The value function is an adaptation of the function proposed by Tversky and Kahneman
in 1992 and in agreement with to present theory and it is the necessary and sufficient
conditions to represent v(x) through the following function:
I Λ1 Xiω1
v(xi) = ) 1 i ω
[- λ2 ∣-x,∣
if 0 ≤ i ≤ s
if -m ≤ i < 0
(3)
where:
v- value function;
xi - results; and,
λ1, λ2, ω1, ω2 - function parameters.
The parameter λ1 does not have any effect on the curvature of the function, given that this
parameter is only responsible for the utility scale (Gonzalez and Wu, 1999).
The decision weights (hi) are defined in a cumulative way through the following
expressions:
where:
hs+ = f +(ps) and hi+
s
= f + ∑ p.
I i
( s ^
- f + ∑ pi .
i +1
+
0 ≤ i ≤ s-1
(4)
h-m- = f -(p-m) and hi
=f-f∑p1
-m
'-f-1∑> '
I-m J
1-m ≤ i ≤ 0
(5)
p - probabilities;
f +, f - - probability weighting functions; and
hs and hm - decision weights.
The value of the decision weights depends on the probability weighting function, that
captures psychologically the distortion of the probabilities on the part of the decision
makers. The probability weighting functions f + and f - are strictly increasing inside of the
interval [0, 1], with f +(0) = f -(0) = 0 and f +(1) = f -(1) = 1. They have been the functions
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