We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score that determines the Bernoulli distributions of pairwise comparisons’ outcomes. Our proposed method aims to infer general ranking properties of the BTL model. The general ranking properties include the “local” properties such as if an item is preferred over another and the “global” properties such as if an item is among the top K-ranked items. We further generalize our inferential framework to multiple testing problems where we control the false discovery rate (FDR) and apply the method to infer the top-K ranked items. We also derive the information-theoretic lower bound to justify the minimax optimality of the proposed method. We conduct extensive numerical studies using both synthetic and real data sets to back up our theory.
Overt visual attention and value computation in complex risky choice
Traditional models of decision making under uncertainty explain human behavior in simple situations with a minimal set of alternatives and attributes. Some of them, such as prospect theory, have been proven successful and robust in such simple situations. Yet, less is known about the preference formation during decision making in more complex cases. Furthermore, it is generally accepted that attention plays a role in the decision process but most theories make simplifying assumptions about where attention is deployed. In this study, we replace these assumptions by measuring where humans deploy overt attention, i.e. where they fixate. To assess the influence of task complexity, participants perform two tasks. The simpler of the two requires participants to choose between two alternatives with two attributes each (four items to consider). The more complex one requires a choice between four alternatives with four attributes each (16 items to consider). We then compare a large set of model classes, of different levels of complexity, by considering the dynamic interactions between uncertainty, attention and pairwise comparisons between attribute values. The task of all models is to predict what choices humans make, using the sequence of observed eye movements for each participant as input to the model. more »
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