  In many real-world applications of committee elections, the candidates are
associated with certain attributes and the chosen committee is required to
satisfy some constraints posed on the candidate attributes. For instance, when
dress collocation, it is generally acknowledged that when wearing a tie, you'd
better wear a shirt, and wearing a suit, you'd better wear leather shoes. Here,
dresses are categorized by upper garment, lower garment, shoes et.al, and upper
garment is with the attribute tie and shirt, lower garment is with the
attribute suit, and shoes is with the attribute leather. And two constraints
"tie infers shirt" and "suit infers leather shoes" are proposed. We study this
variant of committee elections from the computational complexity viewpoint.
Given a set of candidates, each with some attributes and a profit, and a set of
constraints, given as propositional logical expressions of the attributes, the
task is to compute a set of k candidates, whose attributes satisfy all
constraints and whose total profit achieves a given bound. We achieve a
dichotomy concerning classical complexity with no length limit on constraints:
the problem is polynomial-time solvable, if the following two conditions are
fulfilled: 1) each candidate has only one attribute and 2) each attribute
occurs at most once in the constraints. It becomes NP-hard if one of the two
conditions is violated. Moreover, we examine its parameterized complexity. The
parameterization with the number of constraints, the size of the committee, or
the total profit bound as parameter leads to para-NP-hardness or W[1]-hardness,
while with the number of attributes or the number of candidates as parameter,
the problem turns out to be fixed-parameter tractable.
