Ranking linear budget sets with different available goods: A note

Xu (2004), Kolm (2004; 2009) and Miyagishima (2009) study the problem of ranking linear budget sets in terms of freedom of choice. In their researches, the set of available goods is fixed. However, there would be cases in which new goods become available due to innovation. Recent examples of such goods include commodities and services relevant to information technology. In this paper, we consider the problem of ranking linear budget sets with different available goods. We introduce axioms which are respectively justified in terms of two notions of freedom, “freedom of choice” and “well-being freedom”, as well as two basic axioms. By using these axioms, we characterize two ranking rules on the basis of the two notions of freedom. Our ranking rules could be used for comparing degrees of freedom in different points of time, or in different countries.