In this paper, we seek robust policies for uncertain Markov Decision Processes (MDPs). Most robust optimization approaches for these problems have focussed on the computation of {\em maximin} policies which maximize the value corresponding to the worst realization of the uncertainty.

We examine data from the following 11 real-world sortition panel selection instances, generously provided to us by several groups that specialize in organizing citizens' assemblies. Table 1 shows the instance short-names we use throughout the paper, and which organization was responsible for each panel. The final two columns compare the values of our theoretical upper bounds on the marginal discrepancy, illustrating that in all instances except "obf", the bound from Theorem 3.3 is tighter. Finally, we give some metadata about each instance, which is required for calculating the values of our theoretical upper bounds. In particular, n = number of pool members, k = number panel members, C = set of distinct realized feature-vectors in the pool.

Sortition is an age-old democratic paradigm, widely manifested today through the random selection of citizens' assemblies. Recently-deployed algorithms select assemblies maximally fairly, meaning that subject to demographic quotas, they give all potential participants as equal a chance as possible of being chosen. While these fairness gains can bolster the legitimacy of citizens' assemblies and facilitate their uptake, existing algorithms remain limited by their lack of transparency. To overcome this hurdle, in this work we focus on panel selection by uniform lottery, which is easy to realize in an observable way. By this approach, the final assembly is selected by uniformly sampling some pre-selected set of m possible assemblies. We provide theoretical guarantees on the fairness attainable via this type of uniform lottery, as compared to the existing maximally fair but opaque algorithms, for two different fairness objectives. We complement these results with experiments on real-world instances that demonstrate the viability of the uniform lottery approach as a method of selecting assemblies both fairly and transparently.

We consider the problem of recovering the ground truth ordering (ranking, top-$k$, or others) over a large number of alternatives. The wisdom of crowd is a heuristic approach based on Condorcet's Jury theorem to address this problem through collective opinions. This approach fails to recover the ground truth when the majority of the crowd is misinformed. The surprisingly popular (SP) algorithm cite{prelec2017solution} is an alternative approach that is able to recover the ground truth even when experts are in minority. The SP algorithm requires the voters to predict other voters' report in the form of a full probability distribution over all rankings of alternatives. However, when the number of alternatives, $m$, is large, eliciting the prediction report or even the vote over $m$ alternatives might be too costly. In this paper, we design a scalable alternative of the SP algorithm which only requires eliciting partial preferences from the voters, and propose new variants of the SP algorithm. In particular, we propose two versions -- Aggregated-SP and Partial-SP -- that ask voters to report vote and prediction on a subset of size $k$ ($\ll m$) in terms of top alternative, partial rank, or an approval set. Through a large-scale crowdsourcing experiment on MTurk, we show that both of our approaches outperform conventional preference aggregation algorithms for the recovery of ground truth rankings, when measured in terms of Kendall-Tau distance and Spearman's $\rho$. We further analyze the collected data and demonstrate that voters' behavior in the experiment, including the minority of the experts, and the SP phenomenon, can be correctly simulated by a concentric mixtures of Mallows model. Finally, we provide theoretical bounds on the sample complexity of SP algorithms with partial rankings to demonstrate the theoretical guarantees of the proposed methods.

While there is universal agreement that agents ought to act ethically, there is no agreement as to what constitutes ethical behaviour. To address this problem, recent philosophical approaches to `moral uncertainty' propose aggregation of multiple ethical theories to guide agent behaviour. However, one of the foundational proposals for aggregation - Maximising Expected Choiceworthiness (MEC) - has been criticised as being vulnerable to fanaticism; the problem of an ethical theory dominating agent behaviour despite low credence (confidence) in said theory. Fanaticism thus undermines the `democratic' motivation for accommodating multiple ethical perspectives. The problem of fanaticism has not yet been mathematically defined. Representing moral uncertainty as an instance of social welfare aggregation, this paper contributes to the field of moral uncertainty by 1) formalising the problem of fanaticism as a property of social welfare functionals and 2) providing non-fanatical alternatives to MEC, i.e. Highest k-trimmed Mean and Highest Median.

Bayesian optimization is a technique for optimizing black-box target functions. At the core of Bayesian optimization is a surrogate model that predicts the output of the target function at previously unseen inputs to facilitate the selection of promising input values. Gaussian processes (GPs) are commonly used as surrogate models but are known to scale poorly with the number of observations. We adapt the Vecchia approximation, a popular GP approximation from spatial statistics, to enable scalable high-dimensional Bayesian optimization. We develop several improvements and extensions, including training warped GPs using mini-batch gradient descent, approximate neighbor search, and selecting multiple input values in parallel. We focus on the use of our warped Vecchia GP in trust-region Bayesian optimization via Thompson sampling. On several test functions and on two reinforcement-learning problems, our methods compared favorably to the state of the art.