The Clarke Tax Algorithm
نویسنده
چکیده
The idea behind the Clarke Tax Algorithm is that a tax will be assessed to each individual. The amount of this tax depends on how the individual’s utilities affect the rest of the group. Since people do not want to pay taxes, a big assessment will decrease an individual’s overall utility. To get a better understanding of this statement, it is helpful to restrict the problem a bit. Formally, the Clarke Tax Algorithm (CTA) is applicable only when utilities are quasilinear. We will discuss the definition of a quasilinear utility shortly, but before we do so it is helpful to review the definitions of a social choice function and a mechanism. Recall that a social choice function is a mapping from the set of possible individual agent types, Θi, to some societal outcome, X . Thus, the social welfare function is given by f : Θ1 × Θ2 × . . . × Θn → X , where n is the number of agents in society. In the case of the Clarke Tax algorithm, the set X consists of some publicly available good g that benefits the individuals in the society. For example, the agents may be getting together to decide whether to build a swimming pool and, if they decide to build it, how big of a pool to build. The social welfare function that we want is the one that maximizes the sum of each agent’s utility over this public good,
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