Polynomial

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A few months back I watched a three part BBC documentary, entitled “The Code.” In this documentary Professor Marcus du Sautoy – the Simonyi Professor for the Public Understanding of Science – discussed and demonstrated how our world is underpinned by a myriad of patterns and rhythms, all of which inter-react and inter-relate to one another in sometimes obvious, but mainly not so obvious, ways… However, when we logically work through these anomalies via modes of mathematical inquiry, after much study (so as not to make assumptions based on pure inference alone) we can quite discernibly trace out the workings behind most of their seemingly undefinable methods of unfolding. Thus, through this penetrating gaze of mathematical scrutiny, we can tell a lot about the processes of the world in which we live… As well as how we ourselves – as biological systems that are also based on mathematical unfolding – relate to the world around us.

This point, which I hope I have not blown too much out of proportion, is somewhat obviously and rather simply called the “Wisdom Of The Crowd.” And before I say any more on the subject, I will introduce this idea properly by presenting a clip from the documentary in question… One that demonstrates this phenomenon in action and the principles behind it.

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The Wisdom Of The Crowd

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So… “The Wisdom Of The Crowd” refers to a process of taking into account the overall collective opinion of a group of individuals, rather than relying on a single expert to answer a particular question. Reason being that a large group’s aggregated answers to particular questions involving quantity estimation, general world knowledge, and spatial reasoning have generally been found to be as good as, and often better than, the answer given by any isolated individuals within the group. An intuitive and often-cited explanation for this phenomenon is that there is idiosyncratic noise associated with each individuals judgement – noise that stems from the varied and multifarious individual experiences that each person has had specifically in their lifetime – and so, taking the average over a large number of responses, usually goes some way towards cancelling the effect of this noise completely.

Still, despite the positive implications that this normalising effect ‘might’ have for us all when directing us towards an all pervading truth (and I only say ‘might’), there is much to be careful of when considering an issue as complex as this… Just as Larissa Conradt notes in her article below, entitled “Collective Behaviour: When It Pays To Share Decisions.”

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Collective Behaviour: When It Pays To Share Decisions

Theory suggests that the accuracy of a decision often increases with the number of decision makers, a phenomenon exploited by betting agents, Internet search engines and stock markets. Fish also use this ‘wisdom of the crowd’ effect.

Having trouble making a decision? The reason is that you’re probably not sure which is the best option. You seldom have perfect information, so might make a bad choice. Sharing decisions with others can help, because several decision makers can pool their information, and also eliminate individual errors. Consequently, the risk of making a mistake and settling on a bad option often decreases with the number of decision makers. For example, in court cases, juries consisting of several people are supposed to make correct decisions more often than can a single judge. In humans, there are numerous examples of this phenomenon. In social animals, the same principle should apply, but empirical demonstrations are rare.

Writing in Proceedings of the National Academy of Sciences, Ward et al. now show that larger shoals of fish not only make more-accurate decisions than do smaller shoals or single fish, but also make these decisions faster. In an elegantly designed experiment, combined with theoretical modelling, the authors gave mosquitofish, Gambusia holbrooki, a choice between a predator-free route and one that led past a predator model. A fish was more likely to make a correct choice (to avoid the predator model) the larger the shoal in which it swam. The size of this increase in accuracy was in close agreement with theoretical predictions. The effect did not arise because large shoals were more likely to contain one particularly clever ‘expert’ fish, which guided the others. In fact, individual fish did not differ much in their ability to make correct decisions and, moreover, were not even good at it. Thus, the authors have demonstrated a genuine ‘wisdom of the crowd’ (or, in biological terms, ‘many eyes’) effect (Fig. 1).

Figure 1: Many eyes — a shoal of blue-striped snapper.

