Sortition, the random selection of political representatives, is increasingly being used around the world to choose participants of deliberative processes like Citizens' Assemblies. Motivated by sortition's practical importance, there has been a recent flurry of research on sortition algorithms, whose task it is to select a panel from among a pool of volunteers. This panel must satisfy quotas enforcing representation of key population subgroups. Past work has contributed an algorithmic approach for fulfilling this task while ensuring that volunteers' chances of selection are maximally equal, as measured by any convex equality objective. The question, then, is: which equality objective is the right one? Past work has mainly studied the objectives Minimax and Leximin, which respectively minimize the maximum and maximize the minimum chance of selection given to any volunteer. Recent work showed that both of these objectives have key weaknesses: Minimax is highly robust to manipulation but is arbitrarily unfair; oppositely, Leximin is highly fair but arbitrarily manipulable. In light of this gap, we propose a new equality objective, Goldilocks, that aims to achieve these ideals simultaneously by ensuring that no volunteer receives too little or too much chance of selection. We theoretically bound the extent to which Goldilocks achieves these ideals, finding that in an important sense, Goldilocks recovers among the best available solutions in a given instance. We then extend our bounds to the case where the output of Goldilocks is transformed to achieve a third goal, Transparency. Our empirical analysis of Goldilocks in real data is even more promising: we find that this objective achieves nearly instance-optimal minimum and maximum selection probabilities simultaneously in most real instances -- an outcome not even guaranteed to be possible for any algorithm.

选择公民代表的随机抽签方法，被越来越多地用于世界各地的议政过程，如公民代表会议。最近的研究集中在抽签算法，其任务是从志愿者中选择一个小组。该小组必须满足代表关键人口子群的配额。我们提出了一个新的平等目标，Goldilocks，旨在通过确保志愿者的被选择机会既不过少也不过多，同时达到这些理想。我们在理论上限制了Goldilocks实现这些理想的程度，并发现在某种重要意义上，Goldilocks在给定实例中能够找到最佳解决方案之一。我们将我们的界限延伸到Goldilocks输出被转换以实现第三个目标：透明度。我们对真实数据中Goldilocks的实证分析更加令人鼓舞：我们发现在大多数实例中，该目标几乎同时实现了实例最优的最小和最大选择概率，这甚至不被任何算法保证是可能的。

公正、抗操纵和透明的抽签