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Behavioural Decision Research. This strategy presupposes that human cognitive processes are limited and proposes various non-utility models of decision processes. There are two
compensatory choice processes, and numerous non-compensatory processes see Payne et al., 1993. Compensatory decision processes confront the trade-offs between probabilities
and consequences and can lead to choices consistent with Expected Utility and other utility theories. Non-compensatory rules, for example Majority of Confirming Decisions MCD
and Elimination By Aspects EBA, are usually less cognitively expensive but are harder to defend as rational.
Buschena and Zilberman 1995 show that both the economists’ and psychologists’ ap- proaches alone are inadequate. They argue a more general paradigm is needed to capture
choice behaviour and account for choice reversals. A number of papers by Georgescu-Roegen 1966 address the issue of psychological thresholds in perception, and the consequences
of assuming the individual is not a ‘. . . perfect choosing instrument’. This paper contends that one of those consequences could provide the foundation for a more general paradigm.
By incorporating the perception effects into Expected Utility theory as the psychologists advocate, the process of preference construction may give rise to both choice patterns con-
sistent with Generalised Expected Utility GEU and choice reversals errors. Section 2 of this paper presents the argument and Section 3 describes an exploratory experiment to test
some of the implications. Section 4 discusses the findings in light of the recent literature, and concludes.
2. Consequences of incomplete preferences
2.1. Constructing preferences Walley 1991 argues that a preference is an underlying behavioural disposition to make
a certain choice. The choice made will reflect this disposition when it is apparent which alternative is implied by it. Savage 1954 defined preference as revealed by choice. His
approach is valid if we can ‘read’ our disposition costlessly, but if choices are required where preferences are incomplete, this simple identification can no longer be satisfactory.
The utility theories assume that individuals possess complete preferences between all pairs of choice objects. The recent economics literature see Section 4 acknowledges that choices
may involve error, and represents it by an appropriately specified error term added to the relevant underlying model. But this strategy would also be called into question if both the
generalised utility theories and the error were caused by the same factor, as eliminating that factor would remove not just the error but the theory.
This paper departs from Savage’s view when: 1. a preference is not costlessly accessible and the attempt to access or create the preference
generates Generalised Expected Utility choice patterns; 2. the clarity of the preference remains too weak to conclude that any one choice object
is preferred, even after an attempt to identify the preference.
1
1
Uncertainty regarding one’s preference is conceptually distinct from indifference, wherein the utilities of the alternatives are known precisely, but happen to be equal.
D.J. Butler J. of Economic Behavior Org. 41 2000 277–297 279
Expected Utility may then be an appropriate model only when there are minimal cognitive constraints present in a choice environment, limiting the scope of the theory. There would
be a need for descriptive and normative models of choice in those cases when one’s prefer- ence is not immediately obvious. Our limited cognitive processing power prevents us from
maintaining an up-to-date fully defined preference ordering. Even the attempt to define one more closely may be judged too costly when compared with the additional benefits a more
complete ordering would offer over a less complete one. Camerer 1995 and Buschena and Zilberman 1996 assert that even if some experimental design offered great incentives for
accuracy, there is a cognitive limit to the fine-grading of preferences. It should not then be possible to force all behaviour to conform to Expected Utility simply by raising incentives
sufficiently high.
Imagine an Expected Utility index against which risky choice objects are measured for their utility. Suppose our ability to discriminate immediately between different values on
this index is restricted to a coarse grading, consistent with Fechner’s 1966 psychophysical concept of ‘just-noticeable differences’ JNDs. Unless the choice objects are more than
a certain distance apart, it will not be immediately apparent which object is preferred. If they are sufficiently distant, our underlying disposition shines through brightly and pref-
erences between the choice objects are clear. Choices should be very confident, although occasional errors could still occur due to white noise. Choice patterns should be consistent
with Expected Utility theory, plus a white-noise term.
