Proposition 5 is intuitive because policy AA’ also levels the playing field in an aggrega-
tive sense: although contestants might not win the contest game if they exert identical
effort under AA’, the heterogeneity between the groups is lower under AA’ than under
ET because the discriminated group is favored in the average. This ameliorates the
disincentive effects due to the differences in cost functions for the two groups. The
assumption on full participation implies then increased competitive pressure between
the two groups which is translated to higher aggregated equilibrium effort.
However, contrary to the full information case individual equilibrium effort increases
only for those contestants whose marginal costs are below a specific cut-off parameter.
The reason is that under policy AA’ higher discrimination does not imply a higher
bias in favor of affected contestants proportional to their level of discrimination (as it
is the case under policy AA with a fully informed contest organizer). Therefore, policy
AA’ remains relative ineffective for those contestants with high level of discrimination.
However, under AA’ higher competitive pressure in the aggregate also has incentive
augmenting effects for contestants with relatively low marginal costs that will increase
equilibrium effort under AA’. The exact threshold level for those group of contestants
is given by the two inequalities in Proposition 5.
6 An Alternative Definition of Affirmative Action
The two policy option specified in Definition 1 and 2 are formulated with respect to
the CSF in the sense that a specific constellation of effort and marginal cost parameter
for two contestants should yield a similar probability of winning the contest game. As
the outcome of the contest game is the relevant equalisandum, those definitions can be
described as procedural notions of fairness. However, an alternative end-state notion
of fairness would be focused instead on equality of expected equilibrium utility. In
the case of affirmative action policy it could be alternatively argued that the outcome
of the contest game for each individual should reflect the ethical perception of the
heterogeneity in the following sense: if the contestants are perceived to be different
because they are discriminated (for which they cannot be held ethically responsible)
then the contest outcome should be as if they would be de facto homogenous. Hence,
the expected utility in equilibrium should be identical for all contestants. This gives
rise to the following alternative ‘end-state notion’ of affirmative action:
Definition 4 A policy is called affirmative action with respect to expected
equilibrium utilities (AU) if the expected utility for each contestant in the contest
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