Voting by Committees under Constraints



conditions (1), (2), and (3) of Theorem 1. Since F is non-dictatorial the
minimal Cylindric decomposition of
Rf cannot consist of just one section
with strictly more than two active components (by (3)). Now, notice that
when preferences are separable but not additively represent able, the active
components of a section can be ordered differently among themselves, de-
pending on which objects are present in another section. This can now be
used to show that we cannot have a section with more than two active com-
ponents together with another section with more than one active component.
To prove it, it is enough to construct profiles where the presence of an object
affects the ordering of the active components in another section. Therefore,
all sections have either only one active component (the objects that are al-
ways selected) or they have just two active components which are of the form
{{0}, {^}}. Hence, all sections in the minimal Cylindric decomposition of
Rf
are singletons.

4 Final Remark

Until now, we have taken the dimension of our problems (i.e., the number
of objects), as well as the feasibility constraints, as given data. Our analysis
admits another reading without any formal change, except for its interpreta-
tion.

Consider a situation where society faces four alternatives, ɑ, b, c, and d.
One possibility is that each of these alternatives might be described by two
characteristics, and that identifying
a = (0,0), b = (1,0), c = (0,1), and
d = (1,1) provides a good description of the actual choices (this particular
choice would indicate that
a and c are similar in the first characteristic but
differ on the second, etc.). It may also be, in another extreme, that these four

19



More intriguing information

1. BEN CHOI & YANBING CHEN
2. Survey of Literature on Covered and Uncovered Interest Parities
3. Giant intra-abdominal hydatid cysts with multivisceral locations
4. A Note on Costly Sequential Search and Oligopoly Pricing (new title: Truly Costly Sequential Search and Oligopolistic Pricing,)
5. The name is absent
6. The Dynamic Cost of the Draft
7. The name is absent
8. The name is absent
9. Towards a framework for critical citizenship education
10. The name is absent
11. Before and After the Hartz Reforms: The Performance of Active Labour Market Policy in Germany
12. Educational Inequalities Among School Leavers in Ireland 1979-1994
13. PROFITABILITY OF ALFALFA HAY STORAGE USING PROBABILITIES: AN EXTENSION APPROACH
14. The Determinants of Individual Trade Policy Preferences: International Survey Evidence
15. ARE VOLATILITY EXPECTATIONS CHARACTERIZED BY REGIME SHIFTS? EVIDENCE FROM IMPLIED VOLATILITY INDICES
16. The name is absent
17. The Value of Cultural Heritage Sites in Armenia: Evidence From a Travel Cost Method Study
18. Robust Econometrics
19. Changing spatial planning systems and the role of the regional government level; Comparing the Netherlands, Flanders and England
20. TOWARDS THE ZERO ACCIDENT GOAL: ASSISTING THE FIRST OFFICER MONITOR AND CHALLENGE CAPTAIN ERRORS