Vote Trading: An Attempt at Clarification
| Date | 01 March 1979 |
| DOI | 10.1111/j.1467-9248.1979.tb01187.x |
| Published date | 01 March 1979 |
| Author | Clifford S. Russell |
| Subject Matter | Article |
VOTE TRADING: AN ATTEMPT AT
CLARIFICATION
CLlFFORD
S.
RUSSELL*
Resources for the Future
Abstruct.
The aim
of
this paper is to clarify the continuing debate about the theoretical
characteristics
of
vote trading.
It
sets about this by first emphasizing existing distinctions
among types of vote trading systems, most importantly, the distinction between trades on
entire platforms characterizing social states (implicit vote trading) and trades on the
individual issues making up the platforms (explicit vote trading). The subdivisions of the latter
type are more carefully explored, with the key results being that: while all vote trading
systems may lead to circularity in the attempt to choose; and while implicit vote trading
inevitably involves such circularity; vote trading over individual, independent issues
may
be
stable. The challenge to the social choice field is therefore to be more careful in specifying the
conditions of foresight, renegotiability and the like, and to compare theoretical systems for
explicit vote trading with actual legislative rules.
INTRODUCTION
THE
study of vote trading has, over the past decade, shown signs of becoming
a respectable
if
slightly remote corner of the broad field of social choice. Papers
have been written proving certain conjectures of earlier writers (for example,
Bernholz, on Downs).’ New and more elegant proofs have been offered for
established propositions (for example, Miller, on the instability
of
implicit
logrolling).2 And a few staple controversies continue to simmer along, absorb-
ing the occasional contribution, but showing no signs of resolution (for
example, the question of the optimality properties
of
vote trading). It is
perhaps not surprising that a subject with such obvious ties to events in real-
world legislatures should be attractive to scholars. In a period when ‘relevance’
is the catch-word, there are definite advantages
to
writing about a
phenomenon with which any regular reader of a major newspaper or any
casual student
of
political biography
or
description will be familiar.3
*
Research for this paper was partially supported by a grant from the Norwegian Research
Council (N.A.V.F.).
I
am grateful to Ed. Haefele, Mancur Olson, Paul Portney, Jon Sonstelie, Eric
Uslaner, and two anonymous referees for very helpful comments on earlier versions. The usual
disclaimer applies.
I
P.
Bernholz, ‘Logrolling, Arrow Paradox and Cyclical Majorities’,
Public Choice,
I5 (1973).
*
N. R. Miller, ‘Logrolling and the Arrow Paradox: A Note’,
Public Choice,
21
(1975). 107-10.
It is worth noting that vote trading
is
not confined to the classic pork-barrel cases; tariffs,
military appropriations, and even civil rights and environmental bills have all been the objects of
trades.
See
R. B. Ripley,
Party
Lecrders
in
the
House
of
Representatives
(Washington, Brookings
Institution, 1967) for a number
of
fascinating examples. More recently, we have seen in the press
details of some fairly exotic ‘side payments’ in the United States Congress.
87-96.
Political
Studies,
Val.
XXVII,
No.
1
(54-70)
CLIFFORD
S.
RUSSELL
55
In addition, however,
I
think interest in the area has been piqued by certain
statements of important contributors; statements which fairly cry out for
careful examination. Buchanan and Tullock, for example, in their discussion of
vote trading (‘explicit logrolling’) conclude that by allowing for the expression
of
preference intensity it prevents ‘the particular type
of
irrationality described
by Arrow’: that is, the cyclical majority of intransitive collective preference
relati~n.~ They recognize that a cardinal system which could produce transitive
social judgements would violate Arrow’s condition of independence of
irrelevant alternatives, but they argue, first, that setting requirements for
‘collective rationality’ is silly, since rationality is a property
of
individuals; and
second, that ruling out the use of information about preference intensities is
especially silly.s Very similar arguments are made by Coleman6 in the
introductory sections of his paper on a market-like vote trading model.
Haefele’s position with respect to vote trading and preference aggregation,
though more carefully worded, seems at least as provocative. Consider the
following passages from his paper,
‘A
Utility Theory of Representative
Government’
:
We have seen, however that once vote trading is allowed the paradox does not hold if
issues are independent. That result is not limited
to
single-peaked preference functions,
which Tullock and Paul Simpson have investigated; nor need
it
come about because of
considerations of utility under uncertainty, as in the work of Coleman; nor does
it
depend on the existence
of
a pseudo-price mechanism, as posited by Robert Wilson.
To
demonstrate this
.
. .
[He gives an example which
1
shall discuss at some length
below.]’
Perhaps even more intriguing is the statement on page
362:
If
the two alternatives [party platforms] are not randomly chosen, but rather are
those two positions, which, when put to
a
vote will result in the same choice as that
chosen by the voters if they engage in vote-trading;
then a method
of
passing from
individual tastes
to
social preferences, excluding inter-personal comparisons
of
utility,
definedfor a wide range
of
sets
of
individual orderings, neither dictatorial nor imposed, is
representative government with a satisfactory two-party system.
(emphasis in original)”
While Haefele does not say
so
explicitly, there are hints here that pairwise
vote trading
on
independent issues is something very special indeed. It appears
that the procedures will lead to social orderings (‘social preferences’) while
certainly satisfying the non-dictatorship condition. Nothing
is
said about the
Pareto condition
or,
in
so
many words, about the independence of irrelevant
alternatives, though in the latter case, the negative references to ‘pseudo-price
mechanisms,’ ‘utility under uncertainty,’ and ‘interpersonal comparisons of
utility’ strongly suggest that Haefele believes there is no violation. In the
second passage there
is
a hedge about the domain, but we must be careful in
J.
Buchanan and
G:
Tullock,
The Calculus
of
Consent
(Ann Arbor, University of Michigan
Buchanan and Tullock,
The Calculus oJConsent,
p.
32.
J.
Coleman, ‘The Possibility
of
a
Social Welfare Function’,
American Economic Review,
56
E.
Haefele, ‘A Utility Theory
of
Representative Government’,
American Economic Review,
61
Press, 1962).
p.
332, note 32.
(1966).
p.
1,106.
(1971).
p.
358.
*
Haefele, ‘A Utility Theory
of
Representative Government’,
p.
362
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