Monday, May 21, 2018

What crosswords can teach us about collective intelligence

Dear reader: it is only fair to give you advance warning that this post will be a thinly-veiled excuse for me to crow about winning the prize for the weekly Times Jumbo Cryptic Crossword...

...that being said, I have long meant to write a post about crosswords, and in particular what they can teach us about collective intelligence. So here we go:
Alexander wept, for there were no more worlds to conquer.
Most weeks I complete several crosswords in The Times (London not New York). I'm not an especially good crossword solver, and solving a typical crossword might take me anywhere from 30min to several hours depending on the difficulty. Clearly solving a cryptic crossword is a task that requires 'intelligence' to perform, though exactly how transferable that concept of intelligence is can be debated. You don't need to be a maths whizz or a language expert - most of it is about learning a few basic rules of cryptic clueing and fostering a reasonably open mind. In the case of The Times it also helps to absorb a lot of weirdly specific knowledge and jargon of the sort that a certain demographic of person possesses - picture an English man in his 50's-70's who went to private or grammar school and then Oxbridge, and who grew up on a diet of Enid Blyton books and cricket. For reasons that are completely inexplicable you also need to know that 'rhino' can be a synonym for 'money'. 

All of that is to say that I am not positing crosswords as a benchmark for general intelligence, but that they can be used as an example of a task that requires some type of intelligence to perform. In terms of crosswords, we can measure 'intelligence' firstly by how many clues one gets right, and among those who get all clues right, by the speed of completion.

What does this have to do with collective intelligence? Well, on many occasions I complete crosswords together with my friend Graham Budd [1]. As the saying goes, two heads are better than one, and when solving together we typically finish the crossword more quickly than on my own, despite us wasting time bemoaning the particularly excruciating clues and otherwise dwelling on our perceptions of ongoing societal collapse. As such, this is an example of collective intelligence - together we are able to solve a problem with greater intelligence than either of us alone.
An excruciating clue: Sunday Times Crytic 4619
So far this is not especially noteworthy. Of course we are faster together!  We can divide the labour. When one of us gets a clue we both get it. Even if we don't agree to split the clues, neither of us has the solve all the clues ourselves. However, what is surprising is that we often finish the crossword in less than half the time it would take me alone. That means that our 'intelligence' has more than doubled. 

Such a case is called superadditive; If I write the performance of some individuals as f(Individuals) then:

f(Me + Graham) > f(Me) + f(Graham)

Or in plain language, Graham and I are 'more than the sum of our parts'

Conversely, many cases of collective intelligence are subadditive, i.e.

f(Me + Graham) < f(Me) + f(Graham)

For instance, one of the most famous examples of collective wisdom comes from Francis Galton. Galton observed punters guessing the weight of a bull at a fair, and noted that the average of their guesses was uncannily accurate. We know that this is a consequence of the Law of Large Numbers, and thus we also know that the error in the average guess scales as 1/N, where N is the number of guessers. This is a subadditive relation. If we double the number of guessers we do not halve the error, but only reduce it by a factor of about 1.4. 

These illustrate two fundamentally different regimes of collective intelligence. The superadditive relationship is one we typically see when groups have evolved specifically to work together, such as a colony of insects or the cells in your brain. An termite colony is truly more intelligent than the sum of its parts: no single termite could build the large intricate nest that the colony inhabits, even if it were given a huge amount of time to try. Likewise, no single neuron in your brain could learn...almost anything. The interactions between individuals produce something far beyond what they can do alone. In these situations the group can grow very large, as the benefits of group living increase with each new member. 
Grand designs
On the flipside, subadditive collective intelligence is what we often see in groups of unrelated individuals, like the punters guessing the weight of Galton's bull. Other examples with similar properties are seen in the way that navigating birds pool their knowledge about how to fly home, or how groups of fish become better at avoiding predators. In each case the group is better than one individual, but there are diminishing benefits of adding more and more group members. In such situations the benefits of being in a group are naturally limited: for example, you might get better at finding or catching food, but then you have to share it with more other individuals. 

