<P> In voting theory, the Condorcet paradox demonstrates a fallacy of composition: Even if all voters have rational preferences, the collective choice induced by majority rule is not transitive and hence not rational . The fallacy of composition occurs if from the rationality of the individuals one infers that society can be equally rational . The principle generalizes beyond the aggregation via majority rule to any reasonable aggregation rule, demonstrating that the aggregation of individual preferences into a social welfare function is fraught with severe difficulties (see Arrow's impossibility theorem and social choice theory). </P> <Ul> <Li> The paradox of thrift is a notable fallacy of composition described by Keynesian economics . </Li> <Li> Division of labour is another economic example, in which overall productivity can greatly increase when individual workers specialize in doing different jobs . An individual worker may become more productive by specializing in making, say, hatpins, but by satisfying the wants of many other individuals for a given product, the specialist worker forces other workers to specialize in making different things . What is true for the part (earning more by investing in the skills or equipment to make a given product faster) is not true for the whole (because not everybody can profitably make the same product). </Li> <Li> Economists use the term representative agent to refer to the typical decision - maker of a certain type (for example, the typical consumer, or the typical firm); when this representative agent is poorly chosen in a model, it can be seen as a fallacy of composition . </Li> <Li> In a tragedy of the commons, an individual can profit by consuming a larger share of a common, shared resource such as fish from the sea; but if too many individuals seek to consume more, they can destroy the resource . </Li> <Li> In the free rider problem, an individual can benefit by failing to pay when consuming a share of a public good; but if there are too many such "free riders", eventually there will be no "ride" for anyone . </Li> </Ul> <Li> The paradox of thrift is a notable fallacy of composition described by Keynesian economics . </Li> <Li> Division of labour is another economic example, in which overall productivity can greatly increase when individual workers specialize in doing different jobs . An individual worker may become more productive by specializing in making, say, hatpins, but by satisfying the wants of many other individuals for a given product, the specialist worker forces other workers to specialize in making different things . What is true for the part (earning more by investing in the skills or equipment to make a given product faster) is not true for the whole (because not everybody can profitably make the same product). </Li>

Who came up with the fallacy of composition