The increase in decision speed with shoal size is especially noteworthy, for two reasons. First, we typically expect a trade-off between decision accuracy and speed, so that decision speed decreases with increasing accuracy and vice versa. This is because more-accurate decisions usually require more information, and information gathering takes time. Second, we expect decision speed to decrease with the number of decision makers, because sharing decisions requires communication between decision makers and it seems plausible that this will also take time. Nevertheless, Ward and colleagues found that both decision speed and decision accuracy increased with the number of decision makers (that is, the number of fish in the shoal).

The reason that larger shoals managed to make not only more accurate but also faster decisions probably lies in the way information is communicated. Fish in shoals often move in a self-organized manner, whereby individuals react rapidly to the movements of close neighbours. Indeed, Ward et al. present convincing evidence that such a reaction to spatially close companions has a crucial role in the mosquitofish choice of route — pairs of fish within less than 6 centimetres of each other reacted very fast to each other’s movement changes; and a fish’s choice of route depended significantly on the average choice of close companions.

This simultaneous, self-organized system of ‘communication’ has two important features. One is that the speed with which information is exchanged is high and hardly decreases with the number of fish in the shoal. The other is that communication is decentralized: that is, information transfer can start from any shoal member. This means that overall decision speed depends crucially on the fastest decision maker(s) within the shoal. For stochastic reasons, a large shoal is more likely than a small one to contain a fish that, by chance, detects a predator relatively quickly, even if the fish do not differ in ‘expertise’.

In short, the higher likelihood of a shoal containing a fast decision maker, coupled with swift, decentralized information transfer, could explain the increase in decision speed with shoal size. However, such fast decision making usually also involves a cost, namely that of an increased risk of false positives. That is, if the fastest decision maker made a mistake (and ‘detected’ a predator that did not exist), this mistake could also be amplified, and the group might stage a costly ‘escape’ when none was necessary. The experiments of Ward and colleagues did not allow for such a situation — there was always one predator model present, and fish could either avoid it (true positive) or not (false negative). It remains to be seen whether accuracy and speed of decision making still increase together if fish are faced with a situation in which false positives are possible.

Fast and accurate decision making is highly desirable in many walks of life, for humans as well as animals. Ward and colleagues’ study shows that it can be achieved by sharing decisions widely and using a self-organized system of communication. This is, of course, exactly the strategy that has long been exploited by Internet search engines, and in this sense the mosquitofish of Ward and co-workers’ experiments are not that dissimilar from Google.

However, there are three caveats about the benefits of decision sharing. First, if the abilities of potential decision makers vary widely, it might still be better to listen to one ‘expert’. Second, there is the danger of information cascades, whereby decision makers no longer contribute independent information but instead amplify shared misconceptions. Finally, in many decisions, the goals of individual decision makers differ: that is, different members of the decision-making group favour different outcomes. In such a context, the sharing of decisions can have disadvantages as well as advantages. Although sharing might still increase the available information, it can also hand influence on the outcome to decision makers whose goals differ from your own. To date, surprisingly little is known about good decision-making strategies in these kinds of conflict situations.

by Larissa Conradt – the Department of Biology, School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QG, UK.

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I feel that Larissa Conradt’s article touches on a interesting tonic to my over zealous feelings about the general “Wisdom of the Crowd”… A wisdom that apparently belongs to the humans that have recently gathered here on Earth… As she points out with regards to “false positives” relating to the decision making of mosquitofish shoals when avoiding predators, there seems – at least for me – to be a very striking and obvious similarity that parallels our own human behaviour relating to climate change and how we react to it so as to avoid any certain catastrophic consequences.

Thus I would recommend that the findings of Ward’s research into the decision making behaviour of mosquitofish should be greatly encouraged and the findings be mirrored against mankind’s present decision making strategies to overcome any assuming notions based on inference alone and, so, steer us better into future times with the a more guided view to the “Wisdom of the Crowd.”

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To find out more about the BBC documentary called “The Code,” please click here.

Or to read more about “The Wisdom Of The Crowd,” please click here.

And to find out where I sourced the Nature article from, please click here.