I'm sure most people reading this will be familiar with the concept of a cognitive bias. There are innumerable papers in experimental psychology highlighting and exploring the various biases that human beings exhibit.

Well, with the term "bias" floating around so often, it's worth stepping back for a moment and asking: what exactly is a bias and how are different kinds of biases related to one another? It's here that I take my lead from Ryan McKay and Charles Efferson. They offer a useful definition of behavioural and cognitive biases that I want outline in this post.

Before getting into their definitions, it's worth calling up the commonsense understanding of a bias, which I understand to be the following:

Bias: For any X, if X can take on a range of values (1...n), then the actual value of X can be said to be biased if it departs systematically from the expected distribution of those values.

That's a little clunky, but I think it captures in an abstract form what we usually mean by "bias".

**1. Behavioural Biases**Moving on then to the concept of a behavioural bias. McKay and Efferson note that there are trivial and non-trivial understandings of a behavioural bias. We'll look first at the trivial sense:

Trivial Behavioural Bias: Assuming there are N possible behaviours that X could engage in, X displays a trivial behavioural bias when the probability distribution over these N behaviours is not uniform.

So, if you are guessing which side of coin will show after it has been flipped, your guesses can be said to be trivially biased if you choose heads more often than tails.

What about a non-trivial behavioural bias? This concept incorporates the notion of error (something that was absent from the trivial definition). To understand this definition, one must assume that the world can take on one of N possible states. One must then assume that X can exhibit one of N possible behaviours. For each possible state of the world, there is one (and only one) correspondingly optimal type of behaviour, which implies there are N(N-1) possible errors that X could make.

This gives us the following definition:

Non-trivial Behavioural Bias: Assuming there N(N-1) possible behavioural errors that X could make, X exhibits a non-trivial behavioural bias if, over a sufficiently large period of time, the empirical distribution over these errors is not uniform.

Going back to the coin example, your selection of heads might be non-trivially biased if the coin more often displays tails (and vice versa).

Note, interestingly, that a behaviour that is trivially biased need not be non-trivially biased; and a behaviour that is non-trivially biased need not be trivially biased. The authors (writing as they do in the context of behavioural biology) appeal to the following example.

Consider the interaction between single men and women at a bar. It is (evolutionarily, anyway) appropriate for a man to approach a woman if she is receptive to his advances; it is embarassing for him to approach her if she is not receptive to his advances. Now imagine a man who approaches 50% of the women in a bar. His behaviour is trivially unbiased according to the earlier definition. But now imagine that the man in question is George Clooney. His behaviour might be non-trivially biased because more than 50% might be receptive to his advances. Or, to put it another way, it is biased because it seems suboptimal.

__2. Cognitive Biases__Behavioural biases relate to the actual patterns of behaviour that agents engage in; cognitive biases relate to the beliefs that agents have about the world. Again, cognitive biases have trivial and non-trivial forms. A trivial cognitive bias can be defined as follows:

Trivial Cognitive Bias: Assuming there are N possible states of the world, X exhibits a trivial bias when their subjective probability distribution over these N states is non-uniform.

To continue with George Clooney's travails at the bar: there are two possible states for the women to be in {receptive to his advances; not receptive to his advances} and so two possible beliefs he can have about their receptivity. He would exhibit a trivial cognitive bias if he happened to attach a probability of greater than 0.5 to the possibility of the woman being receptive to his advances.

Again, as might be obvious with this example, there is no notion of error being incorporated into the trivial definition. George Clooney might be perfectly justified to have a non-uniform subjective probability distribution over the possibility that women are receptive to his advances. We need to bring error into the picture before we get a non-trivial form of cognitive bias.

So how do we do this? Well, if you look at the definition of the trivial form given above you will see that it appeals to subjective probability distributions. We can deal with such probabilities using Bayes theorem. What's more, we can deal with error by appealing explicitly to the beliefs we would expect a Bayesian rational agent to have. This gives us:

Non-trivial Cognitive Bias: An agent X exhibits a non-trivial cognitive bias whenever his or her beliefs depart from the beliefs of a Bayesian rational agent.

A Bayesian rational agent is one that updates his or her subjective probabilities in light of the available evidence (following Bayes' Rule). Bayesian rationality is the typical standard in epistemic game theory.

So those are the definitions. McKay and Efferson go on to show how these definitions might affect findings in behavioural biology and evolutionary psychology. In particular, they worry about the problems arising from the conflation of behaviour with cognition. You can read their paper for all the details on this.