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We could assume that within the consumer™s affordable set of points there in this sense is not considered a problem. Instead, the assumption of strict-
is a conceivable ˜bliss point™, that is, a point where the consumer is ness is criticized for being ˜too strong™ because it is felt that we do not need
satiated, as illustrated with point M in Figure 12.3. If the consumer has a ˜uniqueness proofs™. For example, we may be able to narrow the choice to a
relatively large budget or income (e.g. the budget line furthest from the set of points on the flat portion of the highest indifference curve but the
origin in Figure 12.3), then the consumer™s choice is immediately narrowed choice within that set is quite arbitrary (see points between G and H in
to point M since the consumer will not want more of either good even Figure 12.3). Accepting arbitrariness (so as to avoid ˜strong™ assumptions)
though he or she can afford more of both. While assuming that the may be a helpful method for avoiding arguments over the ˜realism of
individual can afford his or her bliss point would allow us to narrow the assumptions™, but it certainly will not help us to explain why the one point
was chosen over all others.5 Such willingness to avoid strong assumptions
choice it does so by making the prices irrelevant. Since one reason for
developing a theory of the consumer™s demand is to explain how prices are merely leads to arbitrariness without explanation. Since the consumer can
determined in the market, a theory of the consumer which makes prices only choose one point at any single point in time, neoclassical consumer
irrelevant will not be very useful. For this reason, orderings which allow theory must be able to explain not only why the one point was chosen but
˜bliss points™ are usually ruled out. 3 A more common assumption is that the also why all other affordable points were not chosen. Along the lines of the
consumer faces a ˜strictly convex™ preference ordering. Technically two-step procedure noted at the beginning of this section, the assumption of
speaking, a strictly convex ordering is one for which, if we draw a straight a strictly convex preference ordering appears to be essential since it does
line between any two points of equivalent rank, all other points on that line help solve the problem of assuring a unique best point without making
will be preferred to the end points. In Figure 12.3 there are two indifference prices irrelevant.
curves that would be ruled out by an assumption of a strictly convex
preference ordering, namely, the indifference curve through point B and the
AD HOC VS ARBITRARY
one through point C.4
A slight digression on these words ˜ad hoc™ and ˜arbitrary™. The ad hoc
Y characteristic of any assumption is not necessarily a criticism since
Budget lines
assumptions are usually conjectures or guesses as to the nature of the
Indifference curves universe. If the purpose of constructing any theory (i.e. specifying a set of
assumptions) is to attempt to understand some aspect of our universe, then
any ad hoc assumption which would insulate our understanding (viz. our
K
J theory) from criticism or from critical testing is to be avoided unless it too
can be open to criticism. An assumption is arbitrary if we are unwilling to
M
give reasons for why the assumption might be true independently of the
N
G A purposes of the theory itself. Arbitrariness often occurs when the
B possibility of an infinite regress arises, such as when we ask for reasons for
L
E
our reasons for our reasons ... , then arbitrarily stop to say that we will give
C
F H
no more reasons in this chain. Such arbitrariness is problematic only when
D
we are expected to go on, for example when our reasons are suspect and are
to be criticized. These methodological concepts play an important role in
X the understanding of the dissatisfaction with L-orderings.
Figure 12.3 Alternative budget lines and indifference curves

MULTIPLE CRITERIA VS L-ORDERINGS IN A CHOICE
Since neoclassical consumer theory claims to be able to explain why an
PROCESS
observed point on the budget line was chosen, the assumption that there
exists a strictly convex ordering may merely be ad hoc (since it is sufficient Since all creations of human beings can be considered to be solutions to
for the intended job “ to explain a unique point). But of course, ad hocness
specific problems, we can ask, ˜What is the problem solved by such and
© LAWRENCE A. BOLAND
172 Principles of economics Lexicographic orderings 173
such tool or assumption?™ Of course, it is sometimes necessary to the ordering is incomplete, another type of discontinuity. A slightly more
conjecture the problem since the creator of the tool (or idea) may not have general case is illustrated in Figure 12.5 where the consumer compares any
been successful in realizing his or her intention. And, regardless of success, two points by means of two separate criteria rather than by amounts of the
the unintended consequences may still be interesting. It turns out that the goods themselves.
