What do i choose? Gambling vs insurance: different decision models at stake

Abstract
My aim with this thesis is to make some clarity on the occurrence of both gam-
bling and insurance, and on the role of economic theory in general. There is much
confusion, indeed. In primis, I highlight the boundary between these two concepts,
dispelling the idea that buying insurance can be considered a form of gambling, and
underlining that they are pole apart actually. Afterward, similarly, I distinguish
between normative and positive economics.
In this light, after a brief presentation of expected utility theory, I claim that its
failure, asapositivetheory, stemsfromthefactthatityieldspoorpredictions, rather
than from the fact that its assumptions are descriptively false. Indeed, the relevant
question, to test a positive theory, is not whether its assumptions are realistic but
whether they are a good approximation for the purpose. In this sense, only factual
evidence can show whether a theory is ’right’ or ’wrong’.
The failure of expected utility theory had a pivotal role in highlighting the im-
portance of psychological factors in economic behavior. Because of the fact that
deviations of actual behavior from the predicted one are too widespread to be ig-
nored, too systematic to be dismissed as random error and too fundamental to be set
aside, it has been acknowledged that a better psychological understanding was re-
quired. In this light, then, I present some of the evidence that has been fundamental
in assessing the obsolescence of expected utility, as a positive theory.
With the idea of accounting for some of these psychological factors, I present
prospect theory, which revolutionized decision theory. It was psychologically rich,
empirically corroborated and a rigorous account of decision making under risk. The
problems with this theory come from the fact that it allows for the choice of stocha-
stically dominated options. In order to make up for such limitation, cumulative
prospect theory ensured that decision makers would not choose stochastically do-
1
minated options. However, the gains from introducing this new version of prospect
theory were somewhat diminished by a substantial loss in psychological realism.
The last model I present is known as composite cumulative prospect theory. In this
model, the editing phase and the decision phase are joined into a single phase, thus
combining the psychological richness of prospect theory with the more satisfactory
attitudes towards stochastic dominance under cumulative prospect theory.
Before drawing the conclusion, I propose a simple application, related to the insu-
rance context, in order to show how composite cumulative prospect theory provides
a better account of factual evidence with respect to cumulative prospect theory.
Finally, Idrawmyconclusion. Itistruethatexpectedutilityprovidesapooraccount
of factual evidence, both for what concerns gambling and insurance in particular and
for other phenomena in general. In this sense, of the available alternatives at the
moment, composite cumulative prospect theory is possibly the best decision theory,
particularly, under risk. Yet, this may not be so relevant. As a matter of fact, what
I tried to make clear is that expected utility was conceived of as a normative theory,
rather than as a positive one. Thus, it should be tested accordingly. Normative
economics deals with ’what ought to be’, and therefore it raises other and different
issues with respect to positive economics. To me, it is not surprising, therefore, the
fact that this model is poor from a positivisitc standpoint.
In the end, it is just a matter of perspective.
2
1. Introduction
Individuals frequently must, or can, choose among alternatives that differ, among
other things, in the degree of risk to which the individual will be subject. The
clearest examples are provided by insurance and gambling. An individual who buys
fire insurance on a house he owns is accepting a certain loss of a small sum, i.e. the
insurance premium, in preference to the combination of a small chance of a much
larger loss, i.e. the value of the house, and a larger chance of no loss. That is, he
is choosing certainty over uncertainty. On the other hand, an individual who buys
a lottery ticket is subjecting himself to a large chance of losing a small amount,
i.e. the price of the lottery ticket, plus a small chance of winning a large amount,
i.e. a prize, in preference to avoiding both risks. In other words, he is choosing
uncertainty in preference to certainty.
This choice among different degrees of risk, so prominent in insurance and gam-
bling, is clearly present and important in a much broader range of economic choices.
Whether or not they realize it and whether or not they take explicit account of the
varying degree of risk involved, individuals choosing among occupations, securities,
or lines of business activity are making choices analogous to those that they make
when they decide whether to buy insurance or to gamble.
In addition to its general appeal, if we restrict our attention to the sole gambling
and insurance phenomena, it is still worth a thorough analysis. Both the insurance
industry and the gambling one are of tremendous economic impact. To give some
numbers, notice that the total global gross insurance premiums for 2008 were $4.27
trillion, accounting for 6.18% of global GDP
1
. Similarly, in 2007 the gambling in-
dustry had gross revenue, i.e. amounts wagered less the amount paid to bettors,
of $92.27 billions worldwide
2
. If revenue was about 10% of the bet on average, the
amounts wagered would be in the neighborhood of a trillion dollars.
1
Plunkett 2010. Plunkett’s Insurance Industry Almanac, Plunkett Research, Ltd.
2
American Gaming Association.
5
Chapter 1 Introduction
Yet, what can be considered the major paradigm in decision making, i.e. expected
utility theory, finds the phenomenon of both gambling and insuring as puzzling.
