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The paper addresses the problem of aggregating individual choices between three discrete alternatives, and discusses how the likelihood of cyclical aggregate preferences under majority rule depends on social integration in large populations. It is argued that the so-called impartial culture condition gives rather limited information as to the likelihood of the paradox occurring, and an alternative model is outlined. Social structure is introduced, by imposing correlation between the first and second choices. The resulting structure may significantly reduce the likelihood of a cyclical outcome. A measure of similarity between rankings is introduced, and this measure serves as a vehicle for discussing the effects of social integration on the distribution of the population across the six possible rankings of alternatives. It is concluded that integration significantly reduces the likelihood of a cyclical outcome. [ABSTRACT FROM AUTHOR]