Introduction

Influence is a crucial element in any decision-making institution. The role of the decision-making rules or, more generally, institution design, is to affect power relations in institutions where decisions are made.

Quantitative analysis of decision-making rules can be divided into two parts: one based on cooperative games and the other on noncooperative games. Recently, there has been a lively debate between two schools of thought on the appropriate tools and approaches for assessing and designing different constitutional decision-making rules.

Scholars of cooperative game theory apply different power indices to assess the effects of different decision-making rules on actors' influence in decision making. The considered agents have no particular preferences and form winning coalitions that then implement unspecified policies. Individual chances of being part of and influencing a winning coalition are then measured by a power index. The actual distribution of power can be evaluated by defining some desirable distribution of actors' power.

The second approach uses noncooperative game theory to analyze the impact of explicit decision procedures and given preferences over a well-defined policy space. In this approach, conclusions are based on equilibrium analysis. This requires more detailed information regarding the players' preferences. As such, the noncooperative approach is not suitable for the design of constitutional rules, but by considering several realizations of actors' preference configurations, one is able to draw conclusions on the performance of the constitutional rules.