be weaker in aggregated terms: βB > βA .
The specification of the equal treatment policy (Definition 1) for this framework re-
mains as before (αiET = αET for all i ∈ N) because it is defined for all contestants
identically (and therefore also irrespective of group membership). However, the defi-
nition of affirmative action has to be adapted to the limited informational knowledge
of the contest organizer because Definition 2 is based on complete information. As the
contest organizer can only observe group membership, she is restricted to compensate
only for the aggregated (group-specific) level of discrimination. Definition 2 has to be
revised respectively where the normative justification remains as in Section 2.
Definition 3 A policy is called affirmative action (AA’) in a contest game with
a partially informed contest designer if:
βAei = ввej ⇒ Pi(e) = Pj(e) for i ∈ A,j ∈ B. (17)
The following transformation of variables which respects now the limited information
of the contest organizer is useful to proceed in the same line as in the discussion of
Definition 2: zi = βiei where /i can only take two values: /i = /A for i ∈ A and
βi = в B for i ∈ B. The requirement formalized in Eq. (17) then implies that for all
zi = zj it must be true that pi (e) = pj (e) for i ∈ A and j ∈ B. Using the linear CSF as
in Eq. 2 with r = 1 yields then the following specification of weights (αAA,,..., αAA' ):
αAA' = βi for all i ∈{Α,B} . (18)
An alternative interpretation of this limited information case would be to assume two
sources for the heterogeneity of the contestants: one, for which the contestants are not
held responsible (i.e. the discrimination of group B as a whole with βB > βA), and
a second individual one for which the contestants are held ethically responsible. An
example would be the following cost function: ci(ei) = (βA+γi)ei if i ∈ A (analogously
for i ∈ B) where the idiosyncratic parameter γi could be positive or negative.24 The
objective of affirmative action is then limited to balance solely the difference between
βA and βB and not the differences between all the individual parameters γi for all
i ∈ N.25
The comparison between policy ET and AA’ is complex for this kind of set-up because
not all contestants will always be active under AA’ (Lemma 1 does not hold anymore
24With this kind of cost function, where βi = βa + γi, it is generally not the case that /?a = ∑i∈A βi∙
However, the important point is that/?A is known by the contest organizer.
25 I thank Caterina Calsamiglia for suggesting this interpretation.
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