Abstract
One unit of a good has to be divided among a group N of individuals who each
are entitled to a minimal share and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic. The resulting rules are what we refer to as N-path choice functions. If there are only three individuals, the monotonicity property can be weakened. We also consider the issue of rationalizability and show that, for the threeagent
case, excluding cycles of length three in the revealed preference relation implies the strong axiom of revealed preference, that is, the exclusion of cycles of any length.
are entitled to a minimal share and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic. The resulting rules are what we refer to as N-path choice functions. If there are only three individuals, the monotonicity property can be weakened. We also consider the issue of rationalizability and show that, for the threeagent
case, excluding cycles of length three in the revealed preference relation implies the strong axiom of revealed preference, that is, the exclusion of cycles of any length.
| Original language | English |
|---|---|
| Publisher | Maastricht University, Graduate School of Business and Economics |
| DOIs | |
| Publication status | Published - 5 Dec 2017 |
Publication series
| Series | GSBE Research Memoranda |
|---|---|
| Number | 030 |
JEL classifications
- d11 - Consumer Economics: Theory
- d71 - "Social Choice; Clubs; Committees; Associations"
Keywords
- choice functions
- simplex domain
- rationalizability