Cookie Consent Has Disparate Impact on Estimation Accuracy
Authors: Erik Miehling
Rahul Nair
Elizabeth M. Daly
Karthikeyan Natesan Ramamurthy
Robert Nelson Redmond
Venue: NeurIPS 2023 poster (2023)
Keywords: fairness
cookies
recommender systems
TL;DR: When users' cookie consent rates are cohort-dependent, an individual user's consent decision can lead to the recommender agent possessing disparate estimation errors of their latent attributes.

Abstract: Cookies are designed to enable more accurate identification and tracking of user behavior, in turn allowing for more personalized ads and better performing ad campaigns. Given the additional information that is recorded, questions related to privacy and fairness naturally arise. How does a user's consent decision influence how much the system can learn about their demographic and tastes? Is the impact of a user's consent decision on the recommender system's ability to learn about their latent attributes uniform across demographics? We investigate these questions in the context of an engagement-driven recommender system using simulation. We empirically demonstrate that when consent rates exhibit demographic-dependence, user consent has a disparate impact on the recommender agent's ability to estimate users' latent attributes. In particular, we find that when consent rates are demographic-dependent, a user disagreeing to share their cookie may counter-intuitively cause the recommender agent to know more about the user than if the user agreed to share their cookie. Furthermore, the gap in base consent rates across demographics serves as an amplifier: users from the lower consent rate demographic who agree to cookie sharing generally experience higher estimation errors than the same users from the higher consent rate demographic, and conversely for users who choose to disagree to cookie sharing, with these differences increasing in consent rate gap. We discuss the need for new notions of fairness that encourage consistency between a user's privacy decisions and the system's ability to estimate their latent attributes.

Cookie Consent Has Disparate Impact on Estimation Accuracy
Erik Miehling
Rahul Nair
Elizabeth Daly
Karthikeyan Natesan Ramamurthy
Robert Redmond
IBM Research
erik mi www.mmieeliinnnie com
frahul nair, elizabeth. daly)-ie. iim...mm.m..................m... com (knatesa, rredmond]@us iimm com
Abstract
Cookies are designed to enable more accurate identification and tracking of user behavior, in turn allowing for more personalized ads and better performing ad campaigns. Given the additional information that is recorded, questions related to privacy and fairness naturally arise. How does user's consent decision influence how much the system can learn about their demographic and tastes? Is the impact of user's consent decision the recommender system's ability to learn about their latent attributes uniform across demographics? We investigate these questions in the context of an engagement-drrven recommender system using simulation. We empirically demonstrate that when consent rates exhibit demooraphiic-depeddeee user consent has disparate impact the recommender agent's ability esti- mate users' latent attributes. In particular, we find that when consent rates are demographic-deeendeen.
share their cookie may counter- intuitively cause the recommender agent to know more about the user than if the user agreed share their cookie. Furthermore, the gap in base consent rates across demographics serves as an amplifier: users from the lower consent rate demo- graphic who provide consent generally experience higher estimation errors than the same users from the higher consent rate demographic, and conversely for users who choose to withhold consent, with these differences increasing in consent rate gap. We discuss the need for new notions of fairness that encourage consistency between a user's privacy decisions and the system's ability to estimate their latent attributes.
user disagreeing
Introduction
Increased regulation surrounding cookies has emerged in recent years in response to growing concerns over online privacy and data protection. In the EU, cookie policy is driven primarily by the General Data Protection Regulation (13) and the ePrivacy Directive (10) which dictate that if a website wishes use cookies identify and track users, beyond "strictly necessary cookies," then consent must be explicitly obtained from the user. There is currently no federal law regulating the use of cookies in the US, however, several states have imposed regulation that requires websites to disclose their data collection practices to users (5 40
Marketers use cookies narrow in target audiences most likely to buy their products, primarily via improved user tracking and enhanced personalization. The actual mechanisms for obtaining consent can introduce some additional fairness and privacy concerns. Many cookie consent interfaces are designed such that web content is at least partially obscured until the user makes
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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consent decision. These interfaces often exhibit deceptive design patterns (38 34 15 16] practices that incentivize users to make choices that lower their privacy. While some websites do offer a clear "reject all" button, many present the user with a decision between simple "I agree" or "accept all" and much less immediate choice of "manage preferences." This leads to many users agreeing to cookie tracking simply out of convenience (17). Furthermore, and an observation that forms the basis of the current paper, evidence suggests that users exhibit inherent differences in their likelihood of agreeing to cookie tracking. A recent study by YouGov 445) revealed that a user's s consent rate is influenced by their age and culture/geographical location. Of the markets surveyed in the study, users ranged from 64% agree (Poland) to 32% agree (US), with older individuals being less likely to provide consent than younger individuals, perhaps partially due to their overall lowered trust in tech companies when it comes to their personal data (46).
