Just Sort It! A Simple and Effective Approach to Active Preference Learning

We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking, the optimal solution is to use an efficient sorting algorithm, such as Quicksort. But how do sorting algorithms behave if some comparison outcomes are inconsistent with the ranking? We give favorable guarantees for Quicksort for the popular Bradley-Terry model, under natural assumptions on the parameters. Furthermore, we empirically demonstrate that sorting algorithms lead to a very simple and effective active learning strategy: repeatedly sort the items. This strategy performs as well as state-of-the-art methods (and much better than random sampling) at a minuscule fraction of the computational cost.Comment: Accepted at ICML 201

Characterizing behavioral decisions with choice data

This paper provides an axiomatic characterization of choices in a setting where a decision-maker may not fully internalize all the consequences of her choices on herself. Such a departure from rationality, it turns out, is common across a variety of positive behavioral models and admits the standard rational choice model as a special case. We show that choice data satisfying (a) Senís axioms if and fully characterize behavioral decisions, and (b) Senís axiom if and if fully characterize standard decision-making. In addition, we show that (a) it is possible to identify a minimal and a maximal set of psychological states using choice data alone, and (b) under specific choice scenarios, "revealed mistakes" can be inferred directly from choice data

Behavioural decisions & welfare

If decision-makers (DMs) do not always do what is in their best interest, what do choices reveal about welfare? This paper shows how observed choices can reveal whether the DM is acting in her own best interest. We study a framework that relaxes rationality in a way that is common across a variety of seemingly disconnected positive behavioral models and admits the standard rational choice model as a special case. We model a behavioral DM (boundedly rational) who, in contrast to a standard DM (rational), does not fully internalize all the consequences of her own actions on herself. We provide an axiomatic characterization of choice correspondences consistent with behavioral and standard DMs, propose a choice experiment to infer the divergence between choice and welfare, state an existence result for incomplete preferences and show that the choices of behavioral DMs are, typically, sub-optimal

Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.Comment: Published in at http://dx.doi.org/10.1214/12-STS396 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org