arXiv subjects

Zachary Kilpatrick

Publications and source records attributed to Zachary Kilpatrick.

4 recordsLinked to original sources

arXiv2026

Modularity, asymmetry, and polarization shape consensus speed in the voter model

In populations with community structure, the formation of consensus requires both alignment within and diffusion of beliefs across groups, processes that evolve on distinct time scales. How do modularity, asymmetry, and polarization shape this process? We study a variant of the voter model in which a population is divided into two cliques of sizes $N_1$ and $N_2$. At each time step, a pair of nodes is selected; if their binary opinions differ, each agent adopts the opinion of the other with probability $p$. With probability $\alpha$, the pairing occurs with a single clique, and with probability $1-\alpha$, across cliques. We analyze how this coupling strength, population imbalance, and initial polarization jointly determine the time to consensus. Formation of consensus generally starts with inter-clique interactions rapidly synchronizing the two cliques' opinion fractions, after which consensus is reached through a slower diffusion along the synchronized manifold; this slow stage is largely insensitive to $\alpha$ except when the cliques are nearly disconnected. To analyze these dynamics, we derive stochastic differential equations and Fokker-Planck approximations in the large-population limit, and assess their accuracy against the discrete model. While $\alpha$ primarily affects the fast alignment stage, initially polarized and asymmetric populations exhibit nontrivial effects, including regimes in which an intermediate level coupling minimizes consensus time. A small-clique scaling analysis reveals that this optimum arises from a competition between fast alignment drift and noise amplification in the smaller group, and provides an approximate decomposition of consensus time into fast and slow contributions.

physics.soc-ph↗

arXiv2026

Daring few, patient many: division of labor in decentralized foraging collectives

How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh the benefits of globally coordinated decisions, even when local interactions remain tightly organized. This raises a key question: how can groups implement efficient collective decision-making without central coordination? We address this question using a collective foraging model in which individuals share information and rewards, but each must choose whether to bear the cost of exploring or to remain idle. We show that decentralized collectives can match the performance of centrally controlled groups through a division of labor: a small, heterogeneous subset explores even when expected rewards are negative, acquiring information to enable future foraging, while a coordinated majority forages only when expected rewards are positive. Information redundancy causes the optimal number of explorers to grow sublinearly with group size, so that larger groups need proportionally fewer explorers. The heterogeneity of the group is maximized at intermediate ecological pressures, but optimal groups are homogeneous when costs or fluctuations are extreme. Crucially, these group-level policies do not require central coordination, emerging instead from agents following simple threshold-based decision rules. We thus demonstrate a mechanism through which leaderless collectives can make effective decisions under uncertainty and show how ecological pressures can drive changes in the distribution of strategies employed by the group.

q-bio.PE↗

arXiv2020

Diversity Improves Speed and Accuracy in Social Networks

How does temporally structured private and social information shape collective decisions? To address this question we consider a network of rational agents who independently accumulate private evidence that triggers a decision upon reaching a threshold. When seen by the whole network, the first agent's choice initiates a wave of new decisions; later decisions have less impact. In heterogeneous networks, first decisions are made quickly by impulsive individuals who need little evidence to make a choice, but, even when wrong, can reveal the correct options to nearly everyone else. We conclude that groups comprised of diverse individuals can make more efficient decisions than homogenous ones.

physics.soc-ph↗

arXiv2018

Bayesian Evidence Accumulation on Social Networks

To make decisions we are guided by the evidence we collect, as well as the opinions of friends and neighbors. How do we integrate our private beliefs with information we obtain from our social network? To understand the strategies humans use to do so it is useful to compare them to observers that optimally integrate all evidence. Here we derive network models of rational (Bayes optimal) agents who accumulate private measurements and observe decisions of their neighbors to make an irreversible choice between two options. The resulting information exchange dynamics has interesting properties: When one option is preferred, the absence of a decision can be increasingly informative over time. In recurrent networks an absence of a decision can lead to a sequence of belief updates akin to those in the literature on common knowledge. Information obtained from observing repeated non-decisions is independent of realization, unless the private information of agents is redundant. On the other hand, in larger networks a single decision can trigger a cascade of agreements and disagreements that depend on the private information agents have gathered. Our approach provides a bridge between social decision making models in the economics literature, which largely ignore the temporal dynamics of decisions, and the single-observer evidence accumulator models used widely in neuroscience and psychology.

physics.soc-ph↗