We present a method of analyzing the performance of weighted voting algorithms in a fault-tolerant distributed system. In many distributed systems, some processors send messages more frequently than others and all processors share a common communication medium, such as an Ethernet. Typical fault-tolerant voting algorithms require that a certain minimum number of votes be collected from different processors. System performance is significantly affected by the time required to collect those votes. We formulate the problem of weighted voting in terms of probabilistic languages and then use the calculus of generating functions to compute the expected delay to collect that number of votes. An application of the method to a particular voting algorithm, the Total protocol, is given.