In Defence of Voting Power Analysis
| Author | Dennis Leech,Christian List,Dan S. Felsenthal,Moshé Machover |
| Published date | 01 December 2003 |
| Date | 01 December 2003 |
| DOI | http://doi.org/10.1177/146511650344005 |
| Subject Matter | Conference |
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European Union Politics
Forum section I
[1465-1165(200312)4:4]
Volume 4 (4): 473–497: 038140
Copyright© 2003
In Defence of Voting Power
SAGE Publications
London, Thousand Oaks CA,
Analysis
New Delhi
Responses to Albert
Dan S. Felsenthal
University of Haifa, Israel, and Voting Power and Procedures Project,
CPNSS, London School of Economics and Political Science, UK
Dennis Leech
University of Warwick, UK, and Voting Power and Procedures Project,
CPNSS, London School of Economics and Political Science, UK
Christian List
Australian National University and London School of Economics and
Political Science, UK
Moshé Machover
King’s College, London, UK, and Voting Power and Procedures Project,
CPNSS, London School of Economics and Political Science, UK
1 The voting power approach: Response to a
philosophical reproach
Dan S. Felsenthal and Moshé Machover
Introduction
Despite its title, ‘The Voting Power Approach: Measurement without Theory’,
Albert’s (2003) philosophical critique, which appeared in a previous issue of
this journal, is actually directed against the theory of the measure of a priori
voting power, based on the intuition of voting power as I-power. This theory,
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European Union Politics 4(4)
founded by Penrose (1946, 1952), is presented in detail in our book (Felsen-
thal and Machover, 1998) and briefly outlined in Felsenthal and Machover
(2000). As we shall see, Albert has his own reasons for avoiding the terms
‘theory’ and ‘measure’ in this connection; but we have no such reason and
we shall speak of the ‘Penrose measure’ (using this term to refer also to its
derivatives and refinements)1 and the ‘Penrose theory’.
A priori voting power is the component of actual (or a posteriori) voting
power that voters derive solely from the decision rule itself – computed
without regard to (or in ignorance of) all information about the personality
of the voters (their specific interests and preferences, relations of affinity or
disaffinity between them) – and the nature of the bills to be voted upon.
Coleman (1971: 297) aptly describes it as ‘formal power as given by the consti-
tutional rules of a collectivity’.2
I-power is the notion of voting power as a voter’s degree of influence
over the outcome – under a specified decision rule – of a division of a decision-
making body: whether a proposed bill is approved or rejected. Albert does
not seem to have any philosophical objection to the alternative, P-power,
notion of voting power, which regards a decision rule as a simple coopera-
tive game with transferable utility and conceptualizes voting power as a
voter’s relative share in a fixed total payoff.3
Albert has two fundamental philosophical objections to the Penrose
theory. First, he claims that this theory is inapplicable to the real world
because it cannot be used for purposes of prediction or explanation.4 Second,
he alleges that the Principle of Insufficient Reason, which underlies the Penrose
measure, is unsound. We shall rebut these two objections in the next two
sections.
Is the Penrose theory applicable?
Albert spends considerable space arguing that the Penrose theory (or, as he
insists on calling it, ‘the VP approach’) is not empirical. He could have saved
himself the trouble: the theory is avowedly about a priori voting power; and,
if ‘a priori’ means anything, it means ‘prior to or independent of experience;
contrasted with “a posteriori” (empirical)’ (Cambridge Dictionary of Philosophy,
1995: 29). So much is uncontroversial. Nevertheless, as we shall show, this
theory is applicable to the real world and does lead to empirically testable
predictions.5
What is somewhat eyebrow-raising is Albert’s rather extreme disparage-
ment of, not to say hostility towards, non-empirical theories. This is made
quite evident by his choice of terminology. On page 356 he tells us that
‘[a]mong the sciences, one must distinguish between formal sciences, such as
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Felsenthal, Leech, List and Machover
In Defence of Voting Power Analysis
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logic and mathematics, on the one hand, and factual sciences, such as physics
or economics, on the other.’ This choice of terminology is very tendentious:
is the proposition 2 + 2 = 4 or Fermat’s last Theorem any less factual than
Gresham’s Law or the Law of Diminishing Marginal Utility? It seems that for
Albert only empirical facts are really factual; the truths of mathematics, ‘even
truths about numbers’, are, he asserts, ‘empty’, because they ‘do not tell us
anything about the physical or social world. . . . At least according to the
prevailing view, mathematics provides only a language for (some of) the
factual sciences’ (pp. 356–7). Perhaps this is the prevailing view in certain
doctrinaire philosophical circles; but most scientists are aware that mathe-
matics provides not merely a language but also, at the very least, an indis-
pensable deductive apparatus for various sciences.
