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Conceived and designed the experiments: SCN DJTS. Performed the experiments: SCN NZ. Analyzed the data: NZ SCN DJTS. Wrote the paper: DJTS SCN NZ TL.

The authors have declared that no competing interests exist.

Recent experiments on ants and slime moulds have assessed the degree to which they make rational decisions when presented with a number of alternative food sources or shelter. Ants and slime moulds are just two examples of a wide range of species and biological processes that use positive feedback mechanisms to reach decisions. Here we use a generic, experimentally validated model of positive feedback between group members to show that the probability of taking the best of

Several recent studies have begun to investigate the collective rationality of distributed biological systems

Several authors have pointed out that rationality cannot be studied in isolation from mechanisms

For

We assume that each option has an associated quality encoded by the variable

The choice function

The parameter

(a) case

We can however show that it is this multi-stability that can lead to irrationality when the number of choices available to a decision-maker is changed. The first point to note is how the bifurcation diagrams in

The quality of a decision does not simply depend on whether or not the best option is chosen by more individuals than any of the other options. The size of the level of commitment is also important. For example, in

(a) Mean level of commitment for the better option

Decision-making is often associated with a speed-accuracy trade-off, where a more accurate decision requires more time to reach

Our results hold for any number of options.

(a) case

Until now, we assumed that the best option was slightly higher in its quality than the other one (

(a) case

For any given number of options the decision-making outcome is different. In particular, the flow level at which the highest quality option is chosen most often depends on this particular number. In a situation where it is optimal to pick the highest quality option irrespective of initial conditions, then we can see that a value of

Experiments testing the effect of additional choices in decision-making do not start from the premise that one option is always optimal, independent of initial conditions. For house hunting ants or foraging slime mould there is a cost to be paid in switching between options if there is already an established commitment for one particular option. Indeed, when offered two options of similar although not identical quality over multiple trials, ants and slime mould do not aggregate at the same option in every trial

Species differences can, through our model, explain differences in the outcome of rationality experiments. Positive feedback is very strong in slime moulds, suggesting

Many of the standard models of decision-making assume that choice is a linear process

Models of decision-making in the visual cortex and other areas of the brain usually assume feedbacks between groups of neurons, with each group accumulating evidence for a particular option

In summary, we have shown here that concepts such as increasing accuracy with group size, speed-accuracy tradeoffs and "irrational" decisions are strongly correlated to the coexistence of multiple stable steady states. In the context of systems based on positive feedback, "rationality" and "irrationality" appear in some respects to be terms for describing the possibility that decisions can have different outcomes dependent on initial conditions. In particular, "irrationality" can be created in such systems simply by conducting an experiment in which the positive feedback is sufficiently high to generate multiple steady states. The question is not then whether a system is "irrational" or not, but rather why it uses strong positive feedback?

We study the above model in two ways, both as a system of differential equations as defined by eqs.(1) – (2) and as a Monte Carlo simulation. In the latter case, decision-making is modeled as a stochastic process of transitions towards states whose probabilities, given by

We focus on the situation in which one option is better than all the other ones considered to be of equal quality (

A typical way to summarize the behavior of the solutions of eqs.(3) – (6) is to draw bifurcation diagrams as in