As a matter of fact, the hypothesis that the marginal utility of money diminishes
implies that an individual seeking to maximize his utility will never participate in
a ’fair’ game of chance, for instance, a game in which he has an equal chance of
winning or losing a dollar. In fact, the gain in utility from winning a dollar will
be less than the loss in utility from losing a dollar, so that expected utility from
participation in the game is negative. Thus, the model predicts that an individual
would always have to be paid to induce him to bear risk. But this implication is
clearly contradicted by actual behavior. As said above, people not only engage in
fair games of chance, they engage freely and often eagerly in such unfair games as
lotteries.
Throughout what follows, I will go through expected utility theory from a vantage
point that is different from the view widely held with respect to this model. I claim
that its failure is not due to the fact that its hypotheses are a poor representation
of reality. Its defeat does not rest on the fact that people do not consult wiggly
utility curve before gambling or buying insurance or on the fact that most people do
not possess the means needed in order to compute the expected utility of a gamble
or of an insurance plan; rather than this, I claim that the defeat of the expected
utility model comes from the fact that its hypotheses have implications that poorly
match factual evidence, as it is the case of both gambling and insurance. This flaw
can be traced back to the fact that maximizing the expectation of a utility function
accounts only for the monetary consequences of an action. It ignores the thrill, the
hormones, the heart rate and arousal, the bluff and the competition.
Afterward, I venture myself in the presentation of some of the main results that have
been obtained in order to amend the shortcomings of the expected utility model.
Most of the efforts that have been carried out in the last fifty-years are in the di-
rection of trying to single out what are the driving forces of decision under risk,
beyond the monetary value and the utility of outcomes. Thanks to both laboratory
experiments and hypothetical choices and field studies, more and more, the impor-
tance of psychological patterns has been underscored. An accusation that can be
made to those results is that they are not reliable, since hypothetical and artificial
laboratory experiments have limited implications for economic theory.
The method of hypothetical choices relies on the assumption that people often know
6
Introduction
how they would behave in actual situations of choice, and on the further assumption
that the subjects have no special reason to disguise their true preferences. Therefore,
if people are reasonably accurate in predicting their choices, the presence of certain
patterns and heuristic can be inferred safely. Yet, this is just one version of the
story, indeed, not everyone accepts these assumptions. Many believe that unless
subjects are offered an incentive compatible payment schedule, their responses will
not represent what they would do if given the task ’for real’.
This difference of thought arises from the fact that economists presume that expe-
rimental subjects do not work for free and work harder, more persistently, and more
effectively, if they earn more money for better performance. On the other hand,
psychologists believe that intrinsic motivation is usually high enough to produce
steady effort even in the absence of financial rewards and while more money might
induce more effort, the effort does not always improve performance.
The effect of incentives is clearly an important issue for experimental methodology.
Ultimately, the effect of incentives is an empirical question. Consequently, many
experiments, that compare the results from offering real and hypothetical monetary
incentives, have been conducted. These studies show that the effects of incentives
are mixed and complicated.
The presence and amount of financial incentive does seem to affect performance
in many tasks, particularly judgment tasks where effort responds to incentives and
where increased effort improves performance. At the same time, in many tasks
incentives do not matter, presumably because there is sufficient intrinsic motivation
to perform well, or additional effort does not matter because the task is too hard or
it is very easy to do well
3
. In such cases, thus, and this is an important point to bear
in mind throughout the reading, the failure to optimize appears to be cognitive, i.e.
related to the way problems are structured and what decision strategies are used,
rather than motivational, i.e. related to the amount of mental effort expended.
In the end, although a thorough analysis of this issue is beyond the scope of my
work
4
, I deem that there are too many variables at work here; consequently the
extreme positions, i.e. that incentives make no difference at all, or that incentives
alwayseliminatepersistentirrationalities,arelikelytoturnouttobefalse. Monetary
incentives are one part of the tools available to experimentalists, to be deployed
3
In many of the studies where incentives did not affect mean performance, added incentives did
reduce variation.
4
For a further analysis of the role of incentives see [8][11][26].
7
Chapter 1 Introduction
when it is the best way to achieve a desired effect. However, before deciding to use
incentives it is necessary to think about why the incentive is likely to have its effect,
and what the alternative non-incentivised methods are.
Finally, in the last part of my work, I focus on the consequences, from the vantage
point of modeling human behavior, of accounting for some psychological patterns.
In this context I will present in primis the original version of prospect theory and
then its cumulative version, which was developed in order to amend some theoretical
issues related to the original model. Before drawing the conclusions I will present
a minor, yet fundamental, change to the weighing function of cumulative prospect
theory, which allows for a better accounting of the insurance phenomenon. In par-
ticular, it manages to overcome all the problems connected with the editing phase
proposed in the original prospect theory, by merging together the editing and the
evaluation phase in a manner which will become clear later on.
8