2
Hence: H1a: A preference between a pair of lotteries where the generalised expected utilities
are close will be weaker in comparison with another lottery pair where the expected utilities are further apart.
This hypothesis is consistent with evidence from Butler and Loomes 1988 who found that the difficulty of the choice problem increased as the utility difference between the choice
objects decreased. It seems reasonable to assume that when a subject reports a choice to be more difficult, their preference is less clear.
If the choice objects are less than a certain distance apart, cognitive effort may then be expended to interpret the choice in a way that allows the underlying disposition to make
itself felt. This is equivalent to seeking a finer-grading on a utility index, possibly rendering our underlying disposition sufficiently clear to permit a preference-consistent, rather than
an arbitrary, choice
3
. There are different ways in which this cognitive ‘work’ can be done, so we may expect a method choice rule that seems most appropriate given the choice
context to be chosen. But these different interpretations of the problem emphasise different aspects of the choice from which our preference is then formed: that is, the ranking of the
choice objects within a Just Noticeable Difference can be affected by the method used to assign them. Or as Schick 1984 argued, the process of choosing may not simply reveal
our pre-existing preferences, it can help to create them.
2
Persons using the expected value rule, which is a special case of EU, should have very confident preferences even when the choice objects are located very close together on the utility index. This is because the Just Noticeable
Differences given by the rule are infinitely small.
3
Georgescu-Roegen 1966, p. 152 makes the related point that the greater the time spent perceiving the stimuli before formulating a judgement, the smaller will be the perceptual threshold.
280 D.J. Butler J. of Economic Behavior Org. 41 2000 277–297
Aumann 1962 showed that the completeness axiom isn’t necessary to derive a utility that represents preferences, but that the resulting utility is no longer unique. He refers to
‘...the limitation of our discriminatory capacity’ requiring the need to construct the detail of the preference. Leland 1994 and Buschena and Zilberman’s 1995 ‘similarity’ theory
maintains that as the risk-aversion embodied by such a utility function is masked, fewer risk-averse choices may occur in the more similar lottery pair. This aspect of their theory
is also consistent with the arguments of this paper. If the instruction from an underlying utility function is partly smothered, actual choices can then to a degree reflect the impact
of preference constructing heuristics. Hence:
H1b: If H1a holds, lottery pairs where GEU’s are close will exhibit a smaller proportion of risk-averse choices.
When preferences aren’t strong, error rates should exceed that from white noise, but be lower than if choices were arbitrary. Of course, ‘errors’ would then be a misleading
term to use if there is no underlying model of complete preferences against which mistakes can be measured. The neutral term ‘choice reversals’ should be preferred. If the descrip-
tion of the choice problem is particularly ill suited to the construction of a preference, non-compensatory rules might be used. Choices made using such rules may not reflect an
underlying preference. But it is also possible they help to construct a weakly felt prefer- ence, rather than simply produce a choice.
If we still have no preference between two objects even after using some choice pro- cess to pursue a finer-grained discrimination, our ultimate choice can not be said to be
preference-revealing or creating. Such choices will essentially be arbitrary
4
. If the utility difference between the objects is sufficiently small, the true preference can not be accessed
behaviourally equivalent to it not existing, and either choice object would stand a good chance of being selected. Choice reversal rates at the extreme could approach the 50 percent
of fully random choices. The implication is that choice errors result from the remaining gaps in our preference ordering, after whatever cognitive effort to reduce the coarse-grading in
our utility index has been attempted.
