We adopt a utilitarian perspective on social choice, assuming that agents have (possibly latent) utility functions over some space of alternatives. For many reasons one might consider mechanisms, or social choice functions, that only have access to the ordinal rankings of alternatives by the individual agents rather than their utility functions. In this context, one possible objective for a social choice function is the maximization of (expected) social welfare relative to the information contained in these rankings. We study such optimal social choice functions under three different models, and underscore the important role played by scoring functions. In our worst-case model, no assumptions are made about the underlying distribution and we analyze the worst-case distortion-or degree to which the selected alternative does not maximize social welfare-of optimal social choice functions. In our average-case model, we derive optimal functions under neutral (or impartial culture) distributional models. Finally, a very general learning-theoretic model allows for the computation of optimal social choice functions (i.e., that maximize expected social welfare) under arbitrary, sampleable distributions. In the latter case, we provide both algorithms and sample complexity results for the class of scoring functions, and further validate the approach empirically.

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Background: The existence of specific microbial profiles for different periodontal conditions is still a matter of debate. The aim of this study was to test the hypothesis that 40 bacterial species could be used to classify patients, utilising machine learning, into generalised chronic periodontitis (ChP), generalised aggressive periodontitis (AgP) and periodontal health (PH). Method: Subgingival biofilm samples were collected from patients with AgP, ChP and PH and analysed for their content of 40 bacterial species using checkerboard DNA-DNA hybridisation. Two stages of machine learning were then performed. First of all, we tested whether there was a difference between the composition of bacterial communities in PH and in disease, and then we tested whether a difference existed in the composition of bacterial communities between ChP and AgP. The data were split in each analysis to 70% train and 30% test. A support vector machine (SVM) classifier was used with a linear kernel and a Box constraint of 1. The analysis was divided into two parts. Results: Overall, 435 patients (3,915 samples) were included in the analysis (PH = 53; ChP = 308; AgP = 74). The variance of the healthy samples in all principal component analysis (PCA) directions was smaller than that of the periodontally diseased samples, suggesting that PH is characterised by a uniform bacterial composition and that the bacterial composition of periodontally diseased samples is much more diverse. The relative bacterial load could distinguish between AgP and ChP. Conclusion: An SVC classifier using a panel of 40 bacterial species was able to distinguish between PH, AgP in young individuals and ChP.

Absent pharmaceutical interventions, social distancing, lock-downs and mobility restrictions remain our prime response in the face of epidemic outbreaks. To ease their potentially devastating socioeconomic consequences, we propose here an alternating quarantine strategy: at every instance, half of the population remains under lockdown while the other half continues to be active - maintaining a routine of weekly succession between activity and quarantine. This regime minimizes infectious interactions, as it allows only half of the population to interact for just half of the time. As a result it provides a dramatic reduction in transmission, comparable to that achieved by a population-wide lockdown, despite sustaining socioeconomic continuity at  ~50% capacity. The weekly alternations also help address the specific challenge of COVID-19, as their periodicity synchronizes with the natural SARS-CoV-2 disease time-scales, allowing to effectively isolate the majority of infected individuals precisely at the time of their peak infection.

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