design
In this paper, we investigate how demographic-depent recommender system to learn users' latent attributes and offer targeted recommendations, The main finding of our paper that when user consent rates differ by demographics, the recommender system possesses disparate estimation accuracies across users in different demographics. The finding is based on a simple model of recommendations where, prior to the interaction, users provide cookie consent according to demographicc-eeendee for those who have provided consent, allow the recommender agent to form refined beliefs on users' demographics and preferences. Through sequential interaction with the users, the agent learns to personalize content to maximize engagement. We empirically illustrate the following:
consent rates impact the ability of the
probabilities. Users' consent decisions, along with the cookie
1) Disparate impact of consent: Under demographic-dependeee consent rates, users' consent decisions can have a disparate impact on the recommender agent's estimation accuracy of users' latent attributes. In particular, lower estimation errors for users in the lower consent rate population. In other words, a recommender system may know more about person who opts not be tracked compared to those who willingly provide tracking information. Additionally, users from a population with low consent rate who provide consent experience higher estimation errors than the same users from high consent rate population.
find that withholding consent can lead to
2) Amplification effects: The difference in consent rates across cohorts serves as an amplifier for the above effects, with the disparities in estimation errors across cohorts increasing in the consent rate gap.
Note that our model is simple: ads are described by a single feature, the user pool is fixed, and user affnities/preferences do not change over time. This simplicity is intentional, with the goal being to isolate and understand the effects of specific model aspects (i.e., impact of different user consent rates) without the additional noise and confounding factors present real-world settings. The observations on disparate impact that emerge from our setting should serve an indicator that the same negative results may also exist in more complex recommender systems. Additionally, given the fundamental nature of the observed disparities, we believe that the search for mitigation strategies in this simplified setting can provide useful insights for the design of more complex systems.
Background
Recommender systems. The main challenge in recommender systems is making recommendations when only sparse set of preference data is available. Broadly, recommender systems address this missingness via two approaches: content-based filtering, and collaborative filtering I Content-based filtering methods use known information about users and items to suggest content. For example, a content-bard based movie recommender system may compare known features of a movie (degree of humor, action, drama) with known user preferences to suggest movies to users that yield the greatest similarity. Collaborative filtering, on the other hand aims to learn these relevant features based on patterns in the observed preferenceeresponse data. Items in collaborative filtering- pearingg-based based system are recommended to users based on what content other users with similar behavior have consumed (hence the term collaborative).
'Hybrid approaches, well as methods based that leverage more sophisticated learning methods, are also popular. For comprehensive review see 4

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A popular sellabbrraive-filtent algorithm is matrix factorization. Matrix factorization asserts that user data is not missing uniformly at random, but rather according some low rank structure of which it aims to discover. The learned factors can then be used to infer unobserved ratings for other user-item pairs, in turn driving recommendations, Associating each user with factor u, E TR* and each ad with factor % E R* latent factor estimates (á,, û) = ((u,), (Na)a) are obtained under standard matrix factorization via solution of a regularized loss-minimization on the known user responses
Σ |uuil22 + Ellvalla) )]
( 6) = argmin (u,
Σ (i,a)ER
(uf va ri,a)² 2 + A
where R. is the set of user-item pairs (i, a) where a response Ti,a has been recorded. A variety of modifications of standard matrix factorization exist (25), including incorporating ranking biases, user and item side information, varying confidence weights, and temporal effects. The above optimization typically carried out on a mix of both historical data and new interaction data, with the latter data incorporated periodically via retraining.
