The name is absent

be weaker in aggregated terms: βB > βA .

The specification of the equal treatment policy (Definition 1) for this framework re-
mains as before (α_i^ET = α^ET 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 = β_ie_i 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 β_B > β_A), 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
β_A and β_B and not the differences between all the individual parameters γ_i 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 + γ_i, 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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