Applications extracting data from crowdsourcing platforms must deal with the uncertainty of crowd answers in two different ways: first, by deriving estimates of the correct value from the answers; second, by choosing crowd questions whose answers are expected to minimize this uncertainty relative to the overall data collection goal. Such problems are already challenging when we assume that questions are unrelated and answers are independent, but they are even more complicated when we assume that the unknown values follow hard structural constraints (such as monotonicity).

In this vision paper, we examine how to formally address this issue with an approach inspired by [2]. We describe a generalized setting where we model constraints as linear inequalities, and use them to guide the choice of crowd questions and the processing of answers. We present the main challenges arising in this setting, and propose directions to solve them.