  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.
