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Collective Irrationality and Positive Feedback
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: PLoS ONE, ISSN 1932-6203, Vol. 6, no 4, e18901- p.Article in journal (Refereed) Published
Abstract [en]

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 n options depends crucially on the strength of feedback. We show how the probability of choosing the best option can be maximized by applying an optimal feedback strength. Importantly, this optimal value depends on the number of options, so that when we change the number of options the preference of the group changes, producing apparent "irrationalities''. We thus reinterpret the idea that collectives show "rational" or "irrational" preferences as being a necessary consequence of the use of positive feedback. We argue that positive feedback is a heuristic which often produces fast and accurate group decision-making, but is always susceptible to apparent irrationality when studied under particular experimental conditions.

Place, publisher, year, edition, pages
2011. Vol. 6, no 4, e18901- p.
National Category
Biological Sciences Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-153556DOI: 10.1371/journal.pone.0018901ISI: 000290018400016PubMedID: 21541321OAI: oai:DiVA.org:uu-153556DiVA: diva2:417234
Available from: 2011-05-16 Created: 2011-05-16 Last updated: 2017-02-27Bibliographically approved
In thesis
1. Mathematical modelling approach to collective decision-making
Open this publication in new window or tab >>Mathematical modelling approach to collective decision-making
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In everyday situations individuals make decisions. For example, a tourist usually chooses a crowded or recommended restaurant to have dinner. Perhaps it is an individual decision, but the observed pattern of decision-making is a collective phenomenon. Collective behaviour emerges from the local interactions that give rise to a complex pattern at the group level. In our example, the recommendations or simple copying the choices of others make a crowded restaurant even more crowded. The rules of interaction between individuals are important to study. Such studies should be complemented by biological experiments. Recent studies of collective phenomena in animal groups help us to understand these rules and develop mathematical models of collective behaviour. The most important communication mechanism is positive feedback between group members, which we observe in our example. In this thesis, we use a generic experimentally validated model of positive feedback to study collective decision-making.

The first part of the thesis is based on the modelling of decision-making associated to the selection of feeding sites. This has been extensively studied for ants and slime moulds. The main contribution of our research is to demonstrate how such aspects as "irrationality", speed and quality of decisions can be modelled using differential equations. We study bifurcation phenomena and describe collective patterns above critical values of a bifurcation points in mathematical and biological terms. In the second part, we demonstrate how the primitive unicellular slime mould Physarum Polycephalum provides an easy test-bed for theoretical assumptions and model predictions about decision-making. We study its searching strategies and model decision-making associated to the selection of food options. We also consider the aggregation model to investigate the fractal structure of Physarum Polycephalum plasmodia.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2017. 42 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 99
Keyword
collective behaviour, collective decision-making, communication mechanisms, positive feedback, mathematical modelling, bifurcation phenomena, steady state solutions, symmetry breaking, symmetry restoring, diffusion-limited aggregation, fractal dimension
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-314903 (URN)978-91-506-2624-7 (ISBN)
Public defence
2017-04-07, Siegbahnsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Note

Fel serie i tryckt bok /Wrong series in the printed book

Available from: 2017-03-16 Created: 2017-02-07 Last updated: 2017-03-16

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