Cookies, consent, and behavioral ad advertising. Cookies small pieces of data that stored user's s device with the specific purpose ranging from storing login credentials (first-party cookies) to tracking user behavior for targeted ad advertising (third-parte cookies). Given their capability of enabling inference of potentially sensitive user information (9 39), regulation has emerged to increase transparency around their use. While specific laws vary, many countries now require web publishers to present some form of banner or pop-up either informing the user that information is being recorded or requesting the user indicate their cookie consent decision prior to browsing the page.
Behavioral advertising describes the practice using learned user behavior (e.g., user preferences) to make personalized recommendations. Cookies help to facilitate inference of this information via tracking user behavior across websites (e.g., search history, clicks, purchases). The end goal of behavioral advertising is to increase relevancy of recommendations, in turn increasing user engagement and the return of the ad campaign.
3 Related work
Algorithmic feedback loops. Much of the analysis of algorithmic feedback loops in the literature is centered on recommender systems and the trade-off between recommendation accuracy and topic diversity. It is generally accepted that as the recommender system learns to generate high engagement recommendations, topic diversity suffers which in may cause filter bubbles and echo chambers to emerge (51, 26 33 22
27 24 18, 30 500 14). While a variety of mitigation techniques have been proposed including techniques identify and remove these effects (37), slow degeneracy (24), improve user heterogeneity (43), and disentangle user interest from user conformity (49) the question of how to best balance accuracy with diversity, and addressing broader faimeess concerns, is still very much an active area of research.
6
The above papers illustrate the many potential downsides of engagement-drrien recommendation and collaborative filtering. To the best of the authors' knowledge, our paper is the first to analyze the impact of consent rates the dynamics of the recommendation process.
Privacy, fairness, and bias considerations in recommender systems. Given that recommender systems are designed to personalize content to users, questions related to privacy, fairness, and bias naturally arise 23 12 Z). Many notions of recommender system bias have been studied in the literature including participation inequality where system usage varies across a user's attributes (c.g., gender, race, language, etc.), selection bias where the users' choice behavior leads to non- representative item feedback, conformity bias where users in similar groups act similarly, exposure bias where suppliers/items exhibit fundamentally different levels of visibility, and popularity bias where popular items are recommended more often than long tail items, among various others. Furthermore, it is widely recognized that the inherent feedback nature of recommender systems amplifies these biases 30).
Research on the privacy and fairness of recommender systems aims to gain a deeper understanding of how the structure of the recommender system influences these biases and subsequently propose mitigation strategies via modified recommendation algorithms, with a large thread of research
concerning the design of mrivacy-rresevvin recommender systems [ 31 47 3). Most related to
3

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paper are the structural questions of characterizing the ability of the recommender system to recover protected attributes from ratings both a homogeneous user pool (42) and mix of public/private users (44). Notably, (44) demonstrates that only small number of public users (users willing to share preference information) with large number of ratings in a pool of private users (users with hidden preferences) is sufficient to produce accurate system-wide recommendations, In contrast, our paper studies how inherent differences in user consent rates influences the system's ability to estimate users' latent attributes across groups.
Simulators for recommender systems. Given the complexity of the interactions between users and the learning behavior of the agent, simulators have become an increasingly popular tool for understanding the dynamics of recommender systems. Agent-based modeling allows for simulation of fine-graines user interactions, facilitating useful insights without running costly field tests. A variety of open-source recommender system simulators have emerged in recent years, namely RecoGym (35), RecSim (21). PyRecGym (36), Surprise (20), RecSim NG (32), and others (48), (8). The simulator developed for purposes of this study augments RecSim with the ability for the learning agent to maintain asymmetric (Bayesian) uncertainty over users.
A Simple Recommendation Model with Cookie Consent
Consider recommendation environment consisting of recommender, termed the agent, sequentially interacting with a fixed population of n individuals or users (see Fig. T Before the interaction begins, users make consent decisions according to known cohort-dependent probabilities. The agent uses the consent decisions and revealed cookies form refined (interim) beliefs on the users' cohorts, which in turn guide recommendations. The agent is periodically retrained using the updated history of recommendation--rsponss pairs, with the overall goal of recommending content that maximizes engagement.
ads (a,,e) clicks
advertisement sampler
ad pool
attributes
agent
sampler
((,,,,))
{Gra.e]
decisions, ([x,)d))
Figure 1: The recommendation process. The advertisement sampler generates the ad pool (assumed to be refreshed in each round /). The user sampler initializes both latent attributes of users and consent decisions. In each round, the agent generates recommendations (ads) and records user responses (clicks).
