Power distribution in the electoral body with an application to the Russian Parliament

This paper presents several new approaches to evaluate power distribution in an electoral body. We define the index of consistency of two groups’ positions (briefly, the consistency index) which is used to separate possible coalitions in the Parliament. This allows to analyze power distribution within restricted coalition formations. Then we provide several new power indices for the case in which the intensity of factions to coalesce is taken into account. Our analysis of the power distribution model extends the one proposed by Shapley-Owen. A new consistency index is given allowing to construct such an extension. We illustrate these approaches via the analysis of power distribution among factions in the Russian Parliament (Duma) from 1993 to 2005.

Power indices taking into account agents' preferences

A set of new power indices is introduced extending Banzhaf power index and allowing to take into account agents’ preferences to coalesce. An axiomatic characterization of intensity functions representing a desire of agents to coalesce is given. A set of axioms for new power indices is presented and discussed. An example of use of these indices for Russian parliament is given.

Relational-Functional Voting Operations

The operators which transform binary relations of voters to collective choice function are studied. The conditions on operators are given, the main one is the condition of locality. The explicit form of operators for special subclass of local operators is obtained. All study are made in terms of special language—list-form representation of operators

Functional Voting Operators: The Non-Monotonic Case

We extend the non-binary framework of social choice introduced by Aizerman and Aleskerov (1986) , in which individual choice functions are aggregated into a social choice function, by considering non-monotonic operators. We characterize the class of "local" operators and provide the explicit forms of local operators satisfying various combinations of normative and rationality conditions in the absence of monotonicity. Surprisingly, the restriction of monotonicity is not binding for operators satisfying the usual rationality conditions. We identify two rationality restrictions which do admit non-monotonic operators. One restriction admits every sovereign and neutral operator, and the other admits only dictatorship and anti-dictatorship operators. This last result is a direct non-binary counterpart to Wilson's (1972) theorem

Multicriterial ranking approach for evaluating bank branch performance

14 ranking methods based on multiple criteria are suggested for evaluating the performance of the bank branches. The methods are explained via an illustrative example, and some of them are applied to a real-life data for 23 retail bank branches in a large-scale private Turkish commercial bank

Binary Relations, Numerical Comparisons with Errors and Rationality Conditions for Choice

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Relational-Functional Voting Operations

The operators which transform binary relations of voters to collective choice function are studied. The conditions on operators are given, the main one is the condition of locality. The explicit form of operators for special subclass of local operators is obtained. All study are made in terms of special language—list-form representation of operators