MBS 94-26
A Random Utility Model of Subset Choices: New Theory and Applications
Michel Regenwetter
The "Subset Choice" paradigm denotes a situation in which a sample
of decision makers is offered the same set of choice alternatives and asked
to each choose a subset of any size. Building on a "Random Utility Model
for Approval Voting" from Falmagne and Regenwetter (1994), several new
theoretical results as well as the analysis of 30 approval votes are reported.
The main theoretical results are a more detailed analysis of the basic
assumptions showing that an independence axiom in the original paper was
stronger than necessary, two new but equivalent formulations of the "size-independent
model" of subset choices, a representation and uniqueness theorem for the
case of three choice alternatives, a brief study of the stability of the
model under substructures, and various parametrizations of the general
model. The model exhibits good overall performance on the voting data and
gives a detailed description of the voters' support for the candidates
in form of a table - denoting the marginal probability of each candidate
i being ranked at position k in the individual voters' preferences.