Advertisement model. Each ad is described by single topic feature T fr....., T"), where m is the number of possible ad topics. In each round f, subset of < ad topics are sampled to form the current set of recommendable ads At, termed the ad pool.
User model. Each user E [r]] is described by three features: a cookie O; E + = _ 69) a demographic or cohort 0; E = ( "d),, and a vector of topic affinities a; E R. Each user's cookie-cohort pair is drawn from known joint prior μ A θ), i.e., knowledge of a user's 's cookie at least partially informative for its cohort. Consent decisions are dictated by cohert-dependent probabilities qo, θ with each user in cohort 0 revealing its cookie with the agent according to X; Bernoulli(g) distributions. with each user from given cohort 0 possessing affinities a, (ogNormal o where Pa E IR and ag E E are the cohort-dependent means and standard deviations of o; natural logarithm.
Topic affinities are generated according to log-normal
Note that we model every user as possessing underlying cookie, with the agent only being aware of the user's cookie if the user decides share, i..., 2;

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appended the response In each round t, each user is faced with a single ad and makes a binary decision to either click or not click. Specifically,, when user is recommended an ad a. the user first scores the ad via the utility function u((;; o;) a: -, where T, E I is the indicator vector on topics (a vector of zeros with a one in location of the topie of ad a). User i's choice to click on a denoted by G, E {0, 1}, is stochastic and is dictated by Ci ~ Bernoullí(pra)) where Pia is the click probability given by the
following logit model
exp(u(a; a:))
Pi,a exp(u0) + exp(u(a;a:))
(1)
where uo is the no-click-mass used to model the possibility of the user not clicking a, assumed to be homogenous across users.
Recommender agent. The agent faces fundamental trade-off between recommending high- engagement content and learning more about users' tastes. Our recommendation model combines two foundational models from the literature, namely incorporation of confidence weights (19 (25) into
an online matrix factorization procedure (I... Online matrix factorization addresses the conflicting objectives of the agent exploration to improve estimates of latent factors, and exploitation of known high engagement content - by interleaving estimation of the latent factors with specification of recommendations. Including confidence weights allow us to model the agent's 's heterogeneous uncertainty on users due to their consent decisions and personalized recommendations. Note that while this is a stylized recommender model, it possesses the main features seen in more complex systems, specifically online learning and heterogeneous uncertainty across users.
Formally, the recommendation process evolves as follows. Given the agent's 's prior belief, μ E A θ), the users' consent decisions are used to form interim cohort beliefs jı; A(0) for each user i. If user i gives consent (r; = 1) then the agent is informed of the user's cookie, o, and its gep(or,d) updated belief of the user's s cohort is formed as (0) p(1) x; 1, 0x) Eor 9oru(os.0") for
each E θ If user i does not provide consent (z; = 0), no cookie information is revealed and (1-4s) E. M(G,0)
the agent's belief of the user's cohort is given by (0) = p(1 2 0) E. (1-11190) 2or) E (()"
1 O Interim beliefs offline response set Lo of recommendation-rssppnnn
(ji.-..., j..) are used form beliefs J40 (No,1, mO,n) via an
pairs of the form ((a,, Gia)] across users.
The recommender model at round / is represented by pair of user-ad latent factor estimates (ú,, 0t). Recommendations are generated via an e-greedy bandit: with probability E, the ad recommended to user in round f, denoted by di,t, is chosen uniformly at random, ai,t U(At), and with probability E, the recommendation the ad in the current ad pool with the highest estimated value ai argmax 0,, Responses to the recommendations
set, L1+1 L, U [la,, Ci,a) | [mz], a E [m]]. and are used to maintain cumulative count of clicks Ti,a,t across user-ad pairs.
