Browsing by Subject "Monotonicity"

Now showing 1 - 7 of 7

Open Access
Essays on implementability and monotonicity
(2009) Pasin, Pelin
In this thesis we study the implementation problem with regard to the relation between monotonicity and implementability. Recent work in the field has shown that the implementability of a social choice rule strongly depends upon the compatibility between the monotonicity structures of the social choice rule and of the solution concept according to which implementation takes place. Different degrees of monotonicity of the social choice rules and game theoretic solution concepts can be determined via a generalized monotonicity function, strongest of which is called self-monotonicity. In this study, we determine the unique self-monotonicity of the Nash equilibrium concept and show that the monotonicities of a social choice rule are inherited from the unique selfmonotonicity of the Nash equilibrium concept via the mechanisms that implement it. In particular, we show that the essential monotonicity is inherited via the Maskin-Vind type mechanism which is widely used in the characterization results. We also give a new characterization of strong Nash implementable social choice rules via critical profiles. We show that coalitional monotonicity when conjoined with three more conditions is both necessary and sufficient for implementability. Finally we determine a subset of subgame perfect Nash implementable social choice rules that satisfies conditions defined obtained by critical profiles. The results that are obtained in this thesis strongly support the view that implementation theory can be rewritten in terms of monotonicity and that this provides a better understanding of the theory.
Open Access
Explorations on monotonicity in social choice theory
(2007) Doğan, Battal
Due to Maskin (1977), Maskin-monotonicity is known to be a necessary condition for Nash-implementability. Once one classifies social choice rules as the ones which are Maskin-monotonic and those which are not, a natural question one may ask is whether it is possible to further classify the Maskinmonotonic social choice rules according to how strongly monotonic they are. This study utilizes two key notions , namely self-monotonicity and center, which enable us to compare Maskin-monotonic social choice rules among themselves according to the strength of their monotonicities. Moreover, Nashimplementable two-person social choice rules are now characterized via the notion of center, in line with the conjecture that Implementation Theory can be rewritten in terms of monotonicity
Open Access
Implementation via rights structures
(Academic Press, 2018) Koray, Semih; Yildiz, K.
Implementation of socially desirable alternatives can be thought of as a way to design power distribution in a society such that the equilibrium outcomes coincide with the alternatives chosen at each preference profile. In this paper, we introduce a new institutional framework for implementation, which takes power distribution in a society as its point of departure. We use the notion of a rights structure, introduced by Sertel (2001), to formalize the power distribution in a society. We formulate and characterize implementability via rights structures under different specifications, which require having well-defined convergence dynamics and being consistent with farsighted behavior. We identify how implementation via rights structures is related to implementation via mechanisms. In the presence of at least three agents, we find the class of rights structures, implementability via which is equivalent to Nash and strong Nash implementability. We also introduce a strategic counterpart of implementation via rights structures in terms of deviation-constrained mechanisms.
Open Access
Majority voting rule and oligarchic social choice rules
(2001) Pasin, Pelin
In the first part of this study majority voting rule for two alternatives and continuum agents is characterized. As in the finite agent case, symmetry among agents, neutrality between alternatives and positive responsiveness characterize majority voting rule. In the second part, the relation between T-monotonicity and the group which acts as the oligarchy in an oligarchic social choice rule, is analyzed. It is shown that the minimal coalition for which the social choice rule is monotonic constitutes the oligarchy.
Open Access
Self-selective social choice functions verify arrow and gibbard-satterthwaite theorems
(Wiley-Blackwell Publishing Ltd., 2000) Koray, S.
This paper introduces a new notion of consistency for social choice functions, called self-selectivity, which requires that a social choice function employed by a society to make a choice from a given alternative set it faces should choose itself from among other rival such functions when it is employed by the society to make this latter choice as well. A unanimous neutral social choice function turns out to be universally self-selective if and only if it is Paretian and satisfies independence of irrelevant alternatives. The neutral unanimous social choice functions whose domains consist of linear order profiles on nonempty sets of any finite cardinality induce a class of social welfare functions that inherit Paretianism and independence of irrelevant alternatives in case the social choice function with which one starts is universally self-selective. Thus, a unanimous and neutral social choice function is universally self-selective if and only if it is dictatorial. Moreover, universal self-selectivity for such functions is equivalent to the conjunction of strategy-proofness and independence of irrelevant alternatives or the conjunction of monotonicity and independence of irrelevant alternatives again.
Open Access
Some results on monotonicity
(2010) Dindar, Hayrullah
In this thesis, we investigate several issues concerning social choice rules which satisfy different degrees of Maskin type monotonicities. Firstly, we introduce g −monotonicity and monotonicity region notions which enable one to compare monotonicity properties of non Maskin monotonic social choice rules. We compare self-monotonicities of standard scoring rules and study monotonicity of Majoritarian compromise. Secondly we determine domains of impossibility and possibility when the individual preferences are clustered around two opposing norms and the degree of clustering is measured via the M anhattan metric. In the last chapter we investigate the relation between monotonicity and dictatoriality when agents are allowed to have thick indifference classes.
Open Access
Two essays in social choice theory
(2000) Kaya, Ayça
Solution concepts which implement only monotonic social choice rules are characterized in terms of a new notion of monotonicity pertaining to solution concepts. For any given class G of mechanisms, it turns out that a solution concept a implements only monotonic social choice rules via mechanisms in G if and only if a is G-monotonic. Moreover, with each solution concept a, we associate a class G^ of mechanisms such that each a-implementable onto social choice function which takes on at least three different values is dictatorial if and only if a is Go-monotonic. Oligarchic social choice rules are characterized by the conjunction of unanimity and a monotonicity condition, oligarchic monotonicity, which is stronger than Maskin monotonicity. Given an oligarchic social choice rule, the coalition acting as the oligarchy turns out to be the minimal set T of agents such that the social choice mle is Maskin monotonic when the restriction of each profile to T is considered. Finally, the solution concepts which implement only oligarchic social choice rules are characterized in terms of oligarchic monotonicity modified for solution concepts.