# A Personalized Framework for Consumer and Producer Group Fairness
Optimization in Recommender Systems

Hossein A. Rahmani  University College LondonLondonUK
<EMAIL_ADDRESS>,  Mohammadmehdi Naghiaei  University of Southern
CaliforniaCaliforniaUSA<EMAIL_ADDRESS>and  Yashar Deldjoo  Polytechnic
University of BariBariItaly<EMAIL_ADDRESS>
(2024; 20 February 2007; 12 March 2009; 5 June 2009)

###### Abstract.

In recent years, there has been an increasing recognition that when machine
learning (ML) algorithms are used to automate decisions, they may mistreat
individuals or groups, with legal, ethical, or economic implications.
Recommender systems are prominent examples of these machine learning (ML)
systems that aid users in making decisions. The majority of past literature
research on RS fairness treats user and item fairness concerns independently,
ignoring the fact that recommender systems function in a two-sided
marketplace. In this paper, we propose CP-FairRank, an optimization-based re-
ranking algorithm that seamlessly integrates fairness constraints from both
the consumer and producer side in a joint objective framework. The framework
is generalizable and may take into account varied fairness settings based on
group segmentation, recommendation model selection, and domain, which is one
of its key characteristics. For instance, we demonstrate that the system may
jointly increase consumer and producer fairness when (un)protected consumer
groups are defined on the basis of their activity level and main-streamness,
while producer groups are defined according to their popularity level. For
empirical validation, through large-scale on eight datasets and four
mainstream collaborative filtering (CF) recommendation models, we demonstrate
that our proposed strategy is able to improve both consumer and producer
fairness without compromising or very little overall recommendation quality,
demonstrating the role algorithms may play in avoiding data biases. Our
results on different group segmentation also indicate that the amount of
improvement can vary and is dependent on group segmentation, indicating that
the amount of bias produced and how much the algorithm can improve it depend
on the protected group definition, a factor that, to our knowledge, has not
been examined in great depth in previous studies but rather is highlighted by
the results discovered in this study.

Responsible IR, Recommender systems, Fairness, Ranking, Bias Mitigation,
Consumer and Provider, multi-stakeholder

††copyright: acmcopyright††journalyear: 2024††doi:
XXXXXXX.XXXXXXX††conference: ; ; ††price: 15.00††isbn:
978-1-4503-XXXX-X/18/06††ccs: Information systems Recommender systems

##  1\. Introduction

(a) Percentage of research

(b) Evaluation Performance

Figure 1. (a) The percentage of the research studied different aspects of
fairness in recommender systems. (b) N (Fairness-unaware), C (user-oriented),
P (item-oriented), and CP (two-sided fairness-performance) of recommendation
algorithms on the accuracy, novelty, and fairness performance. Consumer
fairness evaluation (DCF) and producer fairness evaluation (DPF) are the two
metrics that make up the mCPF. Note that CP represents the core of our
contribution. The results on each bar show the average of 32 experiments
across datasets and baseline CF models. $\uparrow$ means the higher the better
while $\downarrow$ means the lower the better. Acc., Nov., and mCPF refer to
accuracy, novelty, and consumer-producer fairness evaluation, respectively.

Recommender systems are ubiquitous and support high-stakes decisions in a
variety of application contexts such as online marketing, music discovery, and
high-stake tasks (e.g., job search, candidate screening, and loan
applications). By delivering personalized suggestions, these systems have a
major impact on the content we consume online, our beliefs and decisions, and
the success of businesses. Recently, there has been a growing awareness about
the fairness of machine learning (ML) models in automated decision-making
tasks, such as classification (Mehrabi et al., 2021; Binns, 2018; Salutari et
al., 2023; Naghiaei et al., 2022a), and ranking/filtering tasks (Chen et al.,
2020; Caton and Haas, 2020), with recommender systems serving as a notable
example of the latter. However, unlike classification, fairness in recommender
systems (RS) is a multi-faceted subject, depending on stakeholder, type of
benefit, context, morality, and time among others (Ekstrand et al., 2021;
Deldjoo et al., 2021a; Burke, 2017; Wang et al., 2023; Rahmani et al., 2022a).

A recurring theme in the fairness recommendation literature is that computing
research is often focused on a particular aspect of fairness, framing the
problem as a building algorithm that fulfills a specific criterion, such as
optimizing for producer fairness (Dong et al., 2020; Zhu et al., 2021; Yalcin
and Bilge, 2021) or consumer fairness (Dwork et al., 2012; Islam et al.,
2021). However, this strategy may appear oversimplified, requiring more
nuanced and multidisciplinary approaches to research recommendation fairness.

One overarching aspect that may help to unify studies on fairness in multi-
stakeholder settings is distinguishing the (i) benefit type (exposure vs.
relevance), and (ii) the main stakeholders involved in the recommendation
setting (consumers vs. producers). Exposure refers to how evenly items or
groups of items are exposed to users or groups of users. Relevance
(effectiveness) determines to what extent the items exposition is effective,
i.e., matches with the user’s taste. The second level of the taxonomy is
stakeholder. Almost every online platform we interact with (e.g., Spotify,
Amazon) serves as a marketplace connecting consumers and item
producers/service providers, making them the primary end-beneficiaries and
stakeholders in RS. From the consumers’ perspective, fairness is about
distributing effectiveness evenly among users, whereas producers and item
providers seeking increased visibility are primarily concerned with exposure
fairness.

Fig. 1a illustrates the distribution of research on various aspects of
fairness in recommender systems.111The figures are based on 120 publications
retrieved from DBLP using the keywords “fair/biased recommendation”, “re-
ranking”, and “collaborative filtering”. We may observe a division/split in
the research on fairness-aware recommendation algorithms, with around 49.1% of
articles focusing on consumer fairness and somewhat fewer on producer fairness
(41.8%). Few studies (less than 10%) address consumer and producer fairness
concerns simultaneously. However, the underlying user-item interaction
coexists on (and can impact) both sides of beneficiary stakeholders. For
example, there may be disparities in the consumption of item groups (defined
by protected attributes) between active and inactive users in specific
domains. Active users of Point-of-Interest (POI) may want to visit a variety
of popular and less popular locations, whilst less active users may want to
visit mainly the most popular locations. Prior research on unilateral fairness
optimization raises various questions, including whether optimizing for one
party’s advantages, such as consumers, may ensure/protect the interests of
other parties (i.e., producers) and vice versa? Furthermore, how does
optimizing for one stakeholder’s benefits (e.g., consumers’ relevance) affect
overall system accuracy? Are there ways to explain the key interplay and
trade-offs between fairness restrictions (user relevance, item exposure) and
overall system accuracy in various recommendation scenarios? Are there ways to
explain the key interplay and trade-offs between fairness restrictions (user
relevance, item exposure) and overall system accuracy in various
recommendation scenarios?

In response to the questions raised, this study concentrates on fairness
within a multi-stakeholder setting. Our goal is to harmonize two facets of
fairness: fairness towards consumers and providers. To achieve this, we
introduce a model-agnostic re-ranking methodology. This approach is designed
to optimize marketplace objectives effectively. It ensures equitable exposure
for producers’ items and minimizes unequal treatment of different consumer
groups, all while maintaining the overall accuracy of the recommender system.

To better illustrate the capabilities of our proposed system, in Fig. 1b, we
compare the performance of various recommendation algorithms against
unilateral (or single-sided) fairness objectives according to the perspectives
of different beneficiary stakeholders.

In particular, we consider four distinct variants of recommendation
algorithms. The first, denoted as N, is a baseline recommendation algorithm
that operates without any explicit fairness considerations. The subsequent
three, labeled as C, P, and CP, are specific adaptations of our proposed
methodology, each addressing a unique fairness objective. These objectives
focus on consumer-side fairness in the case of C, provider-side fairness for
P, and both objectives simultaneously for CP. The C variant is closely modeled
on the approach put forth by Li et al. (2021), albeit with a key modification
in our rendition: the parity objectives of users are incorporated directly
into the system’s framework as an unconstrained optimization problem. To yield
an optimal solution within a polynomial timeframe, we have chosen to employ a
suitably efficient greedy algorithm.

Fig. 1b represents the average results of the 128 experimental cases examined
in this work, i.e., $8\ \text{(datasets)}\ \times\ 4\ \text{(CF baselines)}\
\times\ 4\ (\text{fairness constraints type})$. One may observe the drawbacks
of unilateral fairness optimization, in which DCF and DPF are used to measure
unfairness (biases) on the consumer and supplier sides, respectively (cf.
Section 4.1). For example, user-oriented fairness optimization (C-fairness)
can enhance both consumer fairness (i.e., reducing DCF) and total system
accuracy. However, this creates a huge bias against suppliers. Producer-
fairness optimization, on the other hand, can improve novelty and producer
fairness (i.e., reducing DPF), indicating that users’ recommendation lists
contain a greater number of long-tail items. However, this comes at the cost
of a considerable reduction in overall accuracy (from $0.2832$ to $0.2756$)
and worsening of DCF (from $0.3280$ to $0.3234$). The proposed consumer-
provider fairness optimization (CP-fairness) in the present work combines the
benefits of previous system variants, enhancing both producer and consumer
fairness, resulting in increased accuracy (from $0.2832$ to $0.2868$) and even
increased novelty (due to recommendation of more long-tail items). To
summarize, the key contributions of this work are as follows:

  * •

Motivating multi-stakeholder fairness in RS. We motivate the importance of
multi-sided fairness optimization by demonstrating how inherent biases in
underlying data may impact both consumer and producer fairness constraints, as
well as the overall system’s objectives, i.e., accuracy and novelty (cf.
Section 3); these biases and imbalances if left unchecked, could lead to
stereotypes, polarization of political opinions, and the loss of emerging
business.