L-ordering is usually seen to be an attempt to solve a problem created by
Y
the mere existence of more than one relevant non-economic ordering for
Criterion I
any choice (among bundles or points in goods-space). While multiple
criteria are sometimes necessary to ˜narrow the choice™, as noted above, if
C′
the goods-space in question contains an infinity of points (such as when Criterion II
assuming infinite divisibility) we cannot always narrow the choice to one
point in the two-step manner of neoclassical theory.
B
Y

˜better-than™
(? set) set
A
D′
C B
E

A D
X
F
Figure 12.5 Multiple criteria
˜worse-than™
set In Figure 12.4, without in some way ordering the two goods themselves
(? set)
the consumer cannot compare points C and D. Similarly, in Figure 12.5,
without ranking the criteria themselves the consumer is unable to compare
similar points C¢ and D¢. Now, in either case, if the consumer ranks the
X criteria lexicographically he or she can compare these points. For example,
Figure 12.4 Incomplete ordering in Figure 12.5, if the consumer first orders by Criterion I, then by Criterion
II, the consumer would say that D¢ is preferred to C¢. So we can see that, at
To understand more clearly the problem thought to be solved by least, L-orderings can help do the job of narrowing the choice to a single
assuming that any consumer™s preferences can be represented by an point (on the given budget line). However, they do so at the cost of
L-ordering, let us consider a situation where a person has multiple criteria (possible) arbitrariness. If Criterion II were given priority over Criterion I,
that are not ordered in any way “ that is, a situation only slightly different the consumer would then prefer point C¢ to point D¢. In other words,
from the example of Figure 12.1. Specifically, in Figure 12.4, the consumer changing the ordering of the criteria changes the ordering of the points in
claims to be better off if he or she has more of either good. This would question.
mean the consumer cannot compare point A with points not in the ˜better To explain completely the rank ordering of the points we must explain
than™ or ˜worse than™ sets (the cross-hatched areas). With such an the consumer™s rank ordering of the criteria. Should the ordering of
application of this non-ordered criterion, we have ˜holes in the map™ since orderings be lexicographic, or should we opt for some ad hoc utility
there are large areas where there are many points (such as E and F) which function over the criteria such as the higher-level utility function that is
represent more of one good and less of the other. Without introducing more integral to Kelvin Lancaster™s well-known characteristics approach to
consumer theory,6 we could try to order the criteria lexicographically.
criteria, points in these ˜holes™ cannot be compared with point A and thus
© LAWRENCE A. BOLAND
174 Principles of economics Lexicographic orderings 175
Opting for the exclusive use of L-orderings in our explanation in order to UTILITY FUNCTIONS VS L-ORDERINGS
avoid the ad hoc assumption of a monotonic utility function (as in either
Now the importance of this digression is to argue that, when viewed as
Lancaster™s or the ordinary neoclassical approach to the explanation of
alternative to a static utility function, any L-ordering may only be slightly
consumer choice) leads, however, to an infinite regress.
better than a self-referring infinite regress as opposed to a jeopardizing
infinite regress. It is difficult to see how anything new can be brought into
THE INFINITE REGRESS VS COUNTER-CRITICAL ˜AD the infinite regress of an L-ordering method of explaining consumer
HOCERY™ behaviour in the two-step manner of neoclassical demand theory. That is,
nothing new may be put at stake except the next higher L-ordering in the
This observation leads me to another digression. When does the possibility
regress. This criticism of L-orderings, however, cannot be considered an
of infinite regress indicate that an explanation may be inadequate? The
argument in favour of any utility functions which are clearly ad hoc.
answer is clearly that any model which involves a continually self-referring
Counter-critical ˜ad hocery™ cannot be any better than the infinite regress of
infinite regress cannot be considered an adequate explanation. For
˜learning only by experience™.
example, we cannot say that we ˜learn only from experience™ because we
Casual empiricism might indicate that lexicographic behaviour is more
can always ask the self-referencing question ˜How did we learn that we
prevalent than utility maximization primarily because, as a multi-step
learn from experience?™ and to be consistent we must answer that we
process, an L-ordering is easier to learn or teach than a static utility
learned that by experience. This leads to an infinite regress which is
function. Utility maximization may even require more introspective, more
impossible to stop except by violating the original proposition. In such a
self-reliant individuals than is allowed by modern, highly structured
regress nothing new or different is brought into the argument regardless of
societies where self-reliant individualism is not always appreciated. The
how many steps we go back in the regress.
