Power Measurement as Sensitivity Analysis
| Date | 01 October 2004 |
| Author | Stefan Napel,Mika Widgren |
| Published date | 01 October 2004 |
| DOI | 10.1177/0951629804046152 |
| Subject Matter | Articles |
POWER MEASUREMENT AS SENSITIVITY
ANALYSIS
A UNIFIED APPROACH
Stefan Napel and Mika Widgre
´n
ABSTRACT
This paper proposes a unified framework that integrates the traditional index-
based approach and the competing non-cooperative approach to power
analysis. It rests on a quantifiable notion of ex post power as the (counter-
factual) sensitivity of the expected or observed outcome to individual players.
Thus, it formalizes players’ marginal impact on outcomes in both cooperative
and non-cooperative games, for both strategic interaction as well as purely
random behavior. By taking expectations with respect to preferences, actions,
and procedures, one obtains meaningful measures of ex ante power. Estab-
lished power indices turn out to be special cases.
KEY WORDS .decision procedures .equilibrium analysis .power indices .
spatial voting
1. Introduction
Scientists who study power in political and economic institutions seem
divided into two disjoint methodological camps. The first one uses non-
cooperative game theory to analyze the impact of explicit decision pro-
cedures and given preferences over a well-defined – usually Euclidean –
policy space.
1
The second one stands in the tradition of cooperative game
Journal of Theoretical Politics 16(4): 517–538 Copyright &2004 Sage Publications
DOI: 10.1177/0951629804046152 London, Thousand Oaks, CA and New Delhi
Our research has been supported by the Center for Interdisciplinary Research (ZiF), Bielefeld,
the Center for Economic Studies (CES), Munich, the Yrjo Jahnsson Foundation, and the
German Academic Exchange Service (DAAD). The paper has benefitted from discussions at
the 2002 San Sebastian Workshop on Modelling the European Decision-making, the 2002
LSE Workshop on Voting Power Analysis, the 2002 Spring Meeting of Young Economists,
the Fifth Spanish Game Theory Meeting, the Third Meeting of Public Economic Theory,
ICM2002 Game Theory and Applications Satellite Conference and the constructive comments
of three anonymous referees, M. Braham, I. Dittmann, M. J. Holler, S. Seifert and F. Valenciano.
1. See, for example, Steunenberg (1994), Tsebelis (1994, 1996), Crombez (1996, 1997) and
Moser (1996, 1997).
theory with much more abstractly defined voting bodies: the considered
agents have no particular preferences and form winning coalitions which
implement unspecified policies. Individual chances of being part of and influ-
encing a winning coalition are then measured by a power index.
2
Proponents of either approach have recently intensified their debate, which
was sparked by the critique by Garrett and Tsebelis (1996), in the context of
decision-making in the European Union (EU).
3
The non-cooperative camp’s
verdict is that ‘power indices exclude variables that ought to be in a political
analysis (preferences, institutions and strategies) and include variables that
ought to be left out (computational formulas and hidden assumptions)’
(Garrett and Tsebelis, 1999a: 337). The cooperative camp has responded by
clarifying the assumptions underlying its power formulas and giving some
reasons for not making institutions and strategies – corresponding to decision
procedures and rational preference-driven agents – more explicit.
4
There also
have been some attempts to include actors’ preferences in the cooperative
approach.
5
Several authors have concluded that it is time to develop a unified frame-
work for measuring decision power (cf. Steunenberg et al., 1999; Felsenthal
and Machover, 2001a).
6
On the one hand, such a framework should allow
for predictions and ex post analysis of decisions based on knowledge of
procedures and preferences. On the other hand, it must be open to ex ante
and even completely a priori
7
analysis of power when detailed information
518 JOURNAL OF THEORETICAL POLITICS 16(4)
2. See, for example, Brams and Affuso (1985a, b), Widgre
´n (1994), Hosli (1993), Laruelle and
Widgre
´n (1998), Baldwin et al. (2000, 2001), Felsenthal and Machover (2001b) and Leech (2002)
for recent applications of traditional power indices. Felsenthal and Machover (1998) and Nurmi
(1998) contain a more general discussion regarding index-based analysis of power.
3. Cf. the contributions to the symposium in Journal of Theoretical Politics 11(3, 1999),
together with Tsebelis and Garrett (1997), Dowding (2000), Garrett and Tsebelis (2001) and
Felsenthal and Machover (2001a).
4. See, in particular, Holler and Widgre
´n (1999), Berg and Lane (1999), Felsenthal and Mach-
over (2001a), and Braham and Holler (2003).
5. See, for example, Straffin (1977, 1988), Widgre
´n (1995), Kirman and Widgre
´n (1995) and
Hosli (2002).
6. Gul (1989) and Hart and Mas-Colell (1996) already give non-cooperative foundations for
the Shapley value and thus indirectly the Shapley–Shubik index.
7. There has been controversy at several workshops on power analysis about the correct usage
of the terms ‘a priori’ and ‘a posteriori’. We use the term ‘ex ante’ to mean ‘before a decision is
singled out or taken’ and the term ‘ex post’ to mean ‘for a particular expected or observed deci-
sion’. We reserve ‘a priori’ to the complete ignorance about any aspect of decision-making other
than – somewhat arbitrarily – voting weights and quota. Note that this definition makes mean-
ingful ex ante or ex post analysis of real institutions for which more information than weights
and quota – e.g. the strategic resources awarded to players by a particular agenda-setting or
multi-stage voting procedure – is known and relevant necessarily ‘a posteriori’.
To continue reading
Request your trial