  * •

CP-Fairness modeling. Our research builds on and expands earlier work (Li et
al., 2021), in several dimensions: (i) we consider multi-stakeholder
objectives including both consumers’ and producers’ fairness aspects; (ii) we
formalize the re-ranking problem as an integer programming method without
enforcing the fairness objectives as a constraint that is susceptible to
reduction in overall accuracy in a marketplace; (iii) we propose an efficient
greedy algorithm capable of achieving an optimal trade-off within multi-
stakeholder objectives in a polynomial-time (cf. Section 4). In summary, this
makes the proposed contribution more versatile and applicable to various
recommendation models and settings irrespective of their learning criteria and
their recommendation list size.

  * •

Experiments. We conduct extensive experimental evaluations on 8 real-world
datasets from diverse domains (e.g., Music, Movies, E-commerce), utilizing
implicit and explicit feedback preferences (cf. Section 5); this, combined
with four recommendation algorithm baseline amount the number of experiments
carried out to 128 recommendation simulation.

Contributions and enhancements beyond the original version of this work. This
work builds upon our previous research presented in SIGIR 2022 (Naghiaei et
al., 2022c), and extends it in the following ways:

  1. (1)

Revisiting User Group Definitions in Recommender Systems: Building on our
previous research in SIGIR 2022 (Naghiaei et al., 2022c), this work introduces
a novel perspective on the grouping of the users, based on the quality of user
activity in terms of product popularity. We put forth the notion that users
consuming more mainstream popular products rather than a diverse range can
influence collaborative filtering (CF) models to favor popular items. For
instance, if a user predominantly interacts with mainstream, popular products,
this preference could inadvertently bias collaborative filtering (CF) models
towards suggesting more popular items. This introduces a new dimension of
unfairness in recommendation outcomes, which may vary in magnitude and
proportion depending on the number and type of activities a user engages in.
Consequently, we have reanalyzed all experiments from our SIGIR’22 submission,
introducing new fairness scenarios that differentiate between mainstream and
non-mainstream users. The objective is to determine if these groups are
provided with better recommendation quality and to evaluate if our methods can
effectively enhance fairness in these scenarios.

  2. (2)

Enhanced Generalizability and New Statistical Insights: To increase the
applicability of our findings, additional analyses have been incorporated,
including correlation plots and fairness-accuracy trade-off evaluations for
two distinct user groups (refer to Table 5 and Table 6). These new statistical
measures provide a better representation of the generality of our findings
across various domains.

##  2\. Background and Related work

A promising approach to classifying the literature in recommendation fairness
is according to the beneficiary stakeholder (Abdollahpouri et al., 2020;
Ekstrand et al., 2021; Schedl and Lex, 2023). Based on a recent survey
screening results on papers published in fairness during the past years
(Deldjoo et al., 2023), only 9.1% of publications in the field deal with
multi-sided fairness, with even a less percentage of $3.6\%$ proposing an
actual two-sided fairness-aware algorithm, as pursued in our current study.

C-fairness Methods. Dwork et al. (2012) introduces a framework for individual
fairness by including all users in the protected group. Abdollahpouri et al.
(2019b) and Naghiaei et al. (2022b) investigate a user-centered evaluation of
popularity bias that accounts for different levels of interest among users
toward popular items in movies and book domain. Abdollahpouri et al. (2021)
propose a regularization-based framework to mitigate this bias from the user
perspective. Li et al. (2021) address the C-fairness problem in e-commerce
recommendation from a group fairness perspective, i.e., a requirement that
protected groups should be treated similarly to the advantaged group or total
population (Pedreschi et al., 2009). Several recent studies have indicated
that an exclusively consumer-centric design approach, in which customers’
satisfaction is prioritized over producers’ interests, may result in a
reduction of the system’s overall utility (Patro et al., 2020; Wang and
Joachims, 2021). As a result, we include the producer fairness perspectives in
our proposed framework as the second objective in this work.

P-fairness Methods. Several works have studied recommendation fairness from
the producer’s perspective (Yalcin and Bilge, 2021; Wundervald, 2021). Gómez
et al. (2022) assess recommender system algorithms disparate exposure based on
producers’ continent of production in movie and book recommendation domain and
propose an equity-based approach to regulate the exposure of items produced in
a continent. Dong et al. (2020) set a constraint to limit the maximum times an
item can be recommended among all users proportional to its popularity to
enhance the item exposure fairness. In contrast, Ge et al. (2021) investigate
fairness in a dynamic setting where item popularity changes over time in the
recommendation process and models the recommendation problem as a constrained
Markov Decision Process with a dynamic policy toward fairness.

A common observation in C-fairness and P-Fairness research is the type of
attributes used to segment the groups on the consumer and provider side. These
attributes could be internal, e.g., determined via user-item interactions (Li
et al., 2021; Abdollahpouri et al., 2019a; Karimi et al., 2023) or provided
externally, e.g., protected attributes such as gender, age, or geographical
location (Gómez et al., 2022; Boratto et al., 2021). In this work, we
segmented the groups by internal attributes and based on the number of
interactions for both consumers and providers.

CP-fairness Methods. Considering both consumers’ and providers’ perspectives,
Chakraborty et al. (2017) present mechanisms for CP-fairness in matching
platforms such as Airbnb and Uber. Rahmani et al. (2022b) studied the
interplays and tradeoffs between consumer and producer fairness in Point-of-
Interest recommendations. Patro et al. (2020) map fair recommendation problem
to the constrained version of the fair allocation problem with indivisible
goods and propose an algorithm to recommend top-K items by accounting for
producer fairness aspects. Wu et al. (2021) focus on two-sided fairness from
an individual-based perspective, where fairness is defined as the same
exposure to all producers and the same normalized Discounted Cumulative Gain
(nDCG) to all consumers involved.

Do et al. (2021) define the notion of fairness in increasing the utility of
the worse-off individuals following the concept of distributive justice and
proposed an algorithm based on maximizing concave welfare functions using the
Frank-Wolfe algorithm. Lin et al. (2021) investigate sentiment bias, the bias
where recommendation models provide more relevant recommendations on user/item
groups with more positive feedback, and its effect on both consumers and
producers. Numerous research studies have also concentrated on assessing both
consumer and producer fairness (Deldjoo et al., 2021a; Anelli et al., 2023),
as exemplified by (Anelli et al., 2023) for graph CF models.

The inner layer of the circle in Fig. 1a presents approaches for
recommendation fairness that could be classified according to 1) developing
metrics to quantify fairness, 2) developing frameworks for producing fair
models (according to the desired notion of fairness). Contrary to the works
surveyed, we develop a fairness-aware algorithm that simultaneously addresses
user groups and item group fairness objectives jointly via an efficient
optimization algorithm capable of increasing the system’s overall accuracy.

##  3\. Motivating CP-Fairness Concerns

Table 1. Percentage of users and items located at a different number of
interaction thresholds (as $n$ and $r$ represents, respectively) in the
training set of the datasets.

Dataset $n\geq 10$ $n\geq 20$ $n\geq 50$ $n\geq 100$ $r\geq 10$ $r\geq 20$
$r\geq 50$ $r\geq 100$ MovieLens 100% 82.08% 46.98% 26.09% 77.39% 60.49%
34.54% 16.46% Epinion 99.85% 56.60% 8.11% 1.57% 99.81% 63.83% 17.33% 4.61%
Gowalla 100% 86.11% 25.40% 4.87% 100% 84.44% 20.10% 3.95% LastFM 96.33% 72,73%
0.00% 0.00% 73.99% 37.36% 15.00% 4.48%

In this section, we intend to motivate the need of having two-sided fairness
(i.e., user and item) by undertaking both data and algorithm analysis. We
analyze the distribution and properties of two well-known real-world
recommendation datasets, i.e., Epinion and Gowalla, with their details
summarized in Table 2. We observed similar patterns on the other datasets as
shown in Fig. 5 baseline (N) models.

In Table 1, we show the distribution of users and items with different numbers
of interactions in the datasets. As the values show, most users are
concentrated in areas with less interaction with the items. We can also note
that the majority of items have received fewer interactions from the users
(i.e., long-tail items), and a small percentage of items (i.e., popular items)
are recommended frequently. This motivates the need to expand the long-tail
coverage of recommendation lists while encouraging users with fewer
interactions to engage with the system.

(a) MovieLens

(b) Epinion

(c) LastFM

(d) BookCrossing

Figure 2. The difference between short-head and long-tail item groups on item
exposure and novelty.

(a) MovieLens

(b) Epinion

(c) LastFM

(d) BookCorssing

(e) MovieLens

(f) Epinion

(g) LastFM

(h) BookCorssing

Figure 3. Figures (a) and (d) show the difference between active and inactive
user groups and Figures (e) and (d) indicate the difference between mainstream
and non-mainstream user groups on normalized nDCG@10.

