Scott Page, who’s in the political science department at University of Michigan, has written a book that’s valuable on two levels. First, it provides a more rigorous take on some of the issues that James Surowiecki dealt with in his popularizing book, The Wisdom of Crowds. To say that Surowiecki’s book is written for a popular audience of course isn’t to say that it’s bad (to the contrary, see dsquared’s review), but it certainly doesn’t go to the same kinds of lengths as does Page’s to establish careful definitions, dot terminological i’s, and cross conceptual t’s. Page also goes rather further than Surowiecki in specifying his arguments about group decision making (providing a very good, if individually flavoured, account of the relevant cognitive science literature in the process), which means that he’s able to offer more specific claims than Surowiecki about the circumstances under which groups will or will not be able to beat experts. Second, Page uses this to offer a broad defence of the cognitive virtues of diversity. When the members of a group have diverse sets of mental tools, group decision making (under certain assumptions) is less likely to get stuck at suboptimal solutions, and more likely to arrive at superior ways of doing things. As Jim Johnson pointed out a few months ago, this means that Page is able to offer a pragmatic defence of diversity practices in hiring, education etc – having a diverse set of points of view in a group means better decision making.
First, Page’s underlying theory, bits of which have been developed at greater length and in more forbidding detail in his academic work. He starts from basic arguments about heuristics – mental tools or rules of thumb for dealing with complex situations – and perspectives, basic mappings of reality. Given a perspective, a heuristic tells individuals how to search for a solution or to identify an appropriate action; some are simple rules of thumb; others such as simulated annealing are more sophisticated. Individuals can also have different interpetations, which allow them to lump things together into categories by highlighting one dimension and ignoring others in ways that exploit underlying structures of some kind. Finally, predictive models are interpretations which provide a prediction for each set or category created by the interpretation.
This framework allows Page to argue that individuals will build from their perspectives and interpretations towards quite different predictive models. When individuals have different perspectives and/or interpretations, and when they communicate with each other, they are obviously likely to arrive at better solutions than they might in isolation from each other. Different interpretations allow individuals to highlight different aspects of the situation they find themselves in, and thus make them less likely to get stuck at inefficient local optima. This carries a number of interesting implications.
First, there are quite plausible conditions under which groups composed of diverse individuals will be able to outperform groups of ‘experts;’ individuals who are better capable of solving problems on their own. Page uses some simple agent-based modelling to support this claim, and outlines the underlying logic of a “mathematical proof that provides sufficient conditions for the … result.” The necessary conditions are that there have to be enough agents, groups of moderate size, agents who are sufficiently smart, and problems that are sufficiently difficult. The reason why this result holds is fairly straightforward; experts tend to be quite like each other, so that they tend to converge on the same solution, while heterogenous agents have a better chance of coming across other, superior solutions. This suggests both that there is an important role for diverse groups of non-experts, and that the dumbed down versions of the Wisdom of Crowds thesis don’t hold (i.e. that experts will still beat people who don’t have a clue about the underlying problem). In Page’s words:
when solving problems, diversity may matter as much, or even more than, individual ability. From this we can infer that organizations, firms, and universities that solve problems should seek out people with diverse experiences, training, and identities that translate into diverse perspectives and heuristics. Specifically, hiring students who had high grade point averages from the top-ranked school may be a less effective strategy than hiring good students from a diverse set of schools with a diverse set of backgrounds, majors, and electives.
This all suggests that diversity of outlooks holds quite considerable benefits for decision making. Indeed Page argues that the accuracy of prediction models and the success of diverse teams in problem solving provides substantial evidence of these benefits (but see below). However, in the final section of the book, Page complicates things by looking at how diversity of outlooks and diversity of preferences interact. He provides a quick tour of the basic social choice literature, moving from single peaked preferences to the various chaos results in order to illustrate how preference divergence may make it hard (or even impossible) for people to coordinate. More specifically, he argues that where people’s fundamental preferences over basic social goods – conflict, then diversity will obviously lead to political conflict of one sort or another. It’s considerably less problematic where people hold diverse instrumental preferences (i.e. they agree on basic goals, even while they disagree about which means are best to reach these goals). Page argues that overall, diversity is beneficial even if it goes along with the likelihood of increased conflict – but presumably, this claim depends on the degree to which one values better solutions over a higher risk of conflict. Indeed his empirical analysis suggests to me that more risk-averse types may prefer less diversity; this may be associated with worse average results, but also with a lower degree of variance in expected results too.
