Figure 7
Social Utility Functions Based on a Social Discounting Model.
The total utility predicted by a social discounting model of the form shown in Eq. 1 (vertical axis, arbitrary units), is plotted as a function of the offer to the receiver (sj) in a dictator game with an endowment of 24 units (
. Two possible scenarios are shown, either a decreasing offer of painful shocks (horizontal axis, upper scale) or an increasing offer of money (horizontal axis, lower scale). The four lines represent different settings of the social discount parameter, Îş, as labeled. In each case, 
, both given by the quadratic function 
, where 
. For κ = 1 the function has a maximum when allocations to both participants are equal 
corresponding to symmetric inequality aversion. κ < 1 generates a preference for assigning more than half the benefit to oneself, while κ > 1 (hyperaltruism) generates a preference for assigning more than half the benefit to the receiver. For each parameter setting, moving away from one’s preferred allocation carries a non-linear (increasing marginal) cost.