Retraining consists of updating cohort beliefs and latent factor estimates using recommendation- response pairs, and performed every T, rounds. If t retraining round, cohort beliefs are first updated according to Bayesian update μ4, = f(u,,- L, L.-T,) where L, \ C,-7, is the set of responses since the previous retraining round. The heterogeneous beliefs on user cohorts gives rise to weighted procedure. For given set of cohort beliefs μr, the agent computes confidence weights w; = (i,,a, as the expected probability for sceing the current response counts. Specifically, each weight t is the expected binomial probability, given Me, for seeing Ti,o,t defined
Ti,a,, Wi = Eo,-a [px (T,,a,, 0.)]
where Pr(I, r, 0) is the binomial probability at round t given impressions I, positive response counts r. and cohort 0. Updated latent factor estimates are computed via a confidence- -neighence-eeihhted matrix factorization procedure as
(ū,, 0z) = argmin (u,o)EuxV (a).
Σ Wi,as Ua - -ri,,)) + >
Σ
||us|12 +
Σ ||valle ac(m)
(E(m)
where 44 = (( un) )
Ua E IR E [m]] are the latent factor spaces, L, is the current history responses, and X > is regularization weight. t is not a retraining round, then cohort beliefs and latent factor estimates are propagated as is from the previous round. Expressions for the Bayesian updates and expected binomial probabilities can be found in Appendix A, with pscudocode of the recommendation process in Appendix B.
E RRi [ = ((11....... Cm )
5

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Experiments
The following experiments study the dynamics of the recommendation process described in Section 4 particularly relates to users' consent rates. Empirical results were obtained via simulator based on RecSim (I). Full details of the simulator and the experimental setup can be found in the supplementary material (Appendix C). Base model parameters assumed throughout this section are: number of users n = 1000, number of ads m = 200, ad pool size = 50, and number of cohorts d = 2. Sensitivity analyses can be found in Appendix D.
The following notation/termnnllgy will be used throughout this section to aid explanations. Let Nf {i E [n]
1.0, = 0) denote the set of users in cohort & who have decided to share their cookie, with No defined analogously. We refer to NJ as the consent group (in cohort v) and No¹ as the non-consent group. Estimation errors on cohorts for each group are quantified by log loss, i.c., for a set of users N in group z),, the (average) log loss is denoted by L (n) = [N EiEN Eveo 1(0; 0) (1)) Estimation errors topic affinities are given by MSE
5.1 Impact of consent estimation accuracy
The following set of experiments investigates the impact of cohort-dependent consent rates on the agent's estimates of the users' cohorts and topic affinities. Given users' consent decisions, and cookies for those who decided to provide consent, the agent forms interim beliefs on each user, P4, i [m²] as per the model description in Section 4 Fig. Dillustrates the impact of these consent decisions on cohort and affinity estimation errors, for 2)a) and heterogeneous consent rates (Fig. b)).
T0, 0') J. in two cases: homogeneous consent rates (Fig.
cohort errors
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Figure 2: Estimation errors over training rounds / (T₁ 1) function of consent rates under binary cookie space h- = { Φ'} and symmetric prior μ( 0) = 1a(0, 0') = 0.4.
Fig. 2 a) illustrates that when users' consent rates are identical across cohorts, estimation errors for the non-consent group No are higher than the errors for the consent group Ní regardless of their cohort 0.
As seen in Fig. b), this intuitive result breaks down when users' consent rates differ across cohorts. While withholding consent leads to a higher estimation error for the higher consent rate group, 0', withholding consent can lead to lower estimation error for the lower consent rate group, 0. This inversion effect persists for the lower consent rate population for any sufficiently large separation of consent rates across cohorts, illustrated by Fig. 3. These cohort-dependent effects of consent summarized by Observation T
Observation (Comparison within cohorts), Let θ - {0, 0'} and let be any non-fully informative prior. If qe = qø' (consent rates are independent of cohort) then non-consent leads to a higher estimation error than consent. If qe < qe (consent rates are cohort-dependent with users in cohort O providing consent as a lower rate than users in cohort 0'), then:
There exists a (prior-dependent) constant 8y such that for qo qo ōμz the non-consent group in cohort 6, No. experiences lower estimation enrors than the consent group, Nº.
b. The non-consent group in cohort 8', Ng6', experiences higher estimation errors than the consent group, Nºº'

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Observation holds for any non-fully informative prior, meaning that there exists at least one cookie that does not the user's cohort with certainty a property that is almost certainly satisfied in practical (i.e., noisy) recommender systems.