Hypothesis 1 alone does not imply that the GEU models cannot be core theories of preference, but it does suggest that the extra sources of utility GEU models permit in
the choice process are quickly outweighed by parameter changes which increase both EU and GEU gaps between the choice objects. Descriptively, EU would then be the more
parsimonious model in all cases except where the utilities of lotteries are close, just as Newtonian mechanics is still used in preference to the more general relativistic version
except at velocities approaching light speed. It also raises the possibility that GEU models are not core theories at all; the effects they purport to explain might be the consequence
of preference constructing heuristics, as the latter would also lead to choice reversals only when the utilities of the choice objects are close. If this is so, the choice process then used
may lead to violations of one or more of the Expected Utility axioms. Sugden 1995 gave two examples: that complementarities may arise in evaluating the various attributes within
an object, violating the sure-thing principle. Or, if complementarities arise when attributes
4
Though perhaps some pattern may be evidenced if a low-effort, non-compensatory choice process is used as a tie-breaker.
D.J. Butler J. of Economic Behavior Org. 41 2000 277–297 281
are evaluated across objects, the transitivity axiom may be violated. Generalised Expected Utility choice patterns are here predicted to be a consequence of choice rules such as these
being used to reduce the size of the Just Noticeable Differences
5
. Since the various choice processes may be used with different frequencies under different
descriptions of the choice problem or procedures for eliciting choice, the use of some Gener- alised Expected Utility model based on a particular processes might be display-dependent.
Display dependence would be a general feature of tests of the axioms of Expected Utility theory if GEU models only predict behaviours that result from honing preferences rather
than representing core preference structures. Keller 1985 investigated display effects for compliance with the Sure-Thing and Substitution principles and found significant differ-
ences, as Harless 1992 did for regret theory. A second set of hypotheses is thus implied:
H2a: If displays differ in the ease with which individuals can form clear preferences, the proportion of choices based on a clear preference for a fixed lottery pair will vary by
display. The same logic also implies that:
H2b: Given H2a, the proportion of risk-averse choices will be smaller in displays where preferences are less clear.
If GEU theories can be core preference structures, then altering the displays of a fixed lottery pair should not affect the frequency of observed GEU effects. If however, they result
from display-affected preference constructing heuristics, suitably distinct displays should lead to different frequencies of these effects:
H2c: Given H2a, the proportion of GEU effects and choice reversals will be greater in displays where preferences are less clear.
In the experiment reported below, regret theory Loomes and Sugden, 1987 is chosen as an example of a Generalised Expected Utility model. Regret theory was selected because
Butler 1998 has shown it is equivalent to a parameter restriction in an additive-difference choice model, which in turn is prompted to varying degrees in some displays when pref-
erences need constructing.
6
The arguments in Butler 1998 demonstrate that at least in theory, choice heuristics can account for the anomalies predicted by one GEU model.
Regret effects rely on rather sophisticated information processing, which imposes substan- tial cognitive costs on an individual. Starmer and Sugden 1993 and Humphrey 1995
show that some experimental evidence identifying regret effects was actually conflated with ‘Event-Splitting Effects’ ESE’s. This latter effect refers to the tendency of some
individuals to be more inclined to choose those acts where the consequence is shown as
5
Jarvenpaa 1989 provides evidence that different displays lead to the use of different choice rules, and argues for a cognitive costbenefit interpretation of the findings, as did Payne et al. 1992. As those authors point out,
this is unlikely to be the result of a meta-choice process as hardly anyone is consciously aware either of the set of alternative choice rules or of the different outcomes they would generate. Instead, it stems from the passive
encouragement of suitable rules offered by the choice context.
6
Refer to the former article for a description of regret theory, and the latter for a justification of the choice-rule interpretation. It is speculated that other GEU theories could be reduced to their choice-rule foundations in a
similar manner.
282 D.J. Butler J. of Economic Behavior Org. 41 2000 277–297
the outcome for contiguous events, rather than one large event, even though the probability of the consequence being realised is unchanged see Fig. 3. Such effects are inconsistent
with all choice theories derived from a compensatory choice process, though they are con- sistent with the non-compensatory ‘majority of confirming decisions’ MCD rule in the
choice problems of interest to us. They are in themselves highly suggestive of incomplete preferences. A test for ESE’s is designed into the experiment.
3. An exploratory experiment and results