In our next step, we evaluate the recommendation quality of fairness-unaware
baseline algorithms on two datasets for both user and item groups. Figs. 2 and
3 showcase the min-max normalized values of the recommendation algorithms’
quality across the MovieLens, Epinion, LastFM, and BookCrossing datasets. Fig.
2 plots the number of short-head and long-tail items recommended to users, as
well as the novelty of the recommendations. Our results show that despite the
small number of items in the short-head group compared to the long-tail group,
a large proportion of recommended items are popular items, implying a higher
degree of unfairness in the recommendation from the provider’s perspective
(measured in terms of exposure). Moreover, Fig. 3 plots the accuracy (i.e.,
nDCG@10) for all users, active users, inactive users, mainstream users, and
non-mainstream user groups. In Section 6, we present a detailed analysis of
the experiment results in Table 3. Our findings reveal that the active user
group, which represents a small fraction of total users, receives
significantly higher recommendation quality than the inactive user group
(similarly for mainstream and non-mainstream). This demonstrates that
commercial recommendation engines tend to overlook the majority of users. For
instance, from Fig. 3b, we observe that NeuMF and VAECF achieve almost the
best performance (1.0) in the active user group, while for the inactive user
group, the performance is around 0.6. This degradation in overall performance,
which is only slightly above the inactive group at 0.6 for both recommendation
algorithms, highlights the need for fairness in recommendations. In
conclusion, our findings highlight the importance of fairness in
recommendations from both the consumers’ and providers’ perspectives, and thus
developing techniques that better serve disadvantaged users and item groups is
necessary.

##  4\. Proposed CP-fairness algorithm

In this section, we first define fairness in a multi-sided platform based on
deviation from the parity from consumers’ and producers’ perspectives. Then we
propose a mixed-integer linear programming re-ranking algorithm to generate a
fair list of recommendations for each user given a traditional unfair
recommendation list.

Problem Formulation. Let $\mathcal{U}$ and $\mathcal{I}$ be the set of
consumers and items with size $n$ and $m$, respectively. In a traditional
recommender system application, a user, $u\in\mathcal{U}$, is provided a list
of top-N items, $L_{N}(u)$ according to some relevance scores, $s\in
S^{n\times N}$. The goal is to compute a new fair ordered list, $L^{F}_{K}(u)$
from the original unfair baseline recommended items $L_{N}(u)$ where
$L^{F}_{K}(u)\subset L_{N}(u)\ \ where\ \ K\leq N$ such that the new list
would be more appealing to the system as a whole considering the relevance
score to the user $u$ and fairness objectives jointly.

Formally, item $I_{x}$ is presented ahead of item $I_{y}$ in $L_{N}(u)$ if
$s_{ux}>s_{uy}$. Recommending the items to users based solely on the relevance
score is designed to help improve the overall system recommendation accuracy
regardless of the fairness measures in a multi-sided platform. We define a
binary decision matrix $A=[A_{ui}]_{n\times N}$ with value 1 when the item
ranked $i$ in $L_{N}(u)$ is recommended to user $u$ in the new fairness-aware
recommendation list, i.e., $L^{F}_{K}(u)$ and 0 otherwise. Hence, the fair
top-K recommendation list to user $u$, can be represented as
$[A_{u1},A_{u2},...,A_{uN}]$ when $\sum_{i=1}^{N}{A_{ui}}=K$, $K\leq N$. We
discuss below an optimization framework to calculate optimal values for matrix
$A$ and re-rank original unfair recommendation list.

###  4.1. Marketplace Fairness Objectives

The fairness representation target, i.e., the ideal distribution of exposure
or relevance among groups, is the first step to designing a fair
recommendation model that should be decided based on the application and by
the system designers. Kırnap et al. (2021) classified the fairness notions
commonly used in IR literature into three groups based on their ideal target
representation, (1) parity between groups; (2) proportionality in exposure in
groups according to the group/catalog size; and (3) proportionality to the
relevance size to the recommended groups. This work focuses on the notion of
fairness defined based on a “parity-oriented” target representation, leaving
other concepts of fairness for future investigations.

####  4.1.1. Fairness constraint on producer side

On the producer side, fairness may be quantified in terms of two distinct
types of benefit functions: exposure and relevance, both of which can be
binary or graded (Gómez et al., 2022). Given that suppliers’ primary objective
is their products’ visibility, this study focuses its attention exclusively on
the (binary) exposure dimension, leaving the other producer fairness
constraints for future work. To measure the exposure parity, we divide items
into two categories of short-head $\mathcal{I}_{1}$ and long-tail
$\mathcal{I}_{2}$ defined based on their popularity score where
$\mathcal{I}_{1}\cap\mathcal{I}_{2}=\emptyset$. We define the notation of
$\mathcal{MP}$ as a metric that quantifies item groups’ exposition in the
recommendation list decision, $A$. In our experiments, we used the item group
exposure count to quantify this. Deviation from Producer Fairness (DPF) is the
metric that defines the deviation from parity exposition defined by:

(1)
$\mathbf{DPF}(A,\mathcal{I}_{1},\mathcal{I}_{2})=\operatorname{\mathbb{E}}\left[\mathcal{MP}(i,A)|i\in\mathcal{I}_{1}\right]-\operatorname{\mathbb{E}}\left[\mathcal{MP}(i,A)|i\in\mathcal{I}_{2}\right]$

####  4.1.2. Fairness constraint on the consumer side

We divide users into two groups of frequent users, $\mathcal{U}_{1}$, and
less-frequent users, $\mathcal{U}_{2}$ based on their activity level. The
notation $\mathcal{MC}$ is a metric that can evaluate the recommendation
relevance in each group given the recommendation list decision matrix, $A$. In
our experiments, we assessed the relevance using group $nDCG$ calculated on
the training dataset. The ideal fair recommendation would recommend items
based on the user’s known preference regardless of their activity level and
the quality of recommendation on frequent and less-frequent users should not
get amplified by the recommendation algorithm. We define the deviation from
consumer fairness parity as:

(2)
$\mathbf{DCF}(A,\mathcal{U}_{1},\mathcal{U}_{2})=\operatorname{\mathbb{E}}\left[\mathcal{MC}(u,A)|u\in\mathcal{U}_{1}\right]-\operatorname{\mathbb{E}}\left[\mathcal{MC}(u,A)|u\in\mathcal{U}_{2}\right]$

Note that when the values of $DPF\rightarrow 0$ or $DCF\rightarrow 0$, it
shows parity between the advantaged and disadvantaged user and item groups.
However, this may suggest a reduction in the overall system accuracy. The sign
of $DCF$ and $DPF$ shows the direction of disparity among the two groups,
which we decided to keep in this work. It is noteworthy that the proposed
metrics $DPF$ and $DCF$, due to their linear nature with respect to the binary
decision matrix $A$, present computational efficiency over metrics that
necessitate non-linear optimization approaches, thereby simplifying the
integration into existing recommendation system frameworks.

Note on Fairness Evaluation Metrics Selection. Our study employs DCF and DPF
metrics that encapsulate consumer effectiveness and producer exposure,
aligning with fairness concepts prevalent in recommender systems literature
(Deldjoo et al., 2023). While these metrics offer a focused lens on
recommendation fairness, we acknowledge the broader ecosystem of fairness
metrics and prioritize a deeper cross-metric analysis in future work to
understand their interdependencies and collective impact on recommendation
ecosystems.

###  4.2. Proposed Algorithm

In this section, we will use the top-N recommendation list and relevance
scores provided by traditional unfair recommendation algorithm as baseline. We
apply a re-ranking post-hoc algorithm to maximize the total sum of relevance
scores while minimizing the deviation from fairness on the producer and
consumer perspective, $\mathbf{DCF}$ and $\mathbf{DPF}$ respectively. We can
formulate the fairness aware optimization problem given the binary decision
matrix, A, as:

(3) $\displaystyle\max_{A_{ui}}$
$\displaystyle\sum_{u\in\mathcal{U}}\sum_{i=1}^{N}{S_{ui}.A_{ui}}-\lambda_{1}\times\mathbf{DCF}(A,\mathcal{U}_{1},\mathcal{U}_{2})-\lambda_{2}\times\mathbf{DPF}(A,\mathcal{I}_{1},\mathcal{I}_{2})$
s.t. $\displaystyle\sum_{i=1}^{N}{A_{ui}}=K,A_{ui}\in{\\{0,1\\}}$

The solution to the above optimization problem would recommend exactly $K$
items to each user while maximizing the summation of preference scores and
penalizing deviation from fairness. $0\leq\lambda_{1},\lambda_{2}\leq 1$ are
hyperparameters that would be selected based on the application and would
assign how much weight is given to each fairness deviation concern. A complete
user-oriented one-sided system could assign high weight to $\mathbf{DCF}$ and
0 to $\mathbf{DPF}$, and vice versa for a provider-oriented system. Note that
if the value of $\lambda_{1},\lambda_{2}$ are both equal to $0$ then the
optimal solution will be the same as the baseline recommendation system list,
that is, $L^{F}_{K}(u)=L_{K}(u)$. The effect of different values for
$\lambda_{1}$ and $\lambda_{2}$ are studied in the ablation study section.
Parity between groups is defined as the ideal representation of the fairness
in the model but is not enforced as a constraint in our optimization to avoid
resulting in diminishing the total model accuracy in a significant way.