The status of mathematics is relevant to Albert’s polemic, because of the
following assertion he makes about the Penrose theory: ‘Viewed as a scien-
tific theory, it is a branch of probability theory and can safely be ignored by
political scientists (p. 351)’. The first half of this assertion is arguable. But the
second half – if it has any connection at all to the first half – implies that
probability theory as a whole, of which the Penrose theory is (allegedly) but
a branch, can safely be ignored by political scientists. In our view, prudent
political scientists should ignore this fundamentalist philosophical advice.
Because the Penrose theory is non-empirical, Albert not only prefers to
refer to it as a mere ‘approach’ but would even deny it the right to speak of
‘measuring’: ‘Felsenthal and Machover . . . talk as if they were using a positive
theory.6 For instance, . . . [they] repeatedly speak of “measuring” voting
power. But this is a paradigmatic case of measurement without theory’ (p.
359). Measuring is presumably a prerogative of empirical science; hence the
title of his paper. Yet pure mathematics – that non-factual science of empty
truths – abounds with talk of ‘measuring’: one of Archimedes’ best-known
works is On the Measurement of the Circle; and modern pure mathematics has
an important branch (which, as it happens, encompasses probability theory)
called ‘measure theory’.
Albert is much occupied with categorizing the Penrose theory: is it part
of political science (he thinks it isn’t), or a branch of probability theory (he
thinks it is), or perhaps political philosophy (he thinks that under an ‘alterna-
tive interpretation’ it may be). We think that it may partake of all three
branches of knowledge – depending, of course, on how their boundaries are
defined. But we are not really worried about this kind of demarcation dispute,
beloved of certain taxonomically-minded philosophers of science. What we
do wish to argue is that the Penrose theory is applicable and useful in a
political and constitutional context.
Contrary to the impression Albert wishes to create, the Penrose theory
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can and does lead to empirically testable predictions. Here is an example. One
of the concepts of the theory is the a priori probability A that a decision-
making body acting under a given decision rule will adopt a bill rather than
blocking it.7 A is not directly observable, because in the real world decision-
making is mediated by voters’ preferences and other behavioural factors.
However, A does have a definite effect on the actual propensity of the decision-
making body to adopt proposed bills. We have shown (Felsenthal and
Machover, 2001b) that the decision rule known as ‘qualified majority vote’
(QMV) prescribed by the Treaty of Nice for an enlarged 27-member EU
Council of Ministers has reduced the value of A – in other words, lengthened
the a priori odds against a bill being adopted – to such drastic extent,
compared with its past and current values, that the engine of diplomacy will
have great difficulty overcoming this hidden but very real obstacle. On these
grounds we predict in that, if the quota of the QMV rule for the enlarged
Council of Ministers is not considerably lowered, the body will tend to get
bogged down in immobilism. This is a definite prediction of an observable
phenomenon, made on the basis of the Penrose theory.8
However, the main application of the Penrose theory – certainly its
intended aim – is not as a predictive or descriptive tool but as a prescriptive
normative one. Here it may be noted, that the main aim and intended appli-
cation of game theory – a theory that Albert holds up for praise and emula-
tion as truly scientific, in contrast to the ‘VP approach’ – is also normative.
Although game-theoretic models are now used for explaining various empiri-
cal phenomena (such as evolutionary equilibria), the main purpose for which
game theory was invented is as a normative guide for ‘rational behaviour’ in
certain situations of conflict.9
Although the Penrose theory can also be used to prescribe rational behav-
iour in precisely the game-theoretic sense,10 its main prescriptive application
is in the analysis and design of decision rules, especially as part of the consti-
tutional design of a decision-making body. In this connection it is vital to
focus on ‘formal [voting] power, as given by the constitutional rules of a
collectivity’ (Coleman, 1971:...
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