subsumes the WP titled "Can society learn without opinion leaders?"
Whether or not a given social network aggregates information depends not only on the topology of the network and information available to agents but also on the order in which they make their decisions. We consider a model with Bayes-rational agents and identify the topological property sufficient for aggregation for most of the orders. We use this property and the insights from the theory of expander graphs to show that learning is possible without opinion leaders and that it can be robust to the elimination of large groups of agents.
We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two-agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We also study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.
slides (De Aequa Divisione workshop on Fair Division, LUISS, Rome, May 2019)
Siblings inherited several apartments would not be satisfied by an allocation giving them an apartment with probability 50% or envy-free up to one apartment. We suggest a new approach to fair division with valuable items, which bridges the modern "divisible" and "indivisible" literature: sharing minimization. The problem of sharing-minimization among fair Pareto-optimal allocations turns out to be algorithmically-tractable for almost all instances.
This is the first explicit algorithm for computing market equilibria of "non-convex" exchange economies that have disconnected equilibrium set. We avoid the "black-box" of Cell-Enumeration technique, used in the literature, by the novel approach based on enumeration of all the faces of the Pareto frontier via a simple 2-agent reduction.
The results are applied to approximately fair division of indivisible chores.
A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee.
Protecting the Protected Group: Circumventing Harmful Fairness (with Omer Ben-Porat and Moshe Tennenholtz)
May 2019, arXiv:1905.10546
Fairness constraints used for Fair Machine Learning may harm the protected group because the "price of fairness" is reallocated to this group by self-interested decision makers (e.g., a bank giving loans).
slides with a different set of results including exact Price of Fairness for general bargaining (CompEcon seminar at HUJI, May 2019)
We propose a new family of allocation rules that, using minimal statistical information about the environment, achieve fairness and welfare guarantees. These are the first results on dynamic resource allocation that combine both fairness and efficiency design objectives.
In this note, we show that Pareto-optimal and almost-fair (Proportional up to 1 item) allocations of a mixture of indivisible goods and bads always exist and can be computed in strongly-polynomial time. The technique is based on the trading-cycle algorithm for finding divisible Pareto-improvements from the recent working paper "Fair division with minimal sharing" with Erel Segal-Halevi and on an extension of Barman-Krishnamurthy rounding.
Dividing bads under additive utilities (with Anna Bogomolnaia, Herve Moulin, and Elena Yanovskaya)