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People must integrate disparate sources of information when making decisions, especially in social contexts. But information does not always flow freely. It can be constrained by social networks1–3 and distorted by zealots and automated bots4. Here we develop a voter game as a model system to study information flow in collective decisions. Players are assigned to competing groups (parties) and placed on an ‘influence network’ that determines whose voting intentions each player can observe. Players are incentivized to vote according to partisan interest, but also to coordinate their vote with the entire group. Our mathematical analysis uncovers a phenomenon that we call information gerrymandering: the structure of the influence network can sway the vote outcome towards one party, even when both parties have equal sizes and each player has the same influence. A small number of zealots, when strategically placed on the influence network, can also induce information gerrymandering and thereby bias vote outcomes. We confirm the predicted effects of information gerrymandering in social network experiments with n = 2,520 human subjects. Furthermore, we identify extensive information gerrymandering in real-world influence networks, including online political discussions leading up to the US federal elections, and in historical patterns of bill co-sponsorship in the US Congress and European legislatures. Our analysis provides an account of the vulnerabilities of collective decision-making to systematic distortion by restricted information flow. Our analysis also highlights a group-level social dilemma: information gerrymandering can enable one party to sway decisions in its favour, but when multiple parties engage in gerrymandering the group loses its ability to reach consensus and remains trapped in deadlock. In a voter game, information gerrymandering can sway the outcome of the vote towards one party, even when both parties have equal sizes and each player has the same influence; and this effect can be exaggerated by strategically placed zealots or automated bots.

JBP and AJS acknowledge funding from the Burroughs Wellcome Fund, the David and Lucile Packard Foundation, the James S. McDonnell Foundation, the Alfred P. Sloan Foundation, grant #D12AP00025 from the U.S. Department of the Interior and Defense Advanced Research Projects Agency, and grant RFP-12-16 from the Foundational Questions in Evolutionary Biology Fund. AP acknowledges grants from the Natural Environment Research Council (NE/G00563X/1) and the Engineering and Physical Sciences Research Council (EP/F500351/1, EP/I017909/1). AJS also acknowledges an EPSRC PhD Plus fellowship. Background: Changes in gene regulatory networks drive the evolution of phenotypic diversity both within and between species. Rewiring of transcriptional networks is achieved either by changes to transcription factor binding sites or by changes to the physical interactions among transcription factor proteins. It has been suggested that the evolution of cooperative binding among factors can facilitate the adaptive rewiring of a regulatory network. Results: We use a population-genetic model to explore when cooperative binding of transcription factors is favored by evolution, and what effects cooperativity then has on the adaptive re-writing of regulatory networks. We consider a pair of transcription factors that regulate multiple targets and overlap in the sets of target genes they regulate. We show that, under stabilising selection, cooperative binding between the transcription factors is favoured provided the amount of overlap between their target genes exceeds a threshold. The value of this threshold depends on several population-genetic factors: strength of selection on binding sites, cost of pleiotropy associated with protein-protein interactions, rates of mutation and population size. Once it is established, we find that cooperative binding of transcription factors significantly accelerates the adaptive rewiring of transcriptional networks under positive selection. We compare our qualitative predictions to systematic data on Saccharomyces cerevisiae transcription factors, their binding sites, and their protein-protein interactions. Conclusions: Our study reveals a rich set of evolutionary dynamics driven by a tradeoff between the beneficial effects of cooperative binding at targets shared by a pair of factors, and the detrimental effects of cooperative binding for non-shared targets. We find that cooperative regulation will evolve when transcription factors share a sufficient proportion of their target genes. These findings help to explain empirical pattens in datasets of transcription factors in Saccharomyces cerevisiae and, they suggest that changes to physical interactions between transcription factors can play a critical role in the evolution of gene regulatory networks. Publisher PDF