Universal and Symmetric Scoring Rules for Binary Relations
نویسنده
چکیده
Are Plurality voting, the Kemeny rule, Approval voting, and the Borda Mean Dichotomy rule all versions of the same voting rule? Yes, in a sense. In an extension of work by Barthélemy and Monjardet [3], we consider functions F that assign real number scoring weights F (R1, R2) to pairs of binary relations on a finite set A of alternatives, serving as symmetric measures of similarity between R1 and R2. Any such F induces a symmetric binary relational scoring rule F – an abstract aggregation rule with arbitrary binary relations as ballots R1 and as aggregated outcomes R2. The level of generality is surprisingly effective. By restricting the classes of relations allowed as ballots and elections outcomes, F yields more familiar and concrete scoring rules. The symmetric assignment F , for example, arises from an inner product in a simple and natural way, and restrictions of the induced scoring rule F yield all the aformentioned familiar voting rules. Moreover, the inner product formulation yields a Euclidean form of distance rationalization for F , resulting in a universal distance rationalization for all concrete scoring rules obtained as restrictions.
منابع مشابه
Fuzzy number-valued fuzzy relation
It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...
متن کاملPutting Peer Prediction Under the Micro(economic)scope and Making Truth-Telling Focal
Peer-prediction [18] is a (meta-)mechanism which, given any proper scoring rule, produces a mechanism to elicit privately-held, non-verifiable information from self-interested agents. Formally, truth-telling is a strict Nash equilibrium of the mechanism. Unfortunately, there may be other equilibria as well (including uninformative equilibria where all players simply report the same fixed signal...
متن کاملWave Propagation in a Layer of Binary Mixture of Elastic Solids
This paper concentrates on the propagation of waves in a layer of binary mixture of elastic solids subjected to stress free boundaries. Secular equations for the layer corresponding to symmetric and antisymmetric wave modes are derived in completely separate terms. The amplitudes of displacement components and specific loss for both symmetric and antisymmetric modes are obtained. The effect of ...
متن کاملGeneration of Bangla Text from Universal Networking Language Expression
This paper presents a work on generating Bangla sentences from an interlingua representation called Universal Networking Language (UNL). UNL represents knowledge in the form of semantic network like hyper-graphs which contains disambiguated words, binary semantic relations, and speech act like attributes associated with the words, assisted by the semantically rich lexicon and a set of analysis ...
متن کاملDevelopment of a novel method in TRMC for a Binary Gas Flow Inside a Rotating Cylinder
A new approach to calculate the axially symmetric binary gas flow is proposed Dalton’s law for partial pressures contributed by each species of a binary gas mixture (argon and helium) is incorporated into numerical simulation of rarefied axially symmetric flow inside a rotating cylinder using the time relaxed Monte-Carlo (TRMC) scheme and the direct simulation Monte-Carlo (DSMC) method. The res...
متن کامل