Humans are not like insect colonies - we do not live in groups of genetically identical individuals who specialise and collaborate for the common good. But the most interesting examples of human collective intelligence occur when, despite this, we still find superadditive scenarios, where we can become more than the sum of our parts. Some problems naturally lend themselves to this type of collective solution. A good example is mathematics, where someone may work on a problem for years until they meet just the right person with the right knowledge to solve a problem together. On a more humdrum level, consider Graham and I completing the crossword. Despite sharing some things in common, we also have a lot of different knowledge. This means that Graham will easily solve some of the clues I find most difficult and vice versa. And due to the nature of the puzzle, when Graham solves a clue he may make the one I am looking at easier, by giving me some of the letters. We don't just divide the clues at random, we naturally each tend to look at the ones we are most likely to solve. Researchers in the USA have in fact shown that group intelligence is more related to the diversity of group members and the extent to which all individuals are able to participate than it is to the intelligence of the individuals themselves. 

In the example of the crossword, this diversity of skills is a happy accident. But in other cases there are incentives for people to be specialised. Adam Smith noted that division of labour made industrial production much more efficient. Similarly, markets such as the stock exchange can reward a diversity of knowledge - the best way to make a profit is to know something about a company that other people do not. Some of my recent research has looked at how these incentives can be manipulated, and we find exactly this: rewarding people for accurately predicting something that other people were unable to predict creates the best environment for fostering collective intelligence. 

What is the future for collective intelligence. Globalisation, increasing urbanisation and the internet have created ever greater rewards for specialisation. This has fostered economic growth and associated improvements in health and education, especially in what were once under-developed countries now enjoying the fruits of industrialisation. There has thus naturally been a drive to follow this trend further. But we should be wary of continuing this drive to specialisation indefinitely for the sake of group performance. One of the most depressing anecdotes I have ever heard [2] relates to specialisation: an accountant, finding his job rather unfulfilling, began spending large amounts of time playing the online multiplayer game World of Warcraft. In this game [3], players typically join together in 'guilds' to complete 'quests' together. Completing quests can gain players experience points and prizes which can be used to improve their characters in the game. However, when a guild completes quests together, the resources they expend or win, and the new materials they buy or sell must be managed and divided equitably. Slowly over time this accountants guild found they needed to devote more and more time to managing resources - a task that called for some specialisation. Eventually our hero finds himself coming home from 8 hours of real world accountancy only to spend his evening doing the guild's accounts, while other players do the fighting on his behalf! As this anecdote illustrates, if we follow our specialities too closely we may eventually become alienated and lose our motivation to participate in the group at all, which will then reduce the group performance.
Feel the wrath of my double-entry bookkeeping [4]
In contrast, as I noted at the start, I am not a particularly good crossword solver. It can easily take me 4-5 hours in total to solve one of the 'Jumbo' crosswords on Saturdays. Given that one is unlikely to win the prize even if the crossword is completed correctly, and that the prize is a set of books that one could get for about £50 on Amazon, this is not an efficient way for me to acquire an atlas and a dictionary. I complete the crosswords because I find the puzzle intrinsically interesting and diverting. What's more, I value my ability to do a range of tasks, some of which I might even be actively bad at (as erstwhile members of Uppsala Wanderers FC will attest). Robert Heinlein said 'specialisation is for insects', and I'm inclined to agree; while a degree of specialisation is useful, too much goes against what makes us human, and deprives us of motivation and intrinsic reward in activities. To perform well, and to lead fulfilling lives, we need not just diversity between individuals, but also diversity within ourselves and our own minds - to experience the joy of mastering multiple tasks, and to have agency over our own lives rather than to feel like ever smaller cogs in an every larger machine. This also makes us more flexible and robust. Mastering one task makes you vulnerable to that task becoming redundant. Being able to work in many different groups in a multitude of ways makes you more able to contribute as society's needs change. 

So in conclusion, as someone who studies collective intelligence, I am most interested in finding how this can be fostered without crushing individual autonomy. I don't want us to end up looking like an insect colony. I'd rather we ended up like Graham and me, coming together to solve tasks that bring us satisfaction in a job collectively well done. I for one will be enjoying my atlas far more than any I could have bought on Amazon!
To the victor, the spoils

[1] Though not in the case of my immortal triumph in Cryptic Jumbo 1313!
[2] I vaguely recall this coming from Daniel Strömbom, of robot sheepdog fame.
[3] My knowledge of WoW is all at least 3rd hand so please excuse any inaccuracies in this description.
[4] As an academic statistician, I'm aware that I really shouldn't be nerd-shaming anyone.

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