Which leads on to the most politically interesting claim in Page’s book – that his arguments provide quite strong support for hiring or admitting people from diverse identities and backgrounds. He notes that the empirical evidence provides only mixed support for the claim that identity diverse groups are better at problem solving, and argues that this may not only be because identity diversity is not always linked to cognitive diversity, but also because there are tradeoffs between preference diversity and cognitive diversity. There seems to be some plausible evidence of this from studies that show that even while diversity produces higher revenues, say, in business, it also is associated with lower cooperation and employee satisfaction, both of which likely lower revenues and to some extent weaken the positive (putatively cognitive) consequences. Nor is it likely that cognitive diversity is likely to produce positive outcomes when the tasks assigned to the group are simple and repetitive, or when people’s conceptual toolboxes are limited, say, by poor education.
However, the book does nonetheless offer a set of arguments supporting diversity as a means of selecting students, employees, or others who might contribute to group problem solving. If one goes for a narrow pool of the ‘best’ people according to some categorization, one is likely to draw upon a pool of individuals that are quite like each other in some very important ways, and that are likely to have broadly similar conceptual toolkits. If, instead, one draws upon people who are only good, but from a wide variety of backgrounds, one is likely to end up with people who have a much broader range over-all of problem solving tools, and who (communications problems discounted) can probably do a better job of figuring out interesting things. This argument for diversity notably doesn’t suggest that one hires or admits a token group of visible minorities in order, in Walter Benn Michael’s terms, to assuage the class guilt of the rich elites who form the very substantial majority of, say, the student population at elite universities. It means that one should select from a genuinely diverse set of class backgrounds, cultural viewpoints etc, in order to maximize the likelihood of collective problem solving.
As I said at the beginning, there’s a lot to like in this book. There also are a couple of holes. Some of the arguments about the empirical benefits of, say, prediction markets, are more heated than this book suggests; I’ll leave it to those who are better versed in these arguments (e.g. dsquared) to get into this in comments if he feels like it. More to the point however, the big gap in Page’s argument is that there’s little to no discussion of how individuals communicate with each other, or don’t, and how this affects problem solving. His exposition for the most part assumes that individuals communicate with each other in such a way that the additive benefits of different perspectives cumulate unproblematically; where one person’s cognitive tools prove insufficient, and strand them at some not-very-satisfactory local optimum, another person’s cognitive tools kick in without the need for explicit coordination and perhaps get both of them to a better overall outcome. Page does touch on problems of communication a bit when he talks about preference divergence, but only a bit; the basic social choice results that he draws on don’t explicitly model communication processes either, so that whatever discussion there is is mostly in the way of side-arguments that don’t fully connect with his underlying theoretical claims. This is a problem because there is good reason to believe that communication problems can have serious consequences for the nice results that Page is talking about; they can lead (as Cass Sunstein notes) to various failures of deliberation when people are talking to one other, or to various forms of self-reinforcing death-spirals in markets where the participants are watching each other in order to figure out what is going on. Fair enough that Page doesn’t want to go into detail about these issues – he has enough on his plate as it is trying to explain agent based modelling to the masses – but a few pages towards the end which talked to these problems and what they might mean for his findings would have been nice.
My other niggle is writing style – at times, Page goes a bit too far for my tastes in reaching out for homey metaphors to sugercoat the occasional indigestible theoretical horsepills that he has to shove down the reader’s craw in order to get his point across. Trying to make the Gibbard-Satterthwaite Theorem (that any nondictatorial rule for aggregating diverse preference orderings over more than two outcomes is manipulable) more palatable by describing its consequences for recipes for slow-cooked tarragon chicken is less likely to elucidate the subject matter than to induce fits of double-vision-induced migraine in the reader.1 I suspect that this style is in part a response to the success of Gladwell and his scions in identifying or creating a new market segment for the quasi-mathematical bestseller. But I don’t think that this book belongs inside this market segment (although it isn’t entirely outside it either). Its actual virtues are largely academic ones – it’s quite careful in stating the limits of its claims, building up a coherent argument, employing careful terminology etc, none of which sit well with folksy anecdotes and everyday examples (this is not to say that there isn’t a middle ground between Gladwell and the academy, but it’s bloody hard to write for it). What the book does do is to illustrate the benefits of a way of thinking about problem solving, to provide people with the conceptual tools to understand what lies behind some of the more popular treatments of the topics (and to evaluate their more breathless claims) and, perhaps, to reshape the public debate about the benefits and disadvantages of diversity. All of which are good things, which may not land the book on the bestseller list, but which should, I imagine, appeal to a fairly broad swathe of people who have some idea of the basic landscape of these debates, but want to find out more.
1 This said, it has to be acknowledged that Page makes a quite significant contribution to the field of comparative ketchup research. How he knows that Irish people, unlike Americans, don’t keep tomato ketchup in the fridge, I don’t know (unforgivably, he provides no footnotes to document his source for this claim). But it’s undeniably true (and the source of minor domestic friction over appropriate ketchup-heuristics in this cross-cultural household.