A new model of coalition formation

Abstract

In this paper, a new model of multidimensional coalition formation in politics is presented. The model provides an opportunity to analyze a number of different kinds of issues at the same time. A policy space consists of a finite number of independent sub-spaces (policy spaces on certain issues), which can be multidimensional. Any policy sub-space on a certain sub-issue can be either a Euclidean space or (in principle) any other type of set. So, it is possible to include issues which cannot be represented by a Euclidean space or a fixed sum. A government is defined as a pair consisting of a majority coalition and a policy supported by this coalition. The majority coalition may be not minimal winning. Each party is allowed to give one qualification to a policy on a certain issue and to a majority coalition: desirable of a certain degree, acceptable, or unacceptable. By representing party preferences the way we do, we can include both rent-seeking and idealistic motivations in one consistent model. We define the value of a policy/coalition/government to a party, and the notions of a feasible and stable policy/coalition/government. The model uses party preferences in order to predict government policy. Necessary and sufficient conditions for the existence and uniqueness of a stable government are investigated. Moreover, some alternative definitions of a ‘stable’ government are introduced, and relations between these definitions and the chosen definition of a stable government are established. Copyright Springer-Verlag 2005

An interdisciplinary approach to coalition formation

“…In this section, we briefly recall some of the main ideas of the model of coalition formation presented in Rusinowska et al [15], i.e., the notions essential for the application of relational algebra and RelView to the model. Let N be the finite set of political parties and P be the finite set of all policies.…”

“…A precise description of the utility of a government to a party has been given in Rusinowska et al [15]. In Roubens et al [13], the MacBeth technique has been applied to determine these utilities.…”

“…In Rusinowska et al [15] necessary and sufficient conditions for the existence and the uniqueness of stable governments are investigated and, in addition, some variants of the notion of stability are discussed. All this shows that the above definition seems to be the most natural one.…”

“…In Rusinowska et al [15] a government is defined as a pair consisting of a coalition (a set of of parties) and a policy. Different governments may have different utilities (values) for the different parties.…”

A consensus model of political decision-making

“…A policy is a tuple of policies on given issues. In Rusinowska et al (2005), necessary and sufficient conditions for the existence and uniqueness of a stable government are investigated. In this coalition formation model parties are supposed to have preferences regarding each winning coalition and regarding each policy on the given issues.…”