By considering different weight combinations and different goal values, the
GP models presented in previous sections can capture the differences be-
tween individuals, but also the dependency of an individual’s decision on the
particular state of mind during the moment of decision making. The un-
derlying cognitive model is that the decision maker sets goals or aspiration
levels for the objectives under consideration, and then weigh up prospective
alternatives through a dynamic and iterative comparison with the aspiration
Montague (2007) argues that uncertainty will be especially relevant in
new decision making situations but might reduce considerably for repeatedly
played decision games. He further argues, however, that there should always
be some uncertainty as an essential element in social coordination games to
prevent players from being exploitable.
A non-zero level of unpredictability of the weights would be one way in
which this concept of irreducible uncertainty can be modelled. Alternatively,
or in addition, irreducible uncertainty may also arise from uncertainty about
the actual goals values itself.
The GP models presented, and in particular the Chebyshev GP model
of fairness, also offer a way to model how players may exploit information
asymmetry by using deception. As seen in Section 2.5.3, players may ex-
hibit a level of self-deception or try to envoke sympathy by exhibiting sham-
emotions towards other players. In the Chebyshev GP model of fairness, this
may result in players adopting a ToM model of the other player that will lead
to more favourable outcomes for the other player. Self-deception may be a
strategy to make the other player truly believe that you deserve outcomes
4.6 Concluding Remarks
Goal Programming (GP) is widely applied to find practical solutions to many
problems in Operational Research where decision makers have multiple goals
to consider. The foundation of GP is the theory on satisficing by Herbert
Simon, developed in the period between 1955 and 1960.
In this chapter, we are first to have identified striking similarities between
the GP framework and the computational theory of mind (on how humans
make decisions) developed in the field of cognitive neuroscience. While we
do not wish to claim that GP accurately represents the real decision making
processes in the brain, it does seem to capture at an abstract level some of
the key concepts, including the concepts of goals and the multi-valued aspect
of the goal state, efficient biological computation, theory of mind, and reward
prediction error mechanisms.
Both GP and neuroscience find compelling reasons that humans who set
their goals just out of reach fare better. The reason from neuroscience is that
this is essential for humans in order to keep the desire to learn. In weighted
GP, it is an advantage it offers a guarantee of achieving Pareto efficient
outcomes (Romero et al., 1998). We have argued that the latter practical
approach adopted in GP could be explained, at least from a conceptual point
population, and thus must have had an evolutionary advantage. GP also of-
fers a way to incorporate irreducible uncertainty in the context of cooperation
between individuals.
While there are similarities between GP and classic utility function the-
ory in a mathematical sense, the philosophies of satisficing and balancing
underlying Weighted and Chebyshev GP offer advantages in showing the de-
pendency of decisions on multiple goals and in relation to the state of mind
of a person, and how this person thinks about the state of mind of other
relevant players, and how important the latter consideration is when making
decisions. We believe that a GP-based theory of fairness is less bound to
pre-imposed concepts which outcomes are fair in a particular game in com-
parison to the utility based models such as the well-known inequity aversion
model.
We have also identified the possibilities of the GP models to operationalise
some concepts from the field of psychology, including the level of social iden-
5
A GP Approach to Model Fairness in
Human Decision Making
5.1 Introduction
In this chapter, Goal Programming (GP) is applied to modelling the decision
making processes in the well-known Ultimatum Game. The decision model
for a player is a Chebychev GP model that balances one’s individual desires
with the mental model one has of the desires of other relevant players. In
this approach, fairness is modelled as a universal mechanism, allowing play-
ers to differ in their belief of what a fair solution should be in any particular
game. The model’s conceptual framework draws upon elements considered of
importance in the field of cognitive neuroscience, and results from the field
Computer simulations of the GP models, testing a number of Ultimatum,
Dictator and Double Blind Dictator Games, lead to distributions of propos-
als made and accepted that correspond reasonably well with experimental
findings. The statistical analysis is then conducted to support the findings.
Next, the types of goals distribution of accepting and rejecting the offers are
analysed and their associations with the decisions are examined. A parallel is
drawn between the UG and a common real-life situation to help explain the
rationale of the model and the final section summaries the main conclusions.