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

How to formulate a good resolution

We could spend all year living healthier, more productive lives, so why do we only decide to make the change at the start of the year? BBC Future’s psychologist Tom Stafford explains.

Many of us will start 2016 with resolutions – to get fit, learn a new skill, eat differently. If we really want to do these things, why did we wait until an arbitrary date which marks nothing more important than a timekeeping convention? The answer tells us something important about the psychology of motivation, and about what popular theories of self-control miss out.

What we want isn’t straightforward. At bedtime you might want to get up early and go for a run, but when your alarm goes off you find you actually want a lie-in. When exam day comes around you might want to be the kind of person who spent the afternoons studying, but on each of those afternoons you instead wanted to hang out with your friends.

You could see these contradictions as failures of our self-control: impulses for temporary pleasures manage to somehow override our longer-term interests. One fashionable theory of self-control, proposed by Roy Baumeister at Florida State University, is the ‘ego-depletion’ account. This theory states that self-control is like a muscle. This means you can exhaust it in the short-term – meaning that every temptation you resist makes it more likely that you’ll yield to the next temptation, even if it is a temptation to do something entirely different.

Some lab experiments appear to support this limited resource model of willpower. People who had to resist the temptation to eat chocolates were subsequently less successful at solving difficult puzzles which required the willpower to muster up enough concentration to complete them, for instance. Studies of court records, meanwhile, found that the more decisions a parole board judge makes without a meal break, the less lenient they become. Perhaps at the end of a long morning, the self-control necessary for a more deliberated judgement has sapped away, causing them to rely on a harsher “keep them locked up” policy.

A corollary of the ‘like a muscle’ theory is that in the long term, you can strengthen your willpower with practice. So, for example, Baumeister found that people who were assigned two weeks of trying to keep their back straight whenever possible showed improved willpower when asked back into the lab.

Yet the ‘ego-depletion’ theory has critics. My issue with it is that it reduces our willpower to something akin to oil in a tank. Not only does this seem too simplistic, but it sidesteps the core problem of self-control: who or what is controlling who or what? Why is it even the case that we can want both to yield to a temptation, and want to resist it at the same time?

Also, and more importantly, that theory also doesn’t give an explanation why we wait for New Year’s Day to begin exerting our self-control. If your willpower is a muscle, you should start building it up as soon as possible, rather than wait for an arbitrary date.

A battle of wills

Another explanation may answer these questions, although it isn’t as fashionable as ego-depletion. George Ainslie’s book ‘Breakdown of Will‘ puts forward a theory of the self and self-control which uses game theory to explain why we have trouble with our impulses, and why our attempts to control them take the form they do.

Ainslie’s account begins with the idea that we have, within us, a myriad of competing impulses, which exist on different time-scales: the you that wants to stay in bed five more minutes, the you that wants to start the day with a run, the you that wants to be fit for the half-marathon in April. Importantly, the relative power of these impulses changes as they get nearer in time: the early start wins against the lie-in the day before, but it is a different matter at 5am. Ainslie has a detailed account of why this is, and it has some important implications for our self-control.

According to this theory, our preferences are unstable and inconsistent, the product of a war between our competing impulses, good and bad, short and long-term. A New Year’s resolution could therefore be seen as an alliance between these competing motivations, and like any alliance, it can easily fall apart. Addictions are a good example, because the long-term goal (“not to be an alcoholic”) requires the coordination of many small goals (“not to have a drink at 4pm;” “not at 5pm;” “not at 6pm,” and so on), none of which is essential. You can have a drink at 4pm and still be a moderate drinker. You can even have a drink also at 5pm, but somewhere along the line all these small choices add up to a failure to keep to the wider goal. Similarly, if you want to get fit in 2016, you don’t have to go for a jog on 1 January, or even on 2 January, but if you don’t start doing exercise on one particular day then you will never meet your larger goal.

From Ainslie’s perspective willpower is a bargaining game played by the forces within ourselves, and like any conflict of interest, if the boundary between acceptable and unacceptable isn’t clearly defined then small infractions can quickly escalate. For this reason, Ainslie says, resolutions cluster around ‘clean lines’, sharp distinctions around which no quibble is brooked. The line between moderate and problem drinking isn’t clear (and liable to be even less clear around your fourth glass), but the line between teetotal and drinker is crystal.

This is why advice on good habits is often of the form “Do X every day”, and why diets tend to absolutes: “No gluten;” “No dessert;” “Fasting on Tuesdays and Thursdays”. We know that if we leave the interpretation open to doubt, although our intentions are good, we’ll undermine our resolutions when we’re under the influence of our more immediate impulses.

And, so, Ainslie gives us an answer to why our resolutions start on 1 January. The date is completely arbitrary, but it provides a clean line between our old and new selves.

The practical upshot of the theory is that if you make a resolution, you should formulate it so that at every point in time it is absolutely clear whether you are sticking to it or not. The clear lines are arbitrary, but they help the truce between our competing interests hold.

Good luck for your 2016 resolutions!

Cognitive Sciences Stack Exchange

Cognitive Sciences Stack Exchange is a question and answer forum for Cognitive Science. The Stack Exchange model works well for computer programming and now is one of the 150+ sites in their family, which includes topics as diverse as academia, mythology and pets.

There’s a dedicated community of people answering questions and voting on answers, producing  a great resource patterned around the questions people have on Cognitive Science topics. Three examples:

So head over, if you have questions, or if you can lend an evidence-based, citation-supported, hand in working on answers:

Link: Cognitive Sciences Stack Exchange

The Peer Reviewers’ Openness Initiative

pro_lockThe Peer Reviewers’ Openness Initiative” is a grassroots attempt to promote open science by organising academics’ work as reviewers. All academics spend countless hours on peer review, a task which is unpaid, often pretty thankless, and yet employs their unique and hard-won skills as scholars. We do this, despite misgivings about the current state of scholarly publishing, because we know that good science depends on review and criticism.

Often this work is hampered because papers don’t disclose the data upon which the conclusions were drawn, or even share the materials used in the experiments. When journal articles only appeared in print and space was limited this was excusable. It no longer is.

The Peer Reviewers’ Openness Initiative is a pledge scholars can take, saying that they will not recommend for publication any article which does not make the data, materials and analysis code publicly available. You can read the exact details of the initiative here and you can sign it here.

The good of society, and for the good of science, everybody should be able to benefit from, and criticise, in all details, scientific work. Good science is open science.

Link: The Peer Reviewers’ Openness Initiative