action also has an interesting normative interpretation as shown in a more general
framework in Calsamiglia (2004). There, it is justified normatively because it equal-
izes ‘reward to effort’ which guarantees a notion of ‘global equality of opportunity’.13
Both policies, ET and AA, can be considered as principles that guarantee a notion
of procedural fairness because they are defined with respect to the outcome (in the
sense of winning probabilities) of the contest game. An alternative (welfaristic) ap-
proach would be to equalize the expected equilibrium utilities as objective of affir-
mative action. This alternative interpretation is discussed in Section 6 where it is
also shown that the resulting affirmative action bias is identical under both normative
interpretations.
In the introduction it was already remarked that the difference between the contest
game presented here and the literature on rent-seeking is based on the assumption
that exerting effort is perceived as socially valuable (and not as social loss). This
is also implicitly reflected by the citation of Sowell in which less effort of all partic-
ipants is interpreted as socially inferior. Therefore, the positive analysis of the two
normative policy options is carried out by simply comparing the sum of equilibrium
effort that each policy induces (interpreted as a measure of ‘social efficiency’). Us-
ing total equilibrium effort as the standard of comparison seems to be appropriate
because in situations in which affirmative action is potentially implemented, this as-
sumption captures the notion of social loss (or gain).14 The equilibrium effort level
of each contestant will depend on the ex-ante announced policy parameter P and the
standard of comparison will therefore be expressed and denoted in the following way:
Ep = Σ∈N e↑(P) for P ∈ {ET, AA}.
13 Global equality of opportunity in a contest framework is defined as equality of welfare achieved
for individuals that compete in several contests simultaneously and where the respective contest
organizers implement affirmative action that is based on local information which is limited to the
respective contest.
14In the college admission example, the education authorities are interested in high effort levels, i.e.
grades, by all students that are possibly affected by affirmative action irrespective of the fact that
they are admitted. Also in the bonus tournaments the employer is obviously interested in high
effort levels by all employees, irrespective of the identity of the final winner (the interpretation of
this kind of tournament as an incentive device is obvious here). And even in sport competitions
it can be argued that spectators are interested in the overall performance of all athletes because
ex-ante predictable sport competitions are usually perceived as boring. Note that also the quo-
tation by Sowell suggests that the effort of the individuals can be simply summed up to evaluate
affirmative action.