5 research outputs found
A note on extended stable sets
Contains fulltext :
160073pub.pdf (publisher's version ) (Open Access)We study abstract decision problems by introducing an extended dominance
relation with respect to a set of alternatives. This extension is in between the traditional
dominance relation as formulated by Von Neumann and Morgenstern (Theory
of games and economic behavior, Princeton University Press, Princeton, 1944) and
the transitive closure of it. Subsequently, stable sets are defined and studied for this
extended relation. We formulate a characterization of stable sets for this relation and
an existence theorem. Finally, we discuss its relation with Von Neumann–Morgenstern
stable sets and generalized stable sets.12 april 201
Preference aggregation theory without acyclicity: The core without majority dissatisfaction
Acyclicity of individual preferences is a minimal assumption in social choice
theory. We replace that assumption by the direct assumption that preferences
have maximal elements on a fixed agenda. We show that the core of a simple game
is nonempty for all profiles of such preferences if and only if the number of
alternatives in the agenda is less than the Nakamura number of the game. The
same is true if we replace the core by the core without majority
dissatisfaction, obtained by deleting from the agenda all the alternatives that
are non-maximal for all players in a winning coalition. Unlike the core, the
core without majority dissatisfaction depends only on the players' sets of
maximal elements and is included in the union of such sets. A result for an
extended framework gives another sense in which the core without majority
dissatisfaction behaves better than the core.Comment: 27+3 page
The Banks set and the Uncovered Set in budget allocation problems
We examine how a society chooses to divide a given budget among various regions, projects or individuals. In particular, we characterize the Banks set and the Uncovered Set in such problems. We show that the two sets can be proper subsets of the set of all alternatives, and at times are very pointed in their predictions. This contrasts with well-known "chaos theorems," which suggest that majority voting does not lead to any meaningful predictions when the policy space is multidimensional