For partially informative priors (each cookie only partially reveals the user's cohort), the statement of the above observation can be understood by looking at the agent's sources of information. Consider the following signals: i) the cookie value in the event that the user provided consent and, ii) under heterogeneous consent rates, the consent decision itself. The interplay between these two sources of information means that, under some priors, the act of user withholding consent can itself be more informative than providing consent and revealing their cookie. Fig. illustrates the estimation errors for different consent rate regimes under symmetric prior p(0, Φ) r1 Φ') 0.45.
cobost CEE009
coboet ccEsus
cctum
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86
0.7
0.9
(a) Case: go <. 90' < 0.5
(b) Case: go 0.5 qo'
(c) Case: 0.5 <, go qo'
Figure 3: Impact of consent versus non-consent on the agent's 's cohort estimation error in each cohort for various consent rate regimes under symmetric prior μ( B) u(Ø 8') = 0.45.
The above figure, specifically Fig. 3 B). illustrates that under a very informative prior, a small gap in consent rates, (go, qo 0.42, yields consent signal that contains relatively low informativeness compared to the revealed cookie value, causing consent to yield lower estimation errors for both cohorts. However, the absolute consent rates increase in both cohorts, this same consent rate gap (compare Figs. 3(a) and (c)) yields a consent signal that is sufficiently informative to yield lower estimation errors for withholding consent for the lower consent rate group.
Generally the larger the gap in consent rates, the more information the consent signal carries for the user's cohort. Apart from very informative priors, the consent signal carries sufficiently rich information to yield lower estimation errors for withholding consent for the lower consent rate population even for small gaps in the consent rates.
Observation T compares the impact of consent decisions within a given cohort under homogeneous and heterogeneous consent rates. A comparison of the impact of the same consent decision across users in different cohorts is summarized by the following observation.
Observation 2 (Comparison across cohorts). Let θ = {0,0'} and let μ be any partially informative prior If qo d' then the consent group experiences the same estimation errors regardless of cohort (similarly for non-consent). If qo qo', then:
a. There exists a (prioe-dependent) constant πy such that for qe - qo nue the non-consent group in cohort 8', Ng., experiences higher estimation errors than the non-consen group in cohort 0, No-
b. The consent group in cohort 0', Nf', experiences lower estimation errors than the consent group in cohort 8, Nº.
5.2 Amplification effects
The following experiments investigate how the disparities observed in [O and (0 are influenced by the relative consent rates across cohorts. For θ = {0, 0'), define df [ - L (14) as the difference in mean cohort errors between non-consent and consent for users in cohort & E O. Additionally, define 7/" = T. (u+) (1.) ) as the difference in mean cohort errors for consent decision
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In words, the quantities 87, & E θ represent how much worse the agent's estimation error is under non-consent versus consent for users cohort 1). The quantity 't (resp. 7/ represents how much higher the agent's 8 estimation error is for user who withheld (resp. provided) consent if they belonged cohort 6' versus if they belonged cohort Figs. and illustrate Sillstraee how these quantities differ as function of consent rates for given number of training rounds (T 10).
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Figure 4: Relative errors for non-consent versus consent as a function of consent rates (4o, gor) for each cohort and fixed number of training rounds т 10.
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Figure 5: Relative errors for a given consent decision across cohorts as function of consent rates (go. (g)) for fixed number of training rounds 10.
Fig. 4 fillustrates that the relative loss in accuracy for non-consent (compared consent) is greatest in cohort when go is minimal and qe maximal, with the opposite effects observed cohort 0'. Fig. 5 illustrates that the users who withhold consent are average impacted greater by given gap in consent rates than users who consent, e.g., compare the magnitude of the values at (go, g0r) (0.25, 0.75) for non-consent versus consent.
individual user's consent decision. Users from the higher consent rate cohort who withhold consent experience higher estimation errors than the same users from the lower consent rate cohort, with the opposite holding for users in the consent group.
