Volume and decision-making linked by maths

The time it takes to make a choice – independent of the choice itself – permits a precise mathematical description of decision-making behaviour, Portuguese research has shown.

Scientists at the delightfully named Champalimaud Centre for the Unknown, in Lisbon, announce the discovery in the journal Nature Neuroscience.

Principal investigator Alfonso Renart and colleagues worked with rats, but if human trials replicate the finding, the conclusions represent a solid contribution towards the solution of a 200-year-old mystery regarding the relationship between the physical world and the workings of the mind.

The research centres on a little-discussed field known as psychophysics, which emerged in the nineteenth century from the work of German physician Ernst Heinrich Weber.

The discipline attempts to interrogate the relationship between external stimuli and behaviour in ways that are quantifiable and replicable.

Weber’s primary contribution centred on a series of experiments that required human volunteers to guess which of two different handheld weights was heavier. He was able to determine that the probability of a correct guess was directly proportional to the difference between the weights, and not the weights themselves.

For instance, if a volunteer picked correctly between a one-kilogram and 1.1-kilogram weight 75% of the time, the same probability would arise when the choice was between any two objects wherein the weight difference was 10%.

The surprising precision of the finding was subsequently confirmed by many other experimenters and the principle became enshrined as Weber’s Law, considered the bedrock of psychophysics.

Now, Renart and colleagues appear to have found a second mathematical relationship which broadens the foundation of the field.

The scientists initially used trained rats to test a variation of Weber’s Law. They set up the rodents to listen to two sounds, played at different volumes through tiny headphones, with the rats rewarded for angling their heads towards the louder one.

They found that the law held.

“Our experiments confirmed that the animals’ behaviour matched Weber’s Law,” says co-author José Pardo-Vazquez.

“Their ability to tell which of the two sounds was louder only depended on the ratio between the sounds’ intensities. If the rat had to compare the intensities of two sounds that were played softly, its accuracy was just as good as with a pair of sounds that were played loudly, as long as both pairs had the same intensity ratio.”

During the process, however, the researchers noticed something else. The time taken to make a decision varied from test to test. Further investigation revealed a previously unknown relationship.

The number of seconds needed by a rat to identify the relative intensity of two sounds, it turned out, was very directly related to volume. The louder the two sounds in gross terms, the shorter the time required.

Furthermore, the link between time, volume and decision was consistent and therefore predictable.

Renart and colleagues realised that they had discovered a second principle within psychophysics, which they term Time-Intensity Equivalence in Discrimination (TIED). Further tests found that the new law held firm in different types of decision-making tests, involving odours and other stimuli.

The finding looks set to shake up the psychophysics world, because it serves to both underpin the central contention that behaviours can be mathematically described, but also rules out some existing theories that attempt to explain ambiguities arising from earlier work.

“Although less frequently observed, in biology and in the study of behaviour – like in physics – precise experimental results permit precise explanations which resolve previous ambiguities and therefore constitute progress,” says Renart.