Population estimates and decennial census populations are used as the basis for funding from the Federal government to the States and from the States to their localities. These funds are often allocated on a per capita basis. Depending on the law, either the latest decennial or estimated population is used for funding. Likewise, it is often possible for a locality to either conduct a special census or to challenge its estimate. This paper models these processes by assuming that each locality possesses a rational agent who has perfect information about the structure of the model and acts to maximize the locality's income. The actor's cost-benefit analysis is modeled. Challenges are assumed to be costless and lead to a ceteris paribus prediction that the locality's population does not affect its probability of a challenge. Special censuses are costly and lead to a ceteris paribus prediction that the probability of a special census increases with the population size. Implications of these results for population estimates are explored. Statistical tests find that the probabilities of special censuses and challenges both increase in population size.