In summary, the gap consent rates serves as an amplifier

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Discussion
Our results demonstrate that even in simple recommendation model with reasonable modeling assumptions, the impact of a user's s cookie consent decision is not necessarily straightforward. Particularly, when consent rates exhibit cemographie-dependeer acts as signal, carrying information beyond the information contained in the actual cookie value. This leads to a seanoorrppii-deeendeee decision (of disagreeing to share their cookie) potentially causing the system to know more about them than if the user were to intentionally reveal their cookie information.
the user's consent decision itself
impact of consent, resulting in user's prrtecy-r
To draw a comparison with the large body of existing literature in the fairess of recommender systems, many of the existing papers (see the papers referenced in Section 3 draw attention the way in which the system learns similarities among users over the recommendation process as a primary source of unfairness. Indeed, this is fundamental how matrix factorization algorithms (and many more complex recommender systems) operate: users who behave similarly, i.e., how they respond to the same recommendations, will be deemed as being similar (even falsely so). This will lead to these users seeing similar recommendations which can, in turn, lead to undesirable outcomes.
However, one of the goals of our paper is to draw attention the informational effects of consent as a potential additional source of unfairness. When consent is a conscious decision of the user, and the rate of given consent decision differs based on sensitive attributes of the user, e.g., age, then the system can use the consent decision to learn more about the user's sensitive attributes. When embedded within an algorithmic system, platforms may unintentionally profile users based on the absence of data.
These observations have possible implications in the design of recommender systems. Any infor- mation that the system can use to draw similarities will be used, most notably how users respond to recommendations, but also, and the focus of our paper, the inherent likelihood of user to provide consent to cookie sharing. These similarities are used to infer to which group a user belongs and subsequently drive recommendations. The implications for algorithm design is that one must be mindful of the complexities of information revelation especially as it relates to how the algorithm will use the revealed information.
New notions of fairness. The design of recommender systems that are more aware of the informa- tional effects of users' decisions may require new notions of faimess. is well-known in the faimesss community that static fairness metrics are insufficient for dynamic settings, and can actually actively harm the group they intend to protect (28).
In our setting, whether the system possessing heterogeneous accuracy about users results a fair or unfair outcome depends on the product being recommended. Given our observations that the specific impact of a user's consent decision varies depending on the user's demographic, is not hard to that such accuracy disparity may lead to unfair situations. For example, consider an ad recommendation setting where some of the ads may be predatory to older individuals. According to our model, an older individual's desire to remain more private by deciding to disagree to cookic sharing may allow the system to know more about them, simply by virtue that more older individuals choose to not share their cookies, and subsequently make them a more likely target for such ads. Consequently, we emphasize the need for development of fairness metrics that ensure consistency of an individual user's crivacy-protecttv decision and the amount (or accuracy) of information that the system knows about that user.
It is worth noting that this informational consistency property is distinct from the literature on recommender systems. For instance, differentialll-prig -piiaate recommender systems 31 29 ensure individualanonyymity via careful injection of noise, while still enabling extraction of aggregate-Ievel information used to feed the recommendation algorithm. In contrast, a consistency- based approach would hypothetically still allow for some individuals to be (more accurately) identified they choose to be (e.g., to receive more targeted recommendations) while honoring the privacy of individuals who chose to not share their information.
Towards industry reform. Our results contribute to the growing sentiment that the digital advertising space is in need of reform, particularly due to the unintended consequences of "the collection of personal data, tracking, and massive-scale profiling" () As the move away from cookie-bases tracking gains momentum, alternative mechanisms for user profiling are becoming more prevalent.

---

In the context of an advertising environment without cookies (often referred to the cookieless future), the shift to these alternative data collection methods may lead to informational disparities across companies. Given that the current advertising ecosystem contains players of vastly different sizes, ending the use of cookies may give asymmetric power to companies that have already collected significant amounts of personal data. Indeed, tools that facilitate access to user information that would otherwise be tracked by cookies are already in use, e.g., websites that allow users to create an account by using their Google/Microsofi credentials (a practice known "auto-linking").
In general, these issues point to the fact that controls and regulations should be based on the downstream effects of user interactions with the advertising system. In particular, policy must carefully consider how much information has been extracted from a given user, whether be from individual decisions/responses of the user or gleaned from inferred similarities with other users, and effects. To foster transparency, would be beneficial for the industry to derive estimates of the monetary value of user information and share them with the public. In general, the advertising industry can more transparent, not just about user data but also concerning the downstream effects users, since real-world advertising engines are vastly more complex than our simplified setting and may not lend themselves to simple mathematical modeling.
its privacy-compromiig
Limitations, Our findings on the disparate impact of consent should be interpreted with the un- derstanding that our model necessarily has some limitations. Broadly, our model uses a simplified definition of cookies in which cookies serves as proxy for the users' cohorts. While the reason for this simplicity to extract insights that depend directly on the user's cookie consent decisions, extending the definition of cookie to more realistic settings by including user click/behavions information would likely generate additional insights. Secondly, to capture the core aspects of recom- mender systems, our recommendation model is based on foundational recommendation algorithms (namely online confidence-weighteed matrix factorization). While these algorithms form the basis for modern recommender systems, it would be worthwhile to see how the insights extend to more modern algorithms. Lastly, we consider simplified and user pools; consideration of additional ad features and more realistic dynamic user pool could influence the findings.
