Quantifying Human Priors over Social and Navigation Networks

TL;DR

The work tackles quantifying human priors over relational networks (social and navigation) by combining Markov Chain Monte Carlo with People (MCMCP) experiments and a hierarchical maximum-entropy prior framework. It fits priors over graphs using a parameterized ERGM-like model that constrains subgraph densities up to order r and interprets results via graph cumulants, incorporating sparsity scaling. Key findings show robust, domain-consistent patterns: priors become sparser with larger graphs, social priors exhibit stronger triadic closure, and higher model expressivity improves cross-domain discrimination. The approach yields efficient, interpretable representations of latent relational biases and demonstrates how Bayesian modeling of participant responses can enhance data utilization in behavioral priors estimation. This has broad implications for modeling latent graph priors in cognition and for designing experiments that leverage network structure symmetry for tractable inference.

Abstract

Human knowledge is largely implicit and relational -- do we have a friend in common? can I walk from here to there? In this work, we leverage the combinatorial structure of graphs to quantify human priors over such relational data. Our experiments focus on two domains that have been continuously relevant over evolutionary timescales: social interaction and spatial navigation. We find that some features of the inferred priors are remarkably consistent, such as the tendency for sparsity as a function of graph size. Other features are domain-specific, such as the propensity for triadic closure in social interactions. More broadly, our work demonstrates how nonclassical statistical analysis of indirect behavioral experiments can be used to efficiently model latent biases in the data.

Figures (15)

• Figure 1: Screenshots of our main experimental interfacefor two cover stories:social class(left)andnavigation park(right). Our online platform allowed participants to easily "draw" their inferences about the obscured relations of a graph (demo https://www.youtube.com/watch?v=aZNeN293MZs). Note that the two images above are nearly identical: to make the comparisons as fair as possible, we made the experiments identical in every aspect, except for the text specifically related to each cover story. See appendix \ref{['app:experimentalprocedure']} for a detailed description of these experiments and high-resolution versions of these images (figs. \ref{['fig:ScreenshotSocStudent']}class and \ref{['fig:ScreenshotNavTrail']}park).
• Figure 2: Algorithm for generating a round of our experiment. The context of the experiment was given by one of the four cover stories in table \ref{['table:coverstories']}, and an interface allowed participants to easily manipulate the graphs (see demo https://www.youtube.com/watch?v=aZNeN293MZs and fig. \ref{['fig:ScreenshotExperiments']}). Each participant did multiple rounds, corresponding to different chains.
• Figure 3: Priors over larger graphs have lower edge density. Markers in the solid curves correspond to the inferred edge density ($\mu_{}^{ }$) of participants' priors, using the aggregated data of a single cover story with that number of nodes. Shading corresponds to $\pm 1$ standard deviation of the average value that would have been obtained if participants all had this inferred prior, and behaved according to the assumptions of the MCMCP model. Note that the result of this procedure is not necessarily centered around the empirical values (i.e., the solid curves).
• Figure 4: Priors over smaller graphs have fewer hubs. The analysis is the same as in fig. \ref{['fig:sparsepriors']}, but the statistic measured is the scaled cherry cumulant ($\kappa_{}^{ }/\mu_{}^{2}$), which quantifies preference for degree heterogeneity. A negative value indicates that the prior has edges distributed more uniformly than what would be expected by chance (i.e., in an $\textrm{ER}_{n,\mu_{}}$ distribution with the same number of nodes $n$ and edge density $\mu_{}^{ }$).
• Figure 5: Priors over social graphs have more triangles. The analysis is the same as in figs. \ref{['fig:sparsepriors']} and \ref{['fig:egalitarian']}, but the statistic measured is the scaled triangle cumulant ($\kappa_{}^{ }/\mu_{}^{3}$), which quantifies preference for clustering. A negative value indicates that the prior has fewer triangles than what would be expected by chance. In contrast to figs. \ref{['fig:sparsepriors']} and \ref{['fig:egalitarian']}, there is a notable difference between the social (class and work) and navigation (city and park) domains.