Heterogeneous Preference and Local Nonlinearity in Consensus Decision Making

Andrew T. Hartnett, Emmanuel Schertzer, Simon A. Levin, Iain D. Couzin
2016 Physical Review Letters  
In recent years, a large body of research has focused on unveiling the fundamental physical processes that living systems utilize to perform functions, such as coordinated action and collective decision making. Here, we demonstrate that important features of collective decision making among higher organisms are captured effectively by a novel formulation of well-characterized physical spin systems, where the spin state is equivalent to two opposing preferences, and a bias in the preferred state
more » ... represents the strength of individual opinions. We reveal that individuals (spins) without a preference (unbiased or uninformed) play a central role in collective decision making, both in maximizing the ability of the system to achieve consensus (via enhancement of the propagation of spin states) and in minimizing the time taken to do so (via a process reminiscent of stochastic resonance). Which state (option) is selected collectively, however, is shown to depend strongly on the nonlinearity of local interactions. Relatively linear social response results in unbiased individuals reinforcing the majority preference, even in the face of a strongly biased numerical minority (thus promoting democratic outcomes). If interactions are highly nonlinear, however, unbiased individuals exert the opposite influence, promoting a strongly biased minority and inhibiting majority preference. These results enhance our understanding of physical computation in biological collectives and suggest new avenues to explore in the collective dynamics of spin systems. Collective decision making is ubiquitous across cellular [1,2], animal [3], human [4, 5] , and engineered systems [6] . Despite varying greatly in terms of the type and composition of components (agents), common dynamical features allow collectives to make rapid, accurate decisions even in complex environments or amidst conflicting needs [7] . The dynamics of populations of neurons, for example, have been precisely related to binary "spins" (spikes) communicating via pairwise interactions [8, 9] , a characteristic of models employed widely in statistical physics. Neural dynamics also exhibit striking parallels with collective decision making among organisms themselves, such as the process by which honeybee colonies decide among alternative nest sites [10, 11] . Thus, by abstracting microscopic details and relating biological computation directly to that among physical particles, we can obtain considerable insight regarding collective behavior and possibly reveal novel aspects of physical systems. Here, we explore the dynamics of populations making collective decisions. Despite being inspired by recent experimental data from animal groups, we deliberately shift the focus from understanding collective decisions in a particular experimental context to a general understanding of the underlying dynamical interplay among population constitution, space, and the character of local interactions. In doing so we demonstrate that many of the complex, and possibly counterintuitive, features seen when considering collective decision making by organisms can be represented via consideration of a continuum, or "family," of spin system models. A main focus of our work is to consider observations in animal groups that suggest that unbiased (or uninformed) individuals can strongly influence the outcome of collective consensus decisions [11] . Previous phenomenological models, while able to capture some elements in common with experiments [11], provide relatively limited insight into the mechanism of action. Here, we exploit the well-characterized nature of physical spin systems to deepen our theoretical understanding of collective decision making, employing a two-choice decision task for a group with three distinct subpopulations: two subpopulations with conflicting preferences (informed or preference individuals), and a variable proportion of unbiased individuals (who participate in the decision making process, but have no information and/or no preferred outcome).
doi:10.1103/physrevlett.116.038701 pmid:26849620 fatcat:khbgj5q3izhjjpipackdcthu3a