neoclassical theorist™s rejection of L-orderings and the assumption of the
In contrast to this extreme example we can have an infinite regress
existence of utility functions have only been supported by the assumption
which puts more and more at stake with each step of the argument. The
that the neoclassical theory of the consumer is true (i.e. that consumers act
latter type of infinite regress is typical of any theoretical science. One
to maximize their utility in a two-step manner using a static utility
begins usually with some proposition (e.g. a policy recommendation) and
function). To have a maximum in a calculus sense requires a static
attempts to rationalize this with some set of theoretical propositions. If
monotonic utility index or function or something sufficiently similar which
these are in turn questioned, then broader theoretical propositions are
a static L-ordering can never be. The assumption that such a static utility
brought up for support (e.g. neoclassical theory). If questioned further we
function exists is necessarily ad hoc unless there can be constructed an
begin to examine our basic concepts which were brought in for support
independent test of its existence “ that is, independent of the theory in
(e.g. of information needed for profit maximization, the sufficiency of
question. Since such a test has yet to be devised (let alone applied),
utility as a measure of the intrinsic quality in goods, the ability to
lexicographic orderings need not be rejected only because they cannot
rationalize social welfare functions, etc.). 7 Each step is offered as an
formally represent a usable utility index.
explanation of the previous step in the regress “ but in no way is each next
While one can recognize that a choice can be made with multiple
step necessary in the sense that there is no other possible explanation. But
criteria (e.g. Figures 12.4 and 12.5), such an ordering can never be
to say it is not a necessary step is not to say that it is ad hoc or arbitrary.
complete (there are always ˜holes in the map™) until one orders the criteria.
We can always turn to our independently established views of the matter at
A strictly convex preference ordering (such as one implied by a utility
hand which may be broader but which may not have been seen to be
function) over criteria performs this task. But there is no reason why the
important for the original issue. This progressive type of infinite regress in
assumed preference ordering is the only conceivable ordering. This
effect makes our original proposition more testable by allowing us to
consideration of the non-uniqueness of utility functions then leads to an
examine more and more. An ad hoc stopping of such an infinite regress
infinite regress since a complete explanation must explain why one utility
may be against our best scientific interests.
function was chosen over any other conceivable alternative. This line of
criticism will lead to yet a higher-ordered preference ordering which must
implicitly recognize alternative higher-ordered preference orderings
© LAWRENCE A. BOLAND
176 Principles of economics
between which the question is begged as to why one was chosen rather than
13 Revealed Preference
any of the others. And so on.
vs Ordinal Demand
A lexicographic ordering is always a conceivable alternative but only if
it is seen to represent a process rather than the preference ordering used in
the second step of the neoclassical explanation of demand. Since
neoclassical economics is more concerned with representing choice in a
manner analogous to the calculus-type constrained maximization,
neoclassical economists will always choose convex preference orderings
that can be represented by ordinary utility functions. What is the basis for
this choice? The only reason lexicographic orderings are rejected is that
they cannot be represented by formal utility functions even though they can
perform the task of eliminating arbitrariness or incompleteness for the
Instead of dallying in the theory of consistency tests, an older writer
purpose of explaining a unique choice. It is clear to me that neoclassical
on demand theory (one, that is, who was writing before Samuelson)
economists put methodological considerations of mathematical formalism
would have proceeded at once, having laid his foundations, to the
before even casual empirical questions whenever it comes to choosing an derivation of a much more famous principle “ the principle that the
assumption to represent the non-economic basis of consumer choice. demand curve for a commodity is downward sloping. We, in our turn,
must now consider this basic proposition, which remains what it
always was, the centre of the whole matter.
NOTES John Hicks [1956, p. 59]
1 Note, however, that this ordinal ranking does work for the line Z“Z¢ of Figure
12.1 so long as we do not attempt to say anything about points off that line.
