Dominant players and minimum size coalitions

Abstract

Abstract. In this paper we present a result about Peleg's theory of coalition formation in dominated simple games (Peleg 1981). Further, a connection between Peleg's theory and Riker's minimum size theory (Riker 1962, Riker and Ordeshook 1973) is established. This connection leads to a new theory of coalition formation in simple games.

Making the first move

“…Both of these procedures are based on the idea that the only party feature that matters for formateur selection is a party's size, and a conclusion is thus that large parties, and in particular the largest party, should become the formateur. This is in line with the cooperative game theoretical assertion that in systems dominated by one party, the latter is difficult to exclude (see, e.g., Van Deemen 1989), and with the normative expectation that the party with a vote plurality should have an advantage in government formation since it is likely to form a cabinet reflecting the voters' preferences.…”

The Basic Arithmetic of Legislative Decisions

“…This makes P 1 "dominant" in the sense defined by previous authors (Peleg 1981;Einy 1985;van Deemen 1989), whose definition refers to mutually exclusive losing coalitions made winning by adding the largest party. The intuition is more striking if we consider losing parties, and call party P * "strongly dominant"…”

Computations on Simple Games Using RelView

“…This type of simple games plays a prominent role if game theory is used to model and analyze real political situations. See [7,8], for example.…”

“…This kind of games is very important, e.g., in social choice theory, for the comparison and measurement of influence and power of agents in decision-making processes and for the analysis of social and political situations. In respect of the latter application domain we refer to [7,8,17], for example.…”