OfBorder and Jordan (1983)).
In Barberà, Masso, and Neme (1997) we considered the consequences
of introducing feasibility constraints in that larger framework. The range
of feasible choices is no longer a Cartesian product and this requires a more
complex and careful analysis. All strategy-proof rules are still decomposable,
but choices in the different dimensions must now be coordinated in order to
guarantee feasibility. While this previous paper makes an important step
in understanding how this coordination is attained for each given shape of
the range, it is marred by a strong assumption on the domain of admissible
preferences. Specihcally, we assume there that each agent’ bliss point is
feasible. This assumption is not always realistic. Moreover, it makes the
domain of admissible preferences dependent on the range of feasible choices.
In the present paper we study the question of voting under constraints for
two rich and natural sets of admissible preferences: those that are additively
representable or separable on the power set of K, regardless of the type
of constraints faced by choosers. For clarity of exposition, however, we go
back to the case analysed in Barberà, Sonnenschein, and Zhou (1991), which
allows for only two values in each dimension.
Several authors (Serizawa (1994) and Answal, Chatterji, and Sen (1999))
have studied the consequences of specific restrictions on the range, like budget
constraints or limitations on the number of objects that may be chosen. Our
results apply generally and cover all types of infeasibilities within our context:
ranges of all shapes are allowed.
The paper is organized as follows. Section 2 contains preliminary notation
and definitions as well as previous results. In Section 3 we introduce specific
definitions and notation, obtain preliminary results, and present our two
characterizations: Theorem 1 for additive preferences and Theorem 2 for