In 1938 Samuelson offered what he thought was a clear alternative to the
2 Technically, this procedure constitutes a rudimentary lexicographic ordering.
unobservable static utility functions needed in the two-step procedure
Goods are first ordered by increasing costs, then by increasing utility. However,
inherent in the neoclassical demand theory. Rather than having us assume
this is not usually the aspect of L-orderings that is put at issue in the criticism of
such orderings. the individual faces a preference ordering that is assumed to have the
3 Note that we would also have to rule out incomes so low that an individual correct shape (convex, no bliss points, etc.), Samuelson would only require
could not afford the minimum level of utility that is necessary for survival. In
us to assume that the consumer makes well-defined, consistent choices.
this sense it could be said that neoclassical economics is middle-class
Choice will be consistent and well-defined if the individual will (a) choose
economics since we are thereby ruling out both very high and very low
the same bundle whenever he or she faces the same prices and income and
incomes.
4 The curve through point B would allow us to pick two points such as G and H (b) never choose any of the other affordable bundles except when prices
where all points on the line between them are not preferred to G and H (they are and incomes change to levels that make the first (or preferred) bundle
equivalent). In the case of the indifference curve through point C, at point C the
unaffordable. Armed with this notion of consistency and well-defined
curve is actually concave to the origin, that is, we can draw a line between
choices, Samuelson claimed we could dispense with assumptions about
points D and E such that points D and E are preferred to all other points on that
utility functions. Moreover, he claimed that everything necessary for a
line (e.g. point F).
5 Accepting stochasticism has similar consequences [see Boland 1986a, Chapter demand theory was observable (we can observe when a consumer makes an
8]. inconsistent choice).
6 In his approach [Lancaster 1966], the consumer can order points on the basis of
At first it seemed that Samuelson had successfully developed an
intrinsic characteristics such as vitamin content, salt content, or other criteria
alternative to the neoclassical Ordinal Demand Theory of Hicks and Allen
for which the content is proportional to the amount consumed. The consumer
[1934] which was based on the two-step procedure with static utility
then forms a utility function over the amounts obtained of the characteristics to
determine the best point and works backward to determine which bundle of functions being represented by indifference maps. Samuelson eventually
goods provides the best characteristics point. reintroduced the notion of ˜preferences™ by claiming that consistent choices
7 Such an infinite regress as this may seem risky and undesirable to some
reveal the consumer™s preferences since the chosen point is revealed to be
theoretical economists because more and more is put at stake at each step.
© LAWRENCE A. BOLAND
176 Principles of economics Revealed Preference vs Ordinal Demand 177
preferred to all the other affordable points. Unfortunately, it never seems to Demand: the price“consumption curve (PCC) which I briefly discussed in
have been asked why it is sensible to think of individuals being slaves to all Chapter 4.
of their past choices. Moreover, such consistency in behaviour is Unlike Gustav Cassel [1918] or Henry Moore [1929] there is no inten-
indistinguishable from individuals who are slaves to static utility functions. tion here to eliminate utility or preference orderings “ such orderings will
It seems now that everyone agrees that the Ordinal Demand Theory of always be assumed to exist. On the basis of maximizing choice, and some-
Hicks and Allen, which is based on assumptions concerning ordinal utility what like Cassel, the basic empirical assumptions will be to conjecture
functions or preference orderings, and Revealed Preference Analysis, specific demand curves directly. However, where Cassel would simply
which is based on Samuelson™s early work, are in some sense formally assume that they are properly shaped [1918, pp. 66“88], I will put that
equivalent. The primary evidence for this equivalence is that the famous assumption at stake since it is the moot point. That is to say, I will examine
Slutsky equation can be derived either from conditions placed on ordinal the explicit or implicit conditions that must be satisfied by any given set of
utility functions or from some version of Wald™s or Samuelson™s Axiom of demand curves rather than just examine as usual the implicit conditions
Revealed Preference, as applied to price“quantity situations. 1 Samuelson based on properties of metaphysical utility functions. Unlike Moore [1929,
[1953, p. 2] and Hicks [1956, p. 139] even went as far as establishing what pp. 5“10], here it will not be presumed that the theory of consumer
is called the ˜generalized law of demand™, namely that, for normal goods, behaviour can be induced from observations “ statistical or otherwise.
the quantity demanded varies inversely with the price. 2 Consumer theory,
whether based on the Ordinal Demand Theory of Hicks and Allen [1934]
CONSUMER THEORY AND INDIVIDUALISM

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