Browsing by Subject "Social Choice"

Now showing 1 - 6 of 6

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
Explorations on X-self selectivity
(2017-09) Kerman, Toygar
X-self selectivity of a social choice function is de ned as being self selective relative to the set of test functions X and all of its subsets. We explore the self-selectivity of social choice functions which satisfy independence of irrelevant alternatives, against di erent kinds of sets of test functions. We observe that testing against a smaller set can be su cient to deduce that a given social choice function is also self-selective relative to a larger set, under certain conditions. Moreover, we show that X-self selectivity is closed under set intersection and union. This leads to the notion of degree of self-selectivity, which allows us to compare the self-selectivities of two social choice functions under certain conditions.
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
Median rule and majoritarian compromise
(2013) Polat, Ali Oğuz
In this thesis, we analyze the relationship between Majoritarian Compromise (Sertel & Yılmaz, 1984) and the Median Rule (Basset & Persky, 1999). We show that, for the populations with odd size, these two rules are equivalent and we describe the relationship for the case where population size is even. Then, we explore some axiomatic properties of Median Rule. It turns out that Median Rule satisfies all properties that Majoritarian Compromise satisfies in Sertel and Yılmaz (1999) and it fails all properties that Majoritarian Compromise fails in Sertel and Yılmaz (1999). We, then, introduce two axioms which differentiate these rules. We conclude that, the Median Rule can be considered as a viable alternative to Majoritarian Compromise, as it satis- fies all axioms that Majoritarian Compromise is known to satisfy except one particular axiom.
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.
Open Access
Universally selection-closed families of social choice functions
(2009) Şenocak, Talat
In this thesis, we introduce a new notion of consistency for families of social choice functions, called selection-closedness. This concept requires that every member of a family of social choice functions that are to be employed by a society to make its choice from an alternative set it faces, should choose a member of the given family, when it is also employed to choose the social choice function itself in the presence of other rival such functions along with the members of the initial family. We show that a proper subset of neutral social choice functions is universally selection-closed if and only if it is a subset of the set of dictatorial and anti-dictatorial social choice functions. Finally, we introduce a weaker version of selection-closedness and conclude that a “rightextendable scoring correspondence” is strict if and only if the set consisting of its singleton valued refinements is universally weakly selection-closed.