Work in Progress

A Bayesian Reflection on the Judy Benjamin Problem

Bayesian conditioning requires a probability space in which learned information can be represented as an event or constraint. The Judy Benjamin problem shows that this requirement is nontrivial when the information learned takes the form of a conditional probability. I argue that the problem is under-specified: the original story does not determine a unique extended space in which Bayesian conditioning should proceed, and therefore does not determine a uniquely correct Bayesian posterior. Grove and Halpern’s model and Vasudevan’s model use different extended spaces and yield different answers. The former vindicates the intuitive answer, while the latter recovers the minimum-relative-entropy answer. I argue that Vasudevan’s proposed qualitative contrast between conservativity and epistemic charity is not well supported. I then introduce a two-stage model to show that extended spaces encode different structural representations of Judy’s situation. Accuracy considerations can select among these representations only if the story is supplemented with further facts about the actual structure of the situation.

Key Words: The Judy Benjamin Problem, Bayesian Conditioning, Entropy

Conciliation in Social Inquiry: Belief Pooling and Action Choice in Networks

Conciliationism recommends accommodating peers, but it leaves open how one should implement conciliationism in group inquiry. A complete epistemic practice has two components: an aggregation rule (how agents pool peer opinions) and a decision rule (how agents act under uncertainty). Using agent-based simulations of a two-armed bandit, I compare two aggregation rules: consensus-seeking (log-space pooling, which integrates disagreement into a single posterior) and diversity-preserving (mixture pooling, which keeps competing hypotheses represented), together with two decision rules: best-estimate (posterior-mean, myopic choice) and belief-sampling (Thompson sampling, uncertainty-guided exploration). I vary problem difficulty (how informative agents’ priors are) and network density (Erdős–Rényi connectivity) and evaluate whether and how quickly groups converge on the superior arm. The two dimensions define four epistemic practices. Beyond mapping their interaction and identifying which practice performs best across environments, I draw four overarching conclusions: (1) decision rules often matter more than aggregation rules, with belief-sampling improving success in most environments; (2) no single aggregation rule is uniformly better; (3) with full belief exchange, outcomes are largely insensitive to density once networks are connected, and (4) transient diversity is not a universal route to accuracy.

Key Words: Peer disagreement, Conciliationism, Social learning, Agent-based simulations

 Agents’ Priors and Dynamic Network: Two Approaches in Enhancing Group Learning

This paper investigates how two novel network arrangement strategies influence group learning within Zollman's (2007; 2010) epistemic models. Specifically, I explore how arranging networks based on agents’ prior beliefs and implementing dynamic network structures affect a group’s accuracy and speed in reaching consensus. The explanatory framework centers on transient diversity — the temporary heterogeneity in individual beliefs or actions prior to consensus. Results show that arrangements which initially restrict communication and then permit more information exchange significantly improve group learning effectiveness. The underlying mechanism is that such controlled communication allows agents sufficient time to independently gather evidence and develop a more cautious attitude toward belief revision, thereby reducing collective susceptibility to misleading information. These findings contribute novel insights into optimizing group deliberation processes with an emphasis on strategic management of information flow.

Key Words: Epistemic networks, Zollman effect, Agent-based model, Group learning