In this letter, we investigate the asymptotic performance of categorical decision fusion in a human decision making framework. We assume that multiple human agents send categorized information to a moderator for final decision making. The local categorization is performed via a threshold based scheme where thresholds are assumed to be random variables. Considering the cases where the moderator has the knowledge of exact threshold values as well as when it has only probabilistic information of the individual thresholds, we analyze the asymptotic performance of likelihood ratio based decision fusion at the moderator in terms of the Chernoff information. Numerical results are presented for illustration.