baited breath for the good news about why we don’t need to worry about the reliability of psychology research. Come on boys, we need some good news.

UPDATE 3rd March: The website is back! No Evidence for a Replicability Crisis in Psychological Science. Commentary here, and response

…But whatever you do, optimally weight evidence

Speaking of the Reproducibility Project, Alexander Etz produced a great Bayesian reanalysis of the data from that project (possible because it is all open access, via the Open Science Framework). This take on the project is a great example of how open science allows people to more easily build on your results, as well as being a vital complement to the original report – not least because it stops you naively accepting any simple statistical report of the what the reproducibility project ‘means’ (e.g. “30% of studies do not replicate” etc). Etz and Joachim Vandekerckhove have now upgraded the analysis to a paper, which is available (open access, natch) in PLoS One : “A Bayesian Perspective on the Reproducibility Project: Psychology“. And their interpretation of the reliability of psychology, as informed by the reproducibility project?

Overall, 75% of studies gave qualitatively similar results in terms of the amount of evidence provided. However, the evidence was often weak …The majority of the studies (64%) did not provide strong evidence for either the null or the alternative hypothesis in either the original or the replication…We conclude that the apparent failure of the Reproducibility Project to replicate many target effects can be adequately explained by overestimation of effect sizes (or overestimation of evidence against the null hypothesis) due to small sample sizes and publication bias in the psychological literature