I’ve had a pair of papers published recently and I thought I’d have a go at putting simply what the research reported in them shows.

The first is called ‘Pieron’s Law holds during Stroop conflict: insights into the architecture of decision making‘. It reports a variation on the famous Stroop task. The Stroop task involves naming the ink colour of various words, words which can themselves be the name of colours. So you find yourself looking at the word GREEN in red ink and your job is to say “red”. If the word matches the ink colour people respond faster and more accurately; if the word doesn’t match, they are slower and less accurate. What we did was vary the strength of the colour component of the stimilus – e.g. we used more and less intense red ‘ink’ (actually we presented the stimuli on a computer screen, so the ink was pixel values). There’s a well established relationship between stimulus strength and responding – the ‘Pieron’s Law’ of the title – showing how response speed decreases with increasing stimulus strength.

So our experiment simply took two well know psychological findings and combined them in a single experiment. The result is interesting because it can help us arbitrate between different theories of how decisions are made. One popular theory of decision making is that all the information relevant to the decision is optimally combined to produce the swiftest and most accuracte response (Bogacz, 2007). There’s lots of support for this theory, including evidence from looking at responses of humans making simple judgements, recordings from the brain cells of monkeys and deep connections to statistical theory. It’s without doubt that the brain can and does integrate information optimally in some circumstances. What is interesting to me is that this optimal information integration perspective is completely at odds with the most successful research programme in post-war psychology: the heuristics and biases approach. This body of evidence suggest that human decision making is very non-optimal, with all sorts of systemmatic errors creeping into the way people combine information to make a decision. The explanation for these errors is that we process information using heuristics, mental shortcuts which give a good answer most of the time and cut down on the amount of effort which have to expend in deciding (“do what you did last time” is probably the most common decision heuristic).

My experiment connects to these ideas because it asked people to make a simple judgement (the colour of the ink), like the experiments supporting an optimal information integration perspective on decision making, but the judgement requested was just marginally more complex because we manipulate both Stroop condition (whether the word and ink matched) and colour strength. If you are a straight-down-the-line optimal information decision theorists then you must believe that evidence about the decision based on the word is combined with evidence about the decision based on the colour to make a single ‘amount of evidence’ variable which drives the decision. In the paper I call this the ‘common metric’ hypothesis. The logic is a bit involved (see the paper), but a consequence of this hypothesis is that the size of the effect of the word condition should vary across the colour strength condition, and vice versa. In other words, you should see an interaction. Visually, the lines on the graph of results would be non-parallel.

Here’s what we found:

What you’re looking at is a graph of response times (the y-axis) for different colour strengths (the x-axis). The three lines are the three Stroop conditions: when the word matches the colour (‘congruent’), when it doesn’t match (‘conflict’) and when there is no word (‘control’). The result: there is no interaction between these two factors – the lines are parallel.

The implication is that you don’t need to move very far from simple perceptual decision making before human decision making starts to look non-optimal – or at least non optimal in the sense of combining information from different sources. This is important because of the widespread celebration of decision making as informationally optimal. Reconciling this research programme with the wider heuristics and biases approach is important work, and fits more generally with an honourable tradition in science of finding “boundary conditions” where one way the world works gives way to another way.

Coming up next: Infering from behavioural results to underlying cognitive architecture – its not as simple as we were told (Stafford & Gurney, 2011).


Bogacz, R. (2007). Optimal decision-making theories: linking neurobiology with behaviour. Trends in Cognitive Sciences, 11(3), 118–125.

Stafford, T., Ingram, L. and Gurney, K.N.(2011), Pieron’s Law holds during Stroop conflict: insights into the architecture of decision making, Cognitive Science 35, 1553–1566.

Tom Stafford and Kevin N. Gurney (2011), Additive factors do not imply discrete processing stages: a worked example using models of the Stroop task, Frontiers in Psychology, 2:287.