  Judgment aggregation is a general framework for collective decision making
that can be used to model many different settings. Due to its general nature,
the worst case complexity of essentially all relevant problems in this
framework is very high. However, these intractability results are mainly due to
the fact that the language to represent the aggregation domain is overly
expressive. We initiate an investigation of representation languages for
judgment aggregation that strike a balance between (1) being limited enough to
yield computational tractability results and (2) being expressive enough to
model relevant applications. In particular, we consider the languages of Krom
formulas, (definite) Horn formulas, and Boolean circuits in decomposable
negation normal form (DNNF). We illustrate the use of the positive complexity
results that we obtain for these languages with a concrete application: voting
on how to spend a budget (i.e., participatory budgeting).
