The rank aggregation problem has been studied with varying desiderata in varied communities such as Theoretical Computer Science, Statistics, Information Retrieval and Social Welfare Theory. We introduce a variant of this problem we call distributional rank aggregation, where the ranking data is only available via the induced distribution over the set of all permutations. We provide a novel translation of the usual social welfare theory axioms to this setting. As we show this allows for a more quantitative characterization of these axioms: which then are not only less prone to misinterpretation, but also allow simpler proofs for some key impossibility theorems. Most importantly, these quantitative characterizations lead to natural and novel relaxations of these axioms, which as we show, allow us to get around celebrated impossibility results in social choice theory. We are able to completely characterize the class of positional scoring rules with respect to our axioms and show that Borda Count is optimal in a certain sense.

Humans may be exceptional learners but they have biological limitations and moreover, inductive biases similar to machine learning algorithms. This puts limits on human learning ability and on the kinds of learning tasks humans can easily handle. In this paper, we consider the problem of “boosting” human learners to extend the learning ability of human learners and achieve improved performance on tasks which individual humans find difficult. We consider classification (category learning) tasks, propose a boosting algorithm for human learners and give theoretical justifications. We conduct experiments using Amazon’s Mechanical Turk on two synthetic datasets – a crosshair task with a nonlinear decision boundary and a gabor patch task with a linear boundary but which is inaccessible to human learners – and one real world dataset – the Opinion Spam detection task introduced in (Ott et al). Our results show that boosting human learners produces gains in accuracy and can overcome some fundamental limitations of human learners.