(I’ve been through a ridiculously busy period of work-related traveling and thus scarce blogging, and in the next four weeks I’m supposed to be on holiday, so again scarce blogging. But there is still one topic I really want to discuss before the summer break, so here it is.)
Here are a couple of brain-teasers for your amusement on this Monday morning/afternoon (depending on your time zone):
(1) A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents
(2) If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? _____ minutes
(3) In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days
(Answers below the fold.)
Have you answered “10 cents”, “100 minutes”, and “24 days”? If yes, congratulations: you belong to the vast majority of people who provide the wrong answers to these questions.
Fine, “but so what?,” you may be wondering. Now, as it turns out, these three questions form the basis for the so-called ‘Cognitive Reflection Test’ (CRT), first introduced by economist Shane Frederick in a widely cited 2005 paper published in the Journal of Economic Perspective. The CRT has been extensively discussed not only by economists, but also by psychologists and cognitive scientists interested in reasoning; indeed, at the International Conference on Thinking (ICT) which I attended recently in London, nearly 1 out of 2 talks referred to at least one of the three questions of the CRT.
What is puzzling about these three problems is that, if you think a bit about it, they really are not that difficult to solve. And yet, participants overwhelmingly give the same wrong responses, presumably because these are those that ‘first come to mind’. Psychologists have for the most part focused on how those who do provide the right answers overcome the first pull towards the wrong answers, but it seems equally interesting and important to understand why the wrong intuitive answers are intuitive in the first place.
Frederick himself and many of those who have discussed the phenomenon conceptualize it in terms of dual-system theories of cognition: System 1, which is fast, intuitive and associative, is responsible for the fist intuitive, wrong answer; for those individuals who do provide the correct answer, the story goes that they are somehow able to activate reflective, slow System 2 so as to provide the normatively correct answer.
Dual-system theories of cognition remain a very popular framework among psychologists, even though most of them now seem to reject the idea of two ‘systems’ and have switched to the weaker claim of two basic kinds of processes underlying human cognition, yielding dual-process theories of cognition (the latter does not postulate the existence of specific systems for these two kinds of processes). (See this great paper by Keith Frankish at Philosophy Compass explaining the whole thing.) Some of those who have stopped talking about systems are (by their own admission in a joint talk at the ICT) Jonathan Evans and Keith Stanovich, both towering figures in the field of psychology of reasoning. But for the most part, phenomena such as the results of the CRT are still thought to represent strong evidence for dual-process accounts of reasoning.
In the original and still widely endorsed formulations, a basic assumption underlying dual-system/-process accounts of reasoning was that biases and deviations from what is considered ‘normatively correct’ were the result of fast, associative and basically ‘dumb’ type-1 processes, which could then in some cases be overridden by slow, rule-based, ‘smart’ type-2 processes. In a slogan, type-1 processes make the mistakes which can then be corrected by type-2 processes – but only by the individuals who are able to suppress the pull of their first, intuitive but biased reactions. Indeed, in the original paper, Frederick draws correlations between individuals who perform well in the CRT and certain decision-making strategies on problems for which there is no obvious normatively correct answer. He then argues that, if these smart individuals who are getting the CRT right also have a strong tendency towards certain decision-making strategies, then it may well be argued that this may be a sign of the superiority of these decision-making strategies.
Generally speaking, I am no fan of dual-process accounts of reasoning, as I argued quite extensively in chapters 4 and 7 of my forthcoming book. More specifically, I am not a fan of how the distinctions between type-1 and type-2 processes are usually conceptualized by dual-process theorists, in particular the crude dichotomy type-1/biased reasoning vs. type-2/normatively correct reasoning. And indeed, some recent formulations of these theories have parted with this crude dichotomy, and someone like Jonathan Evans now recognizes that type-2 processes can also be biased and systematically deviate from the normatively correct responses. In her talk at ICT, Valerie Thomson had some experimental data showing that participants who are cued to reflect on their answers, and thus presumably are activating type-2 processes, are in no way more likely to give the normatively correct response.
Still, there is the important phenomenon that, with the CRT problems, some (typically, very few) people are able to suppress the pull of the first, intuitive answer, somehow knowing that, despite its intuitiveness, it is the wrong answer. What is going on here?
Here is my tentative explanation for the phenomenon. What prompts people to think of 10 cents, 100 minutes and 24 days are processes related to semantic activation, a highly significant concept extensively investigated by certain groups of psychologists, but to my mind, by and large neglected by psychologists of reasoning. (I briefly review the literature on semantic activation in chapter 6 of my forthcoming book.) Semantic activation is now thought to be a largely automatic process: if you hear or read the word ‘lion’, you basically can’t help yourself – you think of a lion. Now, take the ball/bat problem: as it is formulated, the problem mentions “1.10 dollars” and “1 dollar”: these are the concepts activated in the participant’s mind. No wonder that the most salient response, the first that comes to mind, is “10 cents”. Similarly, in the widget problem, after hearing/reading three times “5” and two times “100”, out pattern-seeking minds go for 100 widgets as the most salient response. Finally, in the lily-patch problem, what the participant registers is “48 days” and “half”, and these two concepts put together make her think of “24 days”. So my first suggestion is that to understand what is going on here, psychologists would do well to probe the processes of semantic activation underlying the so-called ‘type-1’ processes leading to the wrong answers.
My second suggestion, which I have developed more extensively in the book, is that so-called type-2 processes may well be for the most part products of formal education rather than ‘innate’ reasoning patterns. In Frederick’s original paper, the data presented show a high correlation between academic performance and correct responses in the CRT: he conducted the experiment at different universities in the USA, and the ranking of incidence of correct responses looks very much like a Leiter-ranking from the ‘good’ places to the ‘less good’ places (at the top, MIT; at the bottom, the University of Toledo). The usual explanation is that this is not so surprising, given that individuals ranking high on scales of intelligence go to prestigious universities; no wonder they then go on to become more successful individuals. (Eric may be writing a post on this point, focusing on some recent work in economics.) But obviously, individuals who go to prestigious universities are almost invariably those who have had access to good schooling, which in a country like the USA is by and large a matter of how much money their parents had.
More generally, my claim is that, as they stand, dual-process theories of cognition are overly internalistic; researchers have not sufficiently investigated the impact of external factors, formal education and schooling in particular, for the onset of so-called type-2 processes (I elaborate on this in more detail in the book). They rely on empirical data from an incredibly homogeneous population (typically, undergraduates in North-American and western European universities) to make all kinds of universalist claims about human cognition in general. This does not mean that there will not be individual differences in reasoning, but arguably, being able to suppress the first intuitive answer at the CRT problems is something that can be trained for. To a great extent, that is what formal education is about: teaching a student how to think things through. (Admittedly, in practice this ideal is very often not really pursued…) Dual-process theorists themselves are increasingly showing that type-2 processes are also typically prone to all kinds of ‘mistakes’, which clearly suggests that the dual-system explanation for the CRT phenomenon needs to be revisited. I am here proposing that a promising avenue is to bring in the concept of semantic activation and to investigate more systematically the effects of schooling on reasoning.
Oh, and the right answers are: 5 cents, 5 minutes, 47 days.