  This paper presents the first systematic investigation of the potential
performance gains for crowdsourcing systems, deriving from available
information at the requester about individual worker earnestness (reputation).
In particular, we first formalize the optimal task assignment problem when
workers' reputation estimates are available, as the maximization of a monotone
(submodular) function subject to Matroid constraints. Then, being the optimal
problem NP-hard, we propose a simple but efficient greedy heuristic task
allocation algorithm. We also propose a simple ``maximum a-posteriori``
decision rule. Finally, we test and compare different solutions, showing that
system performance can greatly benefit from information about workers'
reputation. Our main findings are that: i) even largely inaccurate estimates of
workers' reputation can be effectively exploited in the task assignment to
greatly improve system performance; ii) the performance of the maximum
a-posteriori decision rule quickly degrades as worker reputation estimates
become inaccurate; iii) when workers' reputation estimates are significantly
inaccurate, the best performance can be obtained by combining our proposed task
assignment algorithm with the LRA decision rule introduced in the literature.