7 Concluding remarks and future directions
We've investigated the question of how heterogeneous cookie consent rates among users influence the recommender agent's ability to learn users' latent features (e.g., their demographies and tastes). We'v 've empirically discovered, through construction of simulator, that disparities in the agent's estimation accuracy across users emerge when consent rates exhibit demnorrphhicddeeeddeneee Our observations show that seemingly simple informational decisions by users (i.e., whether to share their cookie) can have complex effects on the agent's information. Consideration of informational effects of users' decisions is crucial in the design of recommender systems. We encourage the development of new fairness metrics for dynamic settings that enforce consistency between user's privacy decision and the amount of information that the system knows about them.
Future work focuses on studying the downstream effects of our observations via validation in real- world recommender systems. An additional direction is quantification of the aforementioned faimess consistency property such that it can be embedded as a constraint in the design of recommender system algorithms.
Acknowledgments. This research was funded in part by the Horizon Europe project AutoFair (grant agreement ID: #101070568).
10

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A Omitted expressions
Derivation of interim belief update. Given user consent decisions, the agent updates the prior μ to
form interim belief's as follows. For a user who provided consent (I; = 1), with its revealed cookie
Φ sp, the interim belief Ps.o A ((+) is given elementwise by
(v.o(0) = P(O; = 0 x; = 1, - =6)
P(x; = 1 11 = 0, = ()) = pp 0; =
PP(x;; 1, 0: = 4)
P(r; 0; = 0)p(ds = p, 0, = 8)
Ev P(x: = 1 0; P() = 0,00= = 0) qaH(1p))) 0)
Ev 40.11(;p, Q")
Similarly, for a user who did not provide consent (a, 0), its cookie is not revealed and thus interim beliefss are given by
(1,0(1) PO; | x; =
P(z; = 0 0, O)P 0)
PP(r; = 0)
P(r: = 0 0, = 18) Enp P(p: = p.0; = 0)
Σn P(x; = 0 0; = ='') Exp p(o: 00,0; 0
(1 (00) Ex M(p 0)
= En -qw" Eng/ Ml/'' ,8¹)
Cohort belief update. Given set of cohort beliefs across users μ (11 ... pa) and set of recommendatioo--espooss pairs L, the agent forms updated beliefs μ (14....., pr) via a Bayesian update, μ² = f(u, L). This update is carried out independently for each user Let μæ denote the agent's current belief on user i' cohort O,, and denote L, = {(a,,..a)) as the pairs that correspond to user i. The updated belief μ4 is given by n¹ = (u((0)),...,,1)) given by
= Sulmi, Li) where each p4 (0)
pL(0)) = P(O, = Li)
I[ PP(Ci,a = Ciaa A, a, a, ()P = 0
Ev II(ones,,)EC, P(C',a- = Ciaa A = ai 0₁ = P') = 0')
[I(aneeaee)) Pi,a, (1) (Eereww))C) (1 - Pi.as (1))
En [[orees.e) Pi.o (0') ((a (1 Pi,a, (1')) (8')
where C. (resp. C.) are the responses where the user clicked (resp. did not click) on the recommen-
dation and (1) is the expected click probability given 8 defined as
Pi.a(1) =
Ea, LoggooLaa((ppp..ooo o (a;)]
where the click probability Pia from has been written as (r.a(a:) to make the dependence on user i's topic affinities explicit.
Confidence weights. The confidence weights Wz,a,t in computed the expected binomial probability for seeing the current response counts ri,a, given the agent's is current belief on user i's cohort 0,, i.e., Wi,a, Ea,-aa, [pe (Ji,a,t Ti,a,t 0.)]- The binomial probability pt (Je,at Fi,a