This paper develops a constrained expectation maximization algorithm (CEM) that improves the accuracy of truth estimation in unguided social sensing applications. Unguided social sensing refers to the act of leveraging naturally occurring observations on social media as 'sensor measurements', when the sources post at will and not in response to specific sensing campaigns or surveys. A key challenge in social sensing, in general, lies in estimating the veracity of reported observations, when the sources reporting these observations are of unknown reliability and their observations themselves cannot be readily verified. This problem is known as fact-finding. Unsupervised solutions have been proposed to the fact-finding problem that explore notions of internal data consistency in order to estimate observation veracity. This paper observes that unguided social sensing gives rise to a new (and very simple) constraint that dramatically reduces the space of feasible fact-finding solutions, hence significantly improving the quality of fact-finding results. The constraint relies on a simple approximate test of source independence, applicable to unguided sensing, and incorporates information about the number of independent sources of an observation to constrain the posterior estimate of its probability of correctness. Two different approaches are developed to test the independence of sources for purposes of applying this constraint, leading to two flavors of the CEM algorithm, we call CEM and CEM-Jaccard. We show using both simulation and real data sets collected from Twitter that by forcing the algorithm to converge to a solution in which the constraint is satisfied, the quality of solutions is significantly improved.