Fair algorithms for selecting citizen assemblies, in Nature

 Here's a paper that grapples with the problem that not every group in society is equally likely to accept an appointment for which they have been selected, which complicates the problem of selecting representative committees while also giving each potential member approximately the same chance of being selected.

Fair algorithms for selecting citizens’ assemblies. by Bailey Flanigan, Paul Gölz, Anupam Gupta, Brett Hennig & Ariel D. Procaccia, Nature (2021). https://doi.org/10.1038/s41586-021-03788-6

Abstract: Globally, there has been a recent surge in ‘citizens’ assemblies’1, which are a form of civic participation in which a panel of randomly selected constituents contributes to questions of policy. The random process for selecting this panel should satisfy two properties. First, it must produce a panel that is representative of the population. Second, in the spirit of democratic equality, individuals would ideally be selected to serve on this panel with equal probability2,3. However, in practice these desiderata are in tension owing to differential participation rates across subpopulations4,5. Here we apply ideas from fair division to develop selection algorithms that satisfy the two desiderata simultaneously to the greatest possible extent: our selection algorithms choose representative panels while selecting individuals with probabilities as close to equal as mathematically possible, for many metrics of ‘closeness to equality’. Our implementation of one such algorithm has already been used to select more than 40 citizens’ assemblies around the world. As we demonstrate using data from ten citizens’ assemblies, adopting our algorithm over a benchmark representing the previous state of the art leads to substantially fairer selection probabilities. By contributing a fairer, more principled and deployable algorithm, our work puts the practice of sortition on firmer foundations. Moreover, our work establishes citizens’ assemblies as a domain in which insights from the field of fair division can lead to high-impact applications.

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"To our knowledge, all of the selection algorithms previously used in practice (Supplementary Information section 12) aim to satisfy one particular property, known as ‘descriptive representation’ (that the panel should reflect the composition of the population)16. Unfortunately, the pool from which the panel is chosen tends to be far from representative. Specifically, the pool tends to overrepresent groups with members who are on average more likely to accept an invitation to participate, such as the group ‘college graduates’.  

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"Selection algorithms that pre-date this work focused only on satisfying quotas, leaving unaddressed a second property that is also central to sortition: that all individuals should have an equal chance of being chosen for the panel.

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"Although it is generally impossible to achieve perfectly equal probabilities, the reasons to strive for equality also motivate a more gradual version of this goal: making probabilities as equal as possible, subject to the quotas. We refer to this goal as ‘maximal fairness’. 

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"the algorithms in our framework (1) explicitly compute a maximally fair output distribution and then (2) sample from that distribution to select the final panel (Fig. 1). Crucially, the maximal fairness of the output distribution found in the first step makes our algorithms optimal. To see why, note that the behaviour of any selection algorithm on a given instance is described by some output distribution; thus, as our algorithm finds the fairest possible output distribution, it is always at least as fair as any other algorithm."