The optimization problem above is a mixed-integer linear programming (MILP)
and a known NP-hard problem. Although MILP cannot be generally solved
optimally in polynomial time, there exists many fast heuristic algorithms and
industrial optimization solvers that would provide a good feasible solution in
practice222e.g., Gurobi solver at https://www.gurobi.com. The MILP proposed
optimization at Equation 3 can be reduced to a special case of Knapsack
problem where the goal is to select items for each user that would maximize
the total score in which each item has a weight equal to 1 and the total
weight is constrained by fixed size K. Since each item has the same weight in
this instance of Knapsack problem, we can solve it optimally by a greedy
algorithm in polynomial time. Now we are ready to propose the Fair Re-ranking
Greedy algorithm (Algorithm 2) that would give the optimal solution for the
optimization problem in Equation 3. Alternatively, we can relax the binary
constraint of variables to fractional variables with boundary constraints
i.e., $0\leq A_{ui}\leq 1$ and solve the relaxed optimization problem in
polynomial time. The algorithm based on optimization is presented in Algorithm
1. The algorithm based on optimization, Algorithm 1, is designed to solve the
relaxed optimization problem, converting the MILP problem to a standard linear
programming problem. In this relaxed problem, we use a simplex algorithm, a
standard method for numerically solving such linear programming problems. The
simplex algorithm is an iterative method that navigates the corners of the
feasible region defined by the problem constraints to find the optimal
solution, which maximizes the objective function. This approach allows us to
find the best solution that satisfies all the constraints in polynomial time,
making it a practical choice for the type of problems we are addressing in
this study. However, the solution obtained may be fractional and not
necessarily integral, due to the relaxation of the binary constraints.

Input : $\mathcal{U},\mathcal{I},\lambda_{1},\lambda_{2},K$

Output : Item recommendation matrix ${A}^{*}$

/* ${A}^{*}$ is a $n\times N$ binary matrix with elements $1$ when the item is
recommended to the user and $0$ otherwise. */

1 S $\leftarrow$ Run baseline algorithm and store the relevance score matrix
for top-N items for each user

/* $S$ is a $n\times N$ matrix representing the predicted relevance score
generated by unfair baseline algorithms for each user-item pair */

2 Formulate the Optimization Problem as an Integer Programming following
equation 3

3 Solve Relaxed Linear Programming with added boundary constraint $0\leq
A_{ui}\leq 1$, $\forall u\in\mathcal{U},\forall i\in\\{1,2,...,N\\}$

return _$A^{*}$_

Algorithm 1 The Fair Re-ranking Optimization

Input : $\mathcal{U},\mathcal{I},\lambda_{1},\lambda_{2},K$

Output : Fair top-K recommendation list $L^{F}_{K}$

1

2S $\leftarrow$ Run baseline algorithm and store the relevance score matrix
for top-N items for each user

3 $UG_{u}$ $\leftarrow$ Binary vector with elements of $1$ when user
$u\in\mathcal{U}$ is in the protected group and $-1$ otherwise

4 $PG_{i}$ $\leftarrow$ Binary vector with elements of $1$ when item ranked
$i$ in the traditional top-N recommendation list, ${L}_{N}(u)$, is in the
protected group and $-1$ otherwise

5

/* Protected groups are the underrepresented groups in baseline algorithms
such as unpopular items */

6

7foreach  _$u\in\mathcal{U}$_ do

8 foreach  _$i\in\\{1,2,...,N\\}$_ do

9 $CF_{ui}\leftarrow UG_{u}\times\mathcal{MC}(u,i)$

10 $PF_{ui}\leftarrow PG_{i}\times\mathcal{MP}(u,i)$

11 $\hat{S}_{ui}\leftarrow S_{ui}+\lambda_{1}CF_{ui}+\lambda_{2}PF_{ui}$

12 end foreach

13

14 end foreach

15$L^{F}_{K}(u)$ $\leftarrow$ Sort matrix $\hat{S}$ along the rows axis and
select top-$K$ items for recommendation to each users, $\forall$
$u\in\mathcal{U}$

return _$L^{F}_{K}(u)$_

Algorithm 2 The Fair Re-ranking Greedy Algorithm

On the other hand, the proposed Fair Re-ranking Greedy Algorithm aims to re-
rank a list of recommendations in a way that ameliorates biases, particularly
for underrepresented or protected groups. This is accomplished by modifying
the traditional relevance scores with additional terms that account for user
and item group memberships. In the Algorithm 2, for each user
$u\in\mathcal{U}$ and item $i\in\\{1,2,...,N\\}$, the terms $CF_{ui}$ and
$PF_{ui}$ are computed. These terms are indicators of whether a user or item
belongs to a protected group. They are multiplied by $\lambda_{1}$ and
$\lambda_{2}$ respectively, which serve as fairness hyperparameters
controlling the extent of the fairness adjustments. If $\lambda_{1}$ and
$\lambda_{2}$ are chosen judiciously, these adjustments can help rectify
biases in the original relevance scores.

The algorithm then proceeds to re-rank items based on the adjusted scores,
$\hat{S}_{ui}$. The top-$K$ items from this re-ranked list are selected for
recommendation. This ensures that the final list of recommendations is not
solely based on the original relevance scores, but also takes fairness
considerations into account. Theoretically, if the original relevance scores
exhibit biases against certain user or item groups, our algorithm is designed
to rectify those biases, yielding a fairer ranking. This is because it
explicitly incorporates fairness adjustments into the scores and re-ranks
items based on these adjusted scores. Further empirical studies are planned to
corroborate this theoretical analysis and provide concrete evidence of the
algorithm’s effectiveness on various datasets.

We finally discuss the time complexity of the Fair Re-ranking Greedy
algorithm.

###### Lemma 4.1.

The time complexity of the proposed re-ranking algorithm has a worst-case
bound of $\mathcal{O}(n\times N)$

###### Proof.

The first 3 lines of the algorithm will store the traditional relevance score
matrix for Top-N items and store the protected groups in consumers and
providers which can be done in linear time $\mathcal{O}(n+m)$. The second part
in line 4-10 is to re-score all elements in the original relevance matrix by
accounting for fairness measures which needs $\mathcal{O}(n\times N)$
operations in constant time. Lastly, we will sort the new relevance matrix for
all users and select top-K items for recommendation. Using max-heap the worst
case time complexity is $\mathcal{O}(N+K\log(K))$. Hence, considering $N$ and
$K$ are much smaller than $n$, the total time complexity is
$\mathcal{O}(n\times N)$ ∎

##  5\. Experimental Methodology

In this section, we first briefly describe the datasets, baselines and
experimental setup used for experiments. All source code and dataset of this
project has been released publicly. To foster the reproducibility of our
study, we evaluate all recommendations with the Python-based open-source
recommendation toolkit Cornac333https://cornac.preferred.ai/ (Salah et al.,
2020; Truong et al., 2021), and we have made our codes open
source.444https://github.com/rahmanidashti/CPFairRank

Datasets. We use eight public datasets from different domains such as Movie,
Point-of-Interest, Music, Book, E-commerce, and Opinion with different types
of feedback (i.e., explicit or implicit) and characteristics, including
MovieLens, Epinion, Gowalla, and LastFM. We apply $k$-core pre-processing
(i.e., each training user/item has at least $k$ ratings) on the datasets to
make sure each user/item has sufficient feedback. Table 2 shows the statistics
of all datasets. We remind that the size of the datasets employed in our study
was deliberately kept modest to ensure computational efficiency. Despite this,
the robustness of our reranking model is evident across various datasets,
underlining its adaptability to different data volumes and characteristics.

Table 2. Statistics of the datasets Dataset | Users | Items | Interactions | Sparsity
---|---|---|---|---
MovieLens | 943 | 1,349 | 99,287 | 92.19%
Epinion | 2,677 | 2,060 | 103,567 | 98.12%
Gowalla | 1,130 | 1,189 | 66,245 | 95.06%
LastFM | 1,797 | 1,507 | 62,376 | 97.69%
BookCrossing | 1,136 | 1,019 | 20,522 | 98.22 %
Foursquare | 1,568 | 1,461 | 42,678 | 98.13%
AmazonToy | 2,170 | 1,733 | 32,852 | 99.12%
AmazonOffice | 2,448 | 1,596 | 36,841 | 99.05%

Evaluation Method. For the experiments, we randomly split each dataset into
train, validation, and test sets in 70%, 10%, and 20% respectively, and all
the baseline models share these datasets for training and evaluation. We
define Consumer-Producer fairness evaluation (mCPF) metric to evaluate the
overall performance of models w.r.t. two-sided fairness. mCPF computes the
weighted average deviation of provider fairness (DPF) and deviation of
consumer fairness (DCF), i.e., $mCPF(w)=w\cdot DPF+(1-w)\cdot DCF$, where $w$
is a weighting parameter that can be selected by the system designer depending
on the application or priority for each fairness aspect of the marketplace.
DCF and DPF are defined in Equations 1 and 2, respectively, and the lowest
value for mCPF shows the fairest model. To select the model parameters,
$\lambda_{1}$ and $\lambda_{2}$, we treat them as a hyperparameter and set
them to the value that maximizes the average values of mCPF and overall nDCG
for each dataset and model.

Base Ranker Methods. We compare the performance of our fairness method on
several recommendation approaches, from traditional to deep recommendation
models, as suggested by Dacrema et al. (2019). Therefore, we include two
traditional methods (PF and WMF) as well as two deep recommendation models
(NeuMF and VAECF). We also include two baselines approaches, Random and
MostPop, for further investigation of the results. The introduction of
baselines are as the following:

  * •

PF (Gopalan et al., 2015): This method is a variant of probabilistic matrix
factorization where the weights of each user and item latent features are
positive and modeled using the Poisson distribution.

  * •

WMF (Hu et al., 2008; Pan et al., 2008): This method assigns smaller wights to
negative samples and assumes that for two items their latent features are
independent.

