42,581 research outputs found
A Statistical Decision-Theoretic Framework for Social Choice
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.Engineering and Applied Science
Morality, Uncertainty
Non-Consequentialist moral theories posit the existence of moral constraints: prohibitions on performing particular kinds of wrongful acts, regardless of the good those acts could produce. Many believe that such theories cannot give satisfactory verdicts about what we morally ought to do when there is some probability that we will violate a moral constraint. In this article, I defend Non-Consequentialist theories from this critique. Using a general choice-theoretic framework, I identify various types of Non-Consequentialism that have otherwise been conflated in the debate. I then prove a number of formal possibility and impossibility results establishing which types of Non-Consequentialism can -- and which cannot -- give us adequate guidance through through a risky world
A Statistical View of Learning in the Centipede Game
In this article we evaluate the statistical evidence that a population of
students learn about the sub-game perfect Nash equilibrium of the centipede
game via repeated play of the game. This is done by formulating a model in
which a player's error in assessing the utility of decisions changes as they
gain experience with the game. We first estimate parameters in a statistical
model where the probabilities of choices of the players are given by a Quantal
Response Equilibrium (QRE) (McKelvey and Palfrey, 1995, 1996, 1998), but are
allowed to change with repeated play. This model gives a better fit to the data
than similar models previously considered. However, substantial correlation of
outcomes of games having a common player suggests that a statistical model that
captures within-subject correlation is more appropriate. Thus we then estimate
parameters in a model which allows for within-player correlation of decisions
and rates of learning. Through out the paper we also consider and compare the
use of randomization tests and posterior predictive tests in the context of
exploratory and confirmatory data analyses
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