Multidimensional Welfare Aggregation

Most accounts of welfare aggregation in the tradition ofArrow's (1951/1963) and Sen's (1970/1979)social-choice-theoretic frameworks represent the welfare of anindividual in terms of a single welfare ordering or a singlescalar-valued welfare function. I develop a multidimensionalgeneralization of Arrow's and Sen's frameworks, representingindividual welfare in terms of multiple personal welfarefunctions, corresponding to multiple `dimensions' of welfare.I show that, as in the one-dimensional case, the existence ofattractive aggregation procedures depends on certaininformational assumptions, specifically about themeasurability of welfare and its comparability not only acrossindividuals but also across dimensions. I state severalimpossibility and possibility results. Under Arrow-typeconditions, insufficient comparability across individualsleads to dictatorship of a single individual, whileinsufficient comparability across dimensions leads todominance of a single dimension. Given sufficientcomparability both across individuals and across dimensions, arange of possibilities emerges. I discuss the substantiveimplications of the results.