  * •

NeuMF (He et al., 2017): This algorithm learns user and item features using
multi-layer perceptron (MLP) on one side and matrix factorization (MF) from
another side, then applies non-linear activation functions to train the
mapping between users and items features that are concatenated from MLP and MF
layers.

  * •

VAECF (Liang et al., 2018): This method is based on variational autoencoders
which introduce a generative model with multinomial likelihood and use
Bayesian inference for parameter estimation.

Evaluation Settings. We adopt the baseline algorithms with the default
parameter settings, suggested in their original paper. We set the embedding
size for users and items to $50$ for all baseline algorithms. For NeuMF, we
set the size of the MLP with $32,16,8$ and we apply hyperbolic tangent (TanH)
non-linear activation function between layers. We set the learning rate to
$0.001$. Early stopping is applied and the best models are selected based on
the performance on the validation set. We apply Adam (Kingma and Ba, 2014) as
the optimization algorithm to update the model parameters.

###  5.1. Fairness Group Assumption

The protected groups usually are treated as the advantaged groups in group
fairness (Pedreschi et al., 2009). The group of users and items can be divided
under different requirements for different tasks (Abdollahpouri et al., 2019b;
Li et al., 2021). In this work, we examine two different user grouping methods
and one item grouping method. Specifically, we group users based on the level
of activity of users and the consumption of popular items in the user
profiles. We also group items according to the ratio of their popularity.
Hence, we define users and items groups as follows:

###### Definition 5.1.

The level of item popularity (IG): Following (Abdollahpouri et al., 2019b;
Burke et al., 2016), we select the top 20% of items according to the number of
interactions they received from the training set as the popular items (i.e.,
short-head items), and the rest as the unpopular items or long-tail items. We
apply this grouping strategy to our study to highlight and evaluate the
fairness of the recommendation system in terms of how well it can balance the
recommendations between popular and unpopular items. In addition, this metric
can also be used to evaluate the effectiveness of different recommendation
algorithms in terms of their ability to recommend long-tail items.

###### Definition 5.2.

The level of user activity (UG1): In order to investigate potential unfairness
in recommendation systems, we adopt a user grouping strategy similar to that
used by Li et al. (2021). This strategy involves separating users into two
groups based on their level of activity. The top 5% of users, ranked by the
number of interactions, are labelled as the active group, and the remaining
users are labelled as the inactive group. By comparing the performance of
recommendation algorithms for these two groups, we aim to evaluate the
fairness of the system and any potential bias towards active users.

###### Definition 5.3.

The consumption of popular items in user profile (UG2): To further evaluate
the fairness of recommendation systems, we use a user grouping strategy
similar to that described by (Abdollahpouri et al., 2019b). This strategy
involves separating users into two groups based on the number of popular items
in their profiles. Popular items are defined as those with popularity values
that fall within the top 20% of item popularity. The top 20% of users, ranked
by the number of popular items in their profiles, are labelled as the
mainstream group, and the remaining users are labelled as the non-mainstream
group. This approach allows us to investigate any potential bias in the
recommendations towards users who have a higher consumption of popular items.

Table 3. The recommendation performance of all, and different user and item
groups of our re-ranking method and corresponding baselines on Epinion and
LastFM datasets. All re-ranking results here are obtained under the fairness
constraint on nDCG. The evaluation metrics here are calculated based on the
top-10 predictions in the test set. Our best results are highlighted in bold.
$\Delta$ values denote the percentage of relative improvement in $mCPF$
compared to fairness-unaware recommendation algorithm (N). The reported
results for $mCPF$ are based on $w=0.5$. Note that the implementation of C is
aligned with (Li et al., 2021) used as baseline here.

Model Type User Relevance (nDCG) Item Exposure Both All Active Inactive DCF
$\downarrow$ Nov. Cov. Short. Long. DPF $\downarrow$ mCPF $\downarrow$
$\frac{mCPF}{All}$ $\downarrow$ —$\Delta(\%)$— $\uparrow$ Epinion PF N 0.0321
0.0751 0.0298 0.0453 4.9602 0.5073 0.8281 0.1719 0.6562 0.3588 11.1845 0.0 PF
C 0.0337 0.0732 0.0316 0.0415 4.9754 0.5083 0.8243 0.1757 0.6486 0.3524
10.4539 1.7837 PF P 0.0304 0.0757 0.0280 0.0477 5.3172 0.5325 0.6153 0.3847
0.2306 0.1476 4.8553 58.8629 PF CP 0.0313 0.0740 0.0290 0.0450 5.3302 0.5345
0.6113 0.3887 0.2226 0.1418 4.5332 60.4794 WMF N 0.0235 0.0577 0.0217 0.0360
4.9483 0.2913 0.9423 0.0577 0.8846 0.4667 19.868 0.0 WMF C 0.0236 0.0565
0.0219 0.0346 4.9481 0.2898 0.9423 0.0577 0.8846 0.4658 19.754 0.1928 WMF P
0.0234 0.0577 0.0215 0.0361 4.9626 0.3019 0.9322 0.0678 0.8644 0.4567 19.5505
2.1427 WMF CP 0.0234 0.0565 0.0217 0.0348 4.9623 0.3010 0.9322 0.0678 0.8644
0.4558 19.4454 2.3355 NeuMF N 0.0447 0.0840 0.0427 0.0414 3.8733 0.1223 0.9914
0.0086 0.9828 0.5195 11.6089 0.0 NeuMF C 0.0456 0.0770 0.0440 0.0330 3.8745
0.1223 0.9913 0.0087 0.9826 0.5137 11.2555 1.1165 NeuMF P 0.0448 0.0846 0.0427
0.0420 3.8801 0.1262 0.9849 0.0151 0.9698 0.5134 11.4675 1.1742 NeuMF CP
0.0455 0.0749 0.0439 0.0310 3.8816 0.1262 0.9851 0.0149 0.9702 0.5061 11.1255
2.5794 VAECF N 0.0444 0.0801 0.0425 0.0376 4.4061 0.3107 0.9190 0.0810 0.8380
0.4445 10.009 0.0 VAECF C 0.0443 0.0735 0.04280 0.0308 4.4080 0.3102 0.9184
0.0816 0.8368 0.4393 9.9142 1.1699 VAECF P 0.0438 0.0789 0.0420 0.0369 4.4349
0.3218 0.8946 0.1054 0.7892 0.4196 9.5777 5.6018 VAECF CP 0.0439 0.0739 0.0423
0.0316 4.4366 0.3204 0.8943 0.1057 0.7886 0.4157 9.4628 6.4792 LastFM PF N
0.0372 0.0259 0.0378 -0.0119 5.0905 0.6682 0.6945 0.3055 0.3890 0.1885 5.0699
0.0 PF C 0.0373 0.0260 0.0379 -0.0120 5.0904 0.6689 0.6947 0.3053 0.3894
0.1887 5.0590 0.1061 PF P 0.0369 0.0250 0.0375 -0.0125 5.1208 0.6729 0.6792
0.3208 0.3584 0.1729 4.6844 8.2759 PF CP 0.0372 0.0251 0.0378 -0.0127 5.1236
0.6729 0.6784 0.3216 0.3568 0.1721 4.6263 8.7003 WMF N 0.0319 0.0498 0.0309
0.0188 5.5360 0.7804 0.4452 0.5548 -0.1096 -0.0454 -1.4236 0.0 WMF C 0.0334
0.0425 0.0329 0.0096 5.5524 0.7717 0.4406 0.5594 -0.1188 -0.0546 -1.6352
20.2643 WMF P 0.0290 0.0454 0.0282 0.0172 5.7963 0.7930 0.3313 0.6687 -0.3374
-0.1601 -5.5112 252.6432 WMF CP 0.0299 0.0422 0.0292 0.0130 5.8066 0.7877
0.3278 0.6722 -0.3444 -0.1657 -5.5455 264.978 NeuMF N 0.0415 0.0394 0.0416
-0.0022 3.7975 0.0916 0.9940 0.0060 0.9880 0.4929 11.8828 0.0 NeuMF C 0.0444
0.0348 0.0449 -0.0101 3.8015 0.0929 0.9940 0.0060 0.9880 0.4889 11.0113 0.8115
NeuMF P 0.0411 0.0391 0.0412 -0.0021 3.8122 0.0936 0.9811 0.0189 0.9622 0.4801
11.6955 2.5969 NeuMF CP 0.0436 0.0303 0.0443 -0.0140 3.8192 0.0942 0.9773
0.0227 0.9546 0.4703 10.7966 4.5851 VAECF N 0.0560 0.0651 0.0556 0.0095 4.6040
0.4293 0.7730 0.2270 0.5460 0.2777 4.9572 0.0 VAECF C 0.0598 0.0550 0.0600
-0.0050 4.6036 0.4313 0.7738 0.2262 0.5476 0.2713 4.5375 2.3046 VAECF P 0.0544
0.0589 0.0542 0.0047 4.6660 0.4340 0.7294 0.2706 0.4588 0.2317 4.2561 16.5646
VAECF CP 0.0561 0.0549 0.0562 -0.0013 4.6635 0.4360 0.7318 0.2682 0.4636
0.2311 4.1172 16.7807

Table 4. The recommendation performance of all, and different user and item
groups of our re-ranking method and corresponding baselines on Epinion and
LastFM datasets. All re-ranking results here are obtained under the fairness
constraint on nDCG. The evaluation metrics here are calculated based on the
top-10 predictions in the test set. Our best results are highlighted in bold.
$\Delta$ values denote the percentage of relative improvement in $mCPF$
compared to fairness-unaware recommendation algorithm (N). The reported
results for $mCPF$ are based on $w=0.5$. Note that the implementation of C is
aligned with (Li et al., 2021) used as baseline here.

