We present a common approach for handling consumer and provider fairness in recommendations. Our solution requires defining two key components, a classification of items and a target distribution, which together define the case of perfect fairness. This formulation allows distinct fairness concepts to be specified in a common framework. We further propose a novel reranking algorithm that optimizes for a desired trade-of between utility and fairness of a recommendation list.
(P-fairness) — as in [
In this paper, we present a simple unified viewpoint of these fairness concepts, where one only
needs to specify two components: (1) an item classification, and (2) a target distribution over item
classes. The exact definition of these components depends on the specific fairness goal one aims for:
• Consider the C-fairness concept where each user should receive calibrated recommendations that
match her prior preferences, as in [
• In another C-fairness concept, the goal is to provide fair recommendations to a group of users,
as in [
• As an example of P-fairness, consider the scenario where we want to make recommendations
that equally represent all item providers, as in [
These examples illustrate the flexibility of our approach. Distinct notions of fairness can be described in terms of a simple framework, consisting of an item classification and a target distribution.
Once the two components are defined, the fairness of the recommender is measured by the statistical
divergence between the target and the realized distribution — the later being the distribution over
item classes induced by a recommendation list. The divergence essentially quantifies how far from
being perfectly fair the recommendations are. As the goal of a fairness-aware recommender system is
to strike a balance between utility and fairness, similar to prior work [
Overall, our approach allows us to frame various fairness objectives under a common framework,
making it possible to relate and compare them. Moreover, our unified algorithm enables the direct
optimization of the desired utility-fairness trade-of. This is particularly atractive as some fairness
proposals only consider some proxy of fairness.
Item Classification. We assume that items belong to a set of K appropriately defined classes; in
case of P-fairness, these are typically the item producers/providers, while in C-fairness, classes are
specified according to consumer/user properties. We denote as p(κ |t ) the membership of item t in
class κ ∈ K. As an item may belong to diferent classes, we require Íκ ∈K p(κ |t ) = 1.
Target Distribution. A target distribution Q is a discrete probability distribution over K, representing
the desired class representation a recommendation list should exhibit. For example, we may set Q to
the uniform distribution directing the recommender to cover all classes; or to the class distribution of
the user’s consumed items, asking the recommender to respect past preferences.
Realized Distribution. A recommended list τ presents items from possibly diferent classes to the
target user. The realized distribution P (τ ) in a list τ is a discrete probability distribution over the set of
classes K, capturing the level at which each class is presented to the user via τ . There are various
ways to concretely define P (τ ). The simplest is to sum up the class memberships of each item. Another
approach is to account for the position bias in a ranked list, and compute the exposure/atention [
t ∈τ
where γτ = Íκ ∈K Ít ∈τ d(rankτ (t )) · p(κ |t ) ensures that P (τ ) is a probability distribution.
Fairness. A recommended list τ is perfectly fair if its realized distribution is equal to the target. As
perfect fairness may be unatainable, we would like to quantify deviations from the ideal state. The
fairness of a list τ is captured by the similarity of its representation P (τ ) to some given target Q,
and is denoted as F (τ ; Q). When the target Q is understood by the context, we simply denote it as
F (τ ). Dissimilarity between two distributions can be measured in terms of their statistical divergence.
Therefore, we express fairness of τ by a value F (τ ), normalized to [
D(P (τ )∥Q) ,
D+(·∥Q)
where D(·∥·) is a divergence measure of representation P (τ ) from the target Q, and D+(·∥Q) is an
upper bound on the divergence of any possible representation. When the representation P (τ ) equals
the target distribution Q, fairness takes its maximum value F (τ ) = 1. In this work, we consider
the Kullback–Leibler (KL) divergence, as in [
Utility. A list has a (predicted) utility to the target user, captured by a value U (τ ), normalized to
[
U (τ ) = U1+ Õ r (t ) · d(rankτ (t )), (3)
t ∈τ
where U + is the maximum possible utility of any ranked list of N items (similar to the ideal DCG).
Optimization Objective. The goal is to return a recommendation list τ that maximizes a linear
combination of its utility U (τ ) and its fairness F (τ ), for a given value of λ ∈ [
τ Algorithm. The unified algorithm, termed PREFIX, reranks a recommendation list τN of length N that maximizes utility alone. Let T denote the set of items to be reranked. The goal is to create a fairness aware reranked list that approximately solves the aforementioned optimization problem. For any list τ , let S(τ ) = (1 − λ) · U (τ ) + λ · F (τ ) denote its score. The algorithm examines each prefix τk of the initial list, i.e., a list that contains the first k items from τN for k ∈ [0, N ]. For each prefix τk , the algorithm will incrementally append the remaining N − k items in a greedy manner. Let τk (i) denote the list at the i-th step — the final reranked list created from the k-prefix is obtained at the (N − k)-th step. At the i-th step, the algorithm appends the item that maximizes the score of the resulting list, i.e., arg maxt ∈T <τi−1 S(τi−1 ⊔ {t }), where ⊔ denotes the append operation. After considering all prefixes the algorithm has constructed N , possibly distinct, rerankings of the initial list tN , and among them, it returns the one with the highest score.
EVALUATION
Data. We use the MovieLens 20M dataset [
FAR CALIB PREFIX 0.70 (a) Uniform FAR CALIB
PREFIX 0.80 0.85
0.90 Fairness
0.95 (b) User
Figure 1: Utility-Fairness curves
1.00
0.98
0.94
Metrics. We ask each method to return a ranked list of 20 items. For a list, we measure: U: the utility
according to Equation 3; R: recall at position 20, i.e., recall@20; N: normalized DCG at position 20, i.e.,
nDCG@20; F: fairness according to Equation 2; C: class coverage ratio for Uniform as in [
We next set various values to λ within [