Beginning with the introduction of graphical games and related models, there is now a rich body of algorithmic connections between probabilistic inference, game theory and microeconomics. Strategic analogues of belief propagation and other inference techniques have been developed for the computation of Nash, correlated and market equilibria, and have played a significant role in the evolution of algorithmic game theory over the past decade.

There are also important points of departure between probabilistic and strategic graphical models — perhaps most notably that in the latter, vertices are not random variables, but self-interested humans or organizations. It is thus natural to wonder how social network structures might influence equilibrium outcomes such as social welfare or the relative wealth and power of individuals. One logical path that such questions lead to is human-subject experiments on strategic interaction in social networks.

In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space, and a loss function defined on (parameter, decision) pairs, and formulate social choice mechanisms as decision rules that minimize expected loss. This suggests a general framework for the design and analysis of new social choice mechanisms. We compare Bayesian estimators, which minimize Bayesian expected loss, for the Mallows model and the Condorcet model respectively, and the Kemeny rule. We consider various normative properties, in addition to computational complexity and asymptotic behavior. In particular, we show that the Bayesian estimator for the Condorcet model satisfies some desired properties such as anonymity, neutrality, and monotonicity, can be computed in polynomial time, and is asymptotically different from the other two rules when the data are generated from the Condorcet model for some ground truth parameter.