Model Type User Relevance (nDCG) Item Exposure Both All Main. Non-main. DCF
$\downarrow$ Nov. Cov. Short. Long. DPF $\downarrow$ mCPF $\downarrow$
$\frac{mCPF}{All}$ $\downarrow$ —$\Delta(\%)$— $\uparrow$ Epinion PF N 0.0321
0.0369 0.0309 0.0060 4.9602 0.5073 0.8281 0.1719 0.6562 0.3399 10.5954 0.0 PF
C 0.0331 0.0338 0.0330 0.0008 4.9633 0.5058 0.8265 0.1735 0.6530 0.3332
10.0513 1.9712 PF P 0.0304 0.0349 0.0293 0.0056 5.3172 0.5325 0.6153 0.3847
0.2306 0.1229 4.0428 63.8423 PF CP 0.0309 0.0323 0.0306 0.0017 5.3224 0.5325
0.6133 0.3867 0.2266 0.117 3.7876 65.5781 WMF N 0.0235 0.0167 0.0252 -0.0085
4.9484 0.2913 0.9423 0.0577 0.8846 0.4420 18.8165 0.0 WMF C 0.0236 0.0163
0.0255 -0.0092 4.9479 0.2908 0.9423 0.0577 0.8846 0.4413 18.6912 0.1584 WMF P
0.0234 0.0166 0.0250 -0.0085 4.9627 0.3019 0.9322 0.0678 0.8644 0.4317 18.4803
2.3303 WMF CP 0.0234 0.0162 0.0252 -0.0090 4.9619 0.3005 0.9323 0.0677 0.8646
0.4313 18.4316 2.4208 NeuMF N 0.0451 0.047 0.0446 0.0025 3.8923 0.1214 0.9911
0.0089 0.9822 0.5025 11.1518 0.0 NeuMF C 0.0462 0.0462 0.0462 0.0000 3.8945
0.1233 0.9911 0.0089 0.9822 0.5000 10.8108 0.4975 NeuMF P 0.0451 0.047 0.0446
0.0024 3.9049 0.1277 0.9786 0.0214 0.9572 0.4896 10.8655 2.5672 NeuMF CP
0.0462 0.0464 0.0462 0.0002 3.9075 0.1272 0.9786 0.0214 0.9572 0.4875 10.5428
2.9851 VAECF N 0.0444 0.0527 0.0423 0.0103 4.3809 0.2893 0.9229 0.0771 0.8458
0.4407 9.9279 0.0 VAECF C 0.0464 0.0175 0.0536 -0.0362 4.4419 0.3019 0.9153
0.0847 0.8306 0.3873 8.3488 12.1171 VAECF P 0.0376 0.0461 0.0355 0.0106 4.9044
0.318 0.5856 0.4144 0.1712 0.0976 2.5944 77.8534 VAECF CP 0.0388 0.0186 0.0439
-0.0253 4.9316 0.3218 0.5856 0.4144 0.1712 0.0623 1.6048 85.8634 LastFM PF N
0.0372 0.0507 0.0338 0.0169 5.0905 0.6682 0.6945 0.3055 0.3890 0.2054 5.5245
0.0 PF C 0.0372 0.0500 0.0340 0.0160 5.0883 0.6682 0.6951 0.3049 0.3902 0.2055
5.5227 0.0487 PF P 0.0369 0.0509 0.0334 0.0175 5.1208 0.6729 0.6792 0.3208
0.3584 0.1902 5.1531 7.4002 PF CP 0.0370 0.0497 0.0339 0.0159 5.1222 0.6729
0.6784 0.3216 0.3568 0.1886 5.0932 8.1792 WMF N 0.0319 0.0522 0.0268 0.0254
5.5358 0.7804 0.4452 0.5548 -0.1096 -0.0427 -1.339 0.0 WMF C 0.0328 0.0502
0.0284 0.0218 5.5379 0.7711 0.4443 0.5557 -0.1114 -0.0454 -1.3854 6.3232 WMF P
0.0290 0.0443 0.0252 0.0190 5.7961 0.7930 0.3313 0.6687 -0.3374 -0.1612
-5.5491 277.5176 WMF CP 0.0295 0.0435 0.0260 0.0175 5.7963 0.7863 0.3306
0.6694 -0.3388 -0.1626 -5.5137 280.7963 NeuMF N 0.0415 0.0720 0.0338 0.0382
3.7975 0.0916 0.9940 0.0060 0.9880 0.5192 12.5169 0.0 NeuMF C 0.0408 0.0622
0.0355 0.0267 3.7906 0.0942 0.9938 0.0062 0.9876 0.5132 12.5784 1.1556 NeuMF P
0.0411 0.0698 0.0339 0.0359 3.8122 0.0936 0.9811 0.0189 0.9622 0.5050 12.3021
2.735 NeuMF CP 0.0400 0.058 0.0355 0.0225 3.8052 0.0949 0.9809 0.0191 0.9618
0.4981 12.4556 4.0639 VAECF N 0.0555 0.0779 0.0499 0.0280 4.6164 0.4280 0.7790
0.2210 0.5580 0.2965 5.3414 0.0 VAECF C 0.0538 0.0002 0.0672 -0.067 4.5467
0.4333 0.7821 0.2179 0.5642 0.2518 4.6794 15.0759 VAECF P 0.0509 0.0748 0.0449
0.0298 5.1853 0.4605 0.3776 0.6224 -0.2448 -0.1089 -2.1391 136.7285 VAECF CP
0.0470 0.0106 0.0561 -0.0454 5.1287 0.4612 0.3776 0.6224 -0.2448 -0.1467
-3.1233 149.4772

The reason for exploring these two methods is that we believe the difference
between user interactions and popular consumption will reflect their different
activity from both quantitative and qualitative positives and thus in a more
reasonable manner.

##  6\. Results and Discussion

###  6.1. Statements of examined research questions

To gain a better understanding of the merits of the proposed CP fairness
optimization framework, through the course of experiments, we intend to answer
the following evaluation questions:

:

RQ1: In this research question, we wish to investigate whether there is a
trade-off between the three evaluation objectives ¡Acc, DCF, DPF¿ in the
baseline CF models (i.e., the rows denoted with ‘N’ indicating potentially
unfair models), where trade-off may be a result of underlying data biases and
may require algorithmic intervention.

:

RQ2: In the second research question, we seek to determine whether the popular
uni-sided fairness focused on C-Fairness or P-Fairness intervention is
sufficient to reduce unfairness on both the consumer- and producer-sides, or
whether biases persist in one side. This will motivate the potential necessity
of two-sided fairness intervention.

:

RQ3. This research question investigates whether or not the proposed CP-
fairness algorithm based on MIP in this work satisfies the requirements for
fairness on both the consumer and supplier sides concurrently, and whether or
not this compromises the overall accuracy of the system.

We will now proceed to the next section to describe the answers to these
research questions in further detail.

Table 5. The correlation coefficients between evaluation metrics ¡Acc, DCF¿ and ¡Acc, DPF¿ across all eight datasets were explored in this research (for baseline models in the N category).  | model/obj. | ¡Acc, DCF¿ | ¡Acc, DPF¿
---|---|---|---
Activity-lev. (Table 3) | VACEF | 0.0366 | -0.0511
NeuMF | 0.7494 | 0.0356
Mainstream (Table 4) | VACEF | -0.1664 | -0.3679
NeuMF | 0.4497 | -0.0836

###  6.2. Answers to the RQs and Discussion

The result of applying our proposed CP-FairRank optimization algorithm in
detail are presented in Table 3 (for activity-level user segmentation) and
Table 4 (for mainstream-based user segmentation – main. vs. non-main.), where
both tables employ the same popularity-based segmentation on the item side. In
both experimental settings, neural models NeuMF and VAEFCF tend to achieve the
highest levels of accuracy. As a result, we focus on these models when
describing fairness performance, as it would be pointless to analyze fairness
for models with relatively poor performance.

Answers to RQ1 and RQ2. “Bias inherent in the data of unfair models and the
effect of applying one-sided fairness optimization on evaluation objectives
¡Acc, DCF, DPF¿”.

  * •

First, we show some individual examples from Table 3 and Table 4. According to
Table 4, one can note the results of the best models along $<Acc,DCF,DPF>$ for
the Epinion dataset: NeuMF: $<0.0451,0.0025,0.9822>$ and VAECF:
$<0.0444,0.0103,0.8458>$, while for LastFM dataset, we have NeuMF:
$<0.0415,0.00382,0.988>$ and VAECF: $<0.0555,0.028,0.558>$. One immediate
observation is that in at least these two datasets, these models alter DCF and
DPF inconsistently to obtain high performance on accuracy. As an illustration,
in Epinion, VAECF achieves good performance with less compromise on DPF but a
higher compromise on DPF, and this trend is reversed in LastFM. These findings
imply that preexisting biases in the data may be exaggerated differently by
the baseline CF model, necessitating algorithmic intervention.

  * •

Since Table 3, and Table 4, only represent a small subset of the total
experiments conducted, in Table 5 we compute the Pearson correlation
coefficient across all eight datasets examined in this study better to
comprehend the relationship between the various evaluation objectives.
Ideally, a negative correlation between $<Acc\uparrow,DPF\downarrow>$ and
$<Acc\uparrow,DCF\downarrow>$ is desirable, as we need maximal accuracy and
minimal unfairness on the producer and consumer side. The most intriguing
finding is for the VACEF method, which demonstrates a negative correlation
between $<Acc,DCF>$, where this value is subtly better (i.e., lower) than its
NeuMF equivalent, Table 3 (-0.0511 vs. -0.356) vs. Table 4 (0.356 vs.
-0.0836). Quite intriguingly, we observe a strong positive correlation between
and, as opposed to a weak or negative correlation in VACEF. These results
indicate that VACEF is a strategy that employs distinct mechanisms for
retrieving relevant items, is capable of recommending relevant by proposing
items from the long tail (thereby enhancing DPF), and better serves the under-
served user group (improving DCF).

  * •

Now, we will focus on RQ2 and investigate the impact of one-sided fairness
optimization on several evaluation criteria. Table 3 and Table 4 reveal that
the general trend is that C-optimization increases C-Fairness while
P-optimization improves P-Fairness. For instance, from Table 3, we can see
that NeuMF C-optimization could achieve almost 20% improvement compared to the
baseline (i.e., N) on Epinion. Moreover, WMP P-Optimisation (see Table 4)
improved the baseline models by 207%. To account for variation among datasets,
we calculated the coefficients $\frac{DCF}{ACC}$ and $\frac{DPF}{ACC}$ for the
two best models in Table 6. We can observe that the general trend is that
C-Fairness optimization improves DCF, while P-Fairness optimization improves
DPF and this improvement appears to be greater for VACEF. Another intriguing
observation is that uni-sided fairness optimization may not guarantee multi-
sided fairness improvement, e.g., P-optimization may have a negative impact on
$\frac{DCF}{ACC}$, NeuMF (1.091 to 1.094) and $\frac{DCF}{ACC}$, VAECF (0.255
to 0.290).

These results are quite insightful and demonstrate that our suggested strategy
is capable of addressing diverse stakeholder fairness concerns. They also
expose a gap in past research, namely, the failure to investigate multi-sided
fairness evaluation when considering single-sided fairness intervention. Thus,
the results in this part set the ground for simultaneously demonstrating the
performance of our proposed CP-FairRank on all stakeholder evaluation
objectives.

Table 6. We calculated the $\frac{DPF}{ACC}$ and $\frac{DCF}{ACC}$ for each of the 8 datasets utilized in this study, and calculated their average below, in order to demonstrate the interplay and probable trade-off between fairness and overall system accuracy.  | model/obj. | $\frac{DPF}{ACC}\downarrow$ | $\frac{DCF}{ACC}\downarrow$
---|---|---|---
| N | P | C | N | C | P
Activity-lev. (Table 3) | VACEF | 21.238 | 18.786 | 21.006 | 1.051 | 0.942 | 1.002
NeuMF | 50.130 | 49.891 | 49.805 | 1.091 | 0.782 | 1.094
Mainstream (Table 4) | VACEF | 20.869 | 0.976 | 21.499 | 0.255 | -0.802 | 0.290
NeuMF | 46.498 | 46.232 | 46.201 | 0.314 | 0.182 | 0.308

Answers to RQ3. “Examining the effectiveness of CP-FairRank, our proposed CP-
Fairness optimization method for multi-stakeholder fairness optimization”.

The response to this research question is the center of this study. Here are
some insights into the effectiveness of CP-FairRank, our CPFairness
optimization method:

  * •

Upon first inspection of Tables 3 and 4, it is evident that the suggested CP-
Fairness optimization approach is able to simultaneously improve $DCF$ and
$DPF$ of the investigated CF models without sacrificing a great deal of
accuracy, and this holds for both datasets and disadvantaged groups. Due to
their simplicity, we employ the statistics $mCPF$ and $\frac{mCPF}{Acc}$ to
show this effect (the lower these value are the better they are judged). For
instance, we compare here these two statistics for ‘N’ and ‘CP’ for a randomly
selected dataset Epinion and VACEF method, which is equal to VAECF-N =
¡0.4445, 10.0009¿ and VAECF-CP = ¡0.4157, 9.4628¿, whereas for the second user
group VAECF-N = ¡0.4407, 9.9279¿ and VAECF-CP = ¡0.0623, 1.6048¿. These
results demonstrate a clear improvement in joint fairness without affecting
system utility as a whole, and this improvement is significantly greater for
the second user grouping.

  * •

We propose to aggregate the results across all datasets using the plots in
Fig. 4, where the x-axis represents the overall system utility (accuracy) and
the y-axis shows one of fairness objectives (DPF or DCF). In this case, the
plots are the baseline CF model without any fairness intervention (‘N’) and
the models after making ‘CP’ intervention using our proposed CP-FairRank. Note
that the points in these graphs reflect one of the 8 datasets examined in this
study.555Consider that the orange plots (after fairness intervention) should
be below the blue plots (before intervention) since the y-axis represents the
fairness targets and the lower they are, the lower the unfairness. This
tendency can be easily confirmed by examining the results across all models,
demonstrating that our strategy can increase fairness consistently across
models and datasets. In certain circumstances, for instance, NeuMF, the
improvement appears to be greater (looking at the sloping curve downward),
indicating that, depending on how much each model produces biased outcome,
there may be more or less space for improvement.

Summary. To provide a fair recommendation to both disadvantaged consumer and
producer groups, we propose CP-FairRank, a post-hoc method for optimizing the
fairness of ranking lists provided to users by taking into account the
interests of both stakeholders involved in recommendation, consumers and
producers. Through large-scale experiments on 8 datasets broadly adopted used
in recommendation research, we believe our study provides persuasive evidence
that the proposed technique can increase mCPF (joint consumer and producer
fairness) in literally all experimental case without compromising much on
accuracy (in some case the accuracy is also improved). Notable improvement is
also shown in the user grouping based on main-streamness, indicating that
fairness optimization is not a purely mathematical process and that its
quality can be affected by the data distribution provided by the underlying
user and item groups.

(a) NeuMF ¡Acc, DCF¿ (b) NeuMF ¡Acc, DPF¿ (c) VAECF ¡Acc, DCF¿ (d) VAECF ¡Acc,
DPF¿

Figure 4. Correlation plots were produced for the best performing models (in
terms of accuracy), NeuMF, and VACEF, to illustrate the potential trade-off
between accuracy and fairness metrics. Noting that the points in this example
represent datasets, the correlation measures the generalizability of the
findings across domains.

Ablation Study: Distributions of mCPF. In order to thoroughly assess the
effectiveness of our proposed CP-fairness re-ranking algorithm, we conducted a
comprehensive experiment with 128 cases on eight real-world datasets. The
experiment was conducted on two user groups, UG1 and UG2, to examine the
ability of the algorithm to meet the requirements of both user and item
fairness in a two-sided marketplace. The results of the experiment are
presented in Figures 5 and 6. These figures show the distribution of the mCPF
performance for all datasets, using four baseline algorithms (PF, WMF, NeuMF,
and VAECF) on activity-level and mainstream user groups, respectively. The
results indicate that our proposed CP-fairness model outperforms the baseline
algorithms and unilateral fairness models in all datasets, with a lower mCPF.
It is also important to note that the behavior of the unilateral fairness
models varies across datasets. This variability is due to differences in the
underlying data characteristics. For example, in Fig. 5a, the C-fairness
method performs better than the P-fairness method, while in Fig. 5h on the
Foursquare dataset, the P-fairness approach outperforms the C-fairness
approach. In conclusion, the results of our experiment demonstrate that our CP
re-ranking algorithm not only reduces fairness disparities between the two
groups of users and items, but also provides competitive accuracy in
comparison to the unilateral fairness methods and baselines. This is reflected
in the nDCG@10 scores reported on top of the plots in Figures 5 and 6. Our
proposed algorithm is therefore a promising solution for enhancing fairness in
two-sided marketplaces.

Ablation Study: Effect of $\lambda_{1}$ and $\lambda_{2}$. We also analyze the
impact of the optimization regularization parameters $\lambda_{1}$ and
$\lambda_{2}$ from Equation 3. We expect that the bigger $\lambda_{1}$ and
$\lambda_{2}$ are, the fairer our proposed model will be. However, the
excessive pursuit of fairness is unnecessary and could have an adverse impact
on the overall recommendation performance. Therefore, we are interested in
studying how different values of $\lambda_{1}$ and $\lambda_{2}$ in Equation 3
can influence the total performance of the system, i.e., total accuracy, and
novelty of the recommendation, as well as their impact on consumer and
provider groups.

(a) MovieLens

(b) Epinion

(c) AmazonToy

(d) AmazonOffice

(e) BookCrossing

(f) Gowalla

(g) LastFM

(h) Foursquare

Figure 5. Distributions of mCPF for fairness-unaware (N) and fairness-aware
methods (i.e., C, P, and CP) on all 8 datasets. The numbers on top of each
plot show the overall performance (i.e., nDCG@10 for all users) according to
each fairness methodology.

(a) MovieLens

(b) Epinion

(c) AmazonToy

(d) AmazonOffice

(e) BookCrossing

(f) Gowalla

(g) LastFM

(h) Foursquare

Figure 6. Distributions of mCPF for fairness-unaware (N) and fairness-aware
methods (i.e., C, P, and CP) on all 8 datasets. The numbers on top of each
plot show the overall performance (i.e., nDCG@10 for all users) according to
each fairness methodology.

(a) User Groups

(b) User Groups

(c) Item Groups

(d) Item Groups

Figure 7. The metric nDCG@10 and item exposure change on CP-fairness with
respect to the $\lambda_{1}$ and $\lambda_{2}$ on all, active and inactive
user groups and short-head and long-tail item group on activity-level group
(UG1). In each figure, the other $\lambda$ is equal to $0.05$.

(a) User Groups

(b) User Groups

(c) Item Groups

(d) Item Groups

Figure 8. The metric nDCG@10 and item exposure change on CP-fairness with
respect to the $\lambda_{1}$ and $\lambda_{2}$ on all, active and inactive
user groups and short-head and long-tail item group on mainstream group (UG2).
In each figure, the other $\lambda$ is equal to $0.05$.

The results presented in Figures 7 and 8 indicate that $\lambda_{1}$ exhibits
a more “accuracy-centric” behavior, implying that this parameter affects user-
fairness and overall system accuracy with little impact on the items’
expositions. The similarity in the type of items used by both active and
inactive users suggests that there is no significant difference in their
preferences for popular items. However, the $\lambda_{2}$ parameter showcases
an “exposure-centric” behavior that can affect both the accuracy and beyond-
accuracy of the system. An excessive increase in $\lambda_{2}$ may not
necessarily improve overall accuracy as many long-tail items lack sufficient
interaction data, leading to uncertainty in their potential impact on user
satisfaction if included in recommendation lists. Thus, finding the optimal
balance when selecting model parameters is crucial for enhancing the fairness
and overall effectiveness of the marketplace (Wu et al., 2022).

###  6.3. Additional Insight: The Implications of the CP-FairRank on Items and
Users within Subgroups

(a) Distribution of Utility of the top-$k$ rec. lists measured using nDCG.

(b) Distribution of Novelty of the top-$k$ rec. lists

Figure 9. Distribution of the utility (a) and novelty (b) of the top-$k$
recommendation list across users

In this section, we study further the implications of our proposed CP method.
We have previously demonstrated its prowess in enhancing both consumer and
producer fairness without compromising, and sometimes even augmenting, the
overall utility of recommendations. Drawing inspiration from (Wu et al.,
2021), where authors highlighted potential trade-offs between fairness
evaluation objectives and overall recommendation utility, we aim to understand
the potential impact of our algorithm on the exposure of items within various
subgroups. Specifically, we aim to offer a meticulous and in-depth analysis
regarding the impact on both advantaged and disadvantaged groups.

Toward this goal, while Wu et al. (Wu et al., 2021) employed metrics to track
variations in item exposure and recommendation quality, we shift our focus to
distribution representations. As illustrated in Figures 9a and 9b we present
the distribution of recommendation accuracy (NDCG) across users, as well as
the novelty distribution of recommended items for the entire users. It is
noteworthy that we use novelty as a proxy for item exposure, complementing it
as an additional metric beyond accuracy, in line with the exposure metric
(recommendation count) employed in prior sections to measure provider
fairness.

Upon examining the second figure, it becomes evident that both methods, P and
CP, effectively push the novelty of all items to the right, indicating an
increase in item novelty. This observation holds true for both advantaged and
disadvantaged groups, as well as overall. Interestingly, even when comparing C
with N, method C improves the novelty of recommended items, despite not being
explicitly designed for this purpose. These findings suggest that under our
proposed method, producers benefit from increased exposure to their less
popular items, and fairness is achieved at the group level, as demonstrated in
earlier sections. In terms of the impact on the novelty of items, the
hierarchy can be summarized as $CP=P>C>N$. Shifting our attention to the
primary query: does this enhancement in fairness and novelty come at the cost
of recommendation quality, especially when considering specific user
subgroups? An analysis of Fig. 9 reveals that methods C, P, and CP all
experience a decline in recommendation quality for both groups. However, the
decline is most pronounced for the C method. Hence, when focusing on
recommendation quality, the methods can be ranked as $N>CP=P>C$.

Overall, our study confirms the previous findings that there exists an
inherent trade-off between recommendation quality and the attainment of
fairness in recommendation systems. However, our proposed method adeptly
addresses the shortcomings of the consumer fairness method proposed by Li et
al. (Li et al., 2021), effectively minimizing the adverse impacts associated
with this trade-off.

##  7\. Conclusions

In this paper, we study fairness-aware recommendation algorithms from both the
user and item perspectives. We first show that current recommendation
algorithms produce unfair recommendations between different disadvantaged user
and item groups due to the natural biases and imperfections in the underlying
user interaction data. To address these issues, we propose a personalized CP-
fairness-constrained re-ranking method to compensate for the biases against
long-tail items and cold-start users, which are not necessarily groups defined
by sensitive attributes. Our method seeks to balance the representation in the
recommendation space, while maintaining the recommendation quality. Extensive
experiments across eight datasets on two different user grouping methods,
namely, activity-level and mainstreamness, indicate that our method can reduce
the unfair outcomes on beneficiary stakeholders, consumers and providers while
improving the overall recommendation quality. This demonstrates that
algorithmic fairness may play a critical role in mitigating data biases that,
if left uncontrolled, can result in societal discrimination and polarization
of opinions and retail businesses. Although this study has focused on specific
user and item groupings, we postulate that our findings could extend to other
groupings (e.g., based on sensitive attributes) that introduce substantial
disparities, as our re-ranking method’s objective function is designed to
optimize a balance between fairness and accuracy, though this could come at
the expense of accuracy depending on the particularities of the grouping
methodology and the feasibility of achieving such a balance. Hence, in the
future, we intend to extend this work by analyzing other fine-grained fairness
circumstances, such as mis-calibration and individual fairness, to determine
if our system is capable of addressing fairness constraints on these new
definitions of fairness and grouping methodology. Moreover, we anticipate
refining our model to better address the complexities of multi-sided fairness,
in recognition of the significant challenges this presents, as highlighted in
the discussion on uni-sided and multi-sided fairness optimization.
Furthermore, we recognize the necessity of testing our algorithms on larger,
more diverse datasets in future studies, as this will provide further insights
into their scalability and effectiveness in real-world, large-scale scenarios
(Rahmani et al., 2022c; Deldjoo et al., 2018), e.g., in temporal settings
(Rahmani et al., 2022c). In addition, we believe it would be interesting to
analyze the biases induced in each domain based on dataset characteristics
(such as popularity bias, the user gini coefficient representing user activity
distribution, and sparsity) and to explain the results based on these various
characteristics (see, for example, our recent research in this line (Deldjoo
et al., 2021b)). Another research domain that we consider highly pertinent to
this discussion is the study of fairness in the context of generative AI and
large language models (LLMs) applied to recommender systems and machine
learning at large (Deldjoo, 2024, 2023; Zhang et al., 2023; Nazary et al.,
2023; Weidinger et al., 2021). Given that these systems are trained on vast
amounts of internet data, it becomes crucial to examine their potential biases
and to consider strategies for mitigating social and ethical risks, as well as
optimizing overall performance.

###  7.1. Limitations

Despite proposing a practical system to seamlessly and jointly address CO-
Fairness in recommendations, like any research, our work is not without
limitations. The primary constraints of this study, particularly the selection
of fairness baselines, are discussed in detail in the subsequent sections.

Finding suitable baselines for our work presented several challenges,
including (i) the absence of methods that holistically address CP-Fairness
(most research has been focused on single-stakeholder constraints), and (ii)
varying interpretations and assumptions on “what is fair”. For the first
point, most existing work either focuses on evaluating fairness on CP, often
without coherent algorithmic integration (Deldjoo et al., 2023; Amigó et al.,
2023).

The second concern, defining “what is fairness” in a group setting in
recommendation algorithms, as highlighted in (Deldjoo et al., 2023) and
further underscored by Kırnap et al. (2021), is multifaceted and diverse. In
the RecSys literature, we can broadly consider the following notions:

  1. (1)

Fair target representation: This is where fairness hinges on representing
targets (such as user groups, item genres, etc.) in a manner that is either
equal (everyone gets the same representation) or proportional (representation
is aligned with some inherent proportion in the dataset or the real world).
The majority of algorithms focused on fairness enhancement, irrespective of
the stakeholder, belong to this category.

  2. (2)

Guaranteed allocation: This perspective ensures that every identifiable group
receives a spot in the recommendation list, thus ensuring that no group is
entirely left out or overlooked. It is rooted in the principle that fairness
is not only about balanced representation but also about preventing complete
absence, ensuring that every group, regardless of its size or nature, is
acknowledged. For instance, the work Wu et al. (2021) working on CP-fairness
operates on this principle.

Our CP framework primarily focuses on the first approach, that is, achieving
fairness through fair target representation. Integrating other CP-Fairness
perspectives such (Wu et al., 2021), which belongs to the guaranteed
allocation category, into our framework is not straightforward. Such an
adaptation would necessitate a comprehensive revision of how we define
fairness in our method. For these reasons, we decided to compare our proposed
fair CP re-ranking algorithm with unilateral fairness models, C and P-fairness
re-ranking on top of the core base ranker model to show how our method can
achieve the desirable performance on fairness metrics in both stakeholders and
overall recommendation performance (accuracy and beyond-accuracy).
Specifically, the C variation of our system targets consumer-side fairness
objectives, aligned with the approach introduced by Li et al. (2021). Our
approach incorporates users’ parity objectives in an unconstrained
optimization problem and employs a greedy algorithm for optimal polynomial-
time solutions. On the other hand, the P variation emphasizes provider-side
fairness objectives.

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