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We present an analytic solution for a race model of n stochastic accumulators for multiple choice reaction time. We show that to maintain a constant level of accuracy, the response criterion needs to be increased approximately logarithmically with n, to compensate for the increase with n in the likelihood that an incorrect alternative will be most active after any fixed amount of time accumulating information. Assuming that participants monitor and maintain a constant level of performance can then explain the logarithmic dependency of the response latency on n as specified by Hick's law. Moreover, we show that for short time intervals, the Shannon information that observers extract from a stimulus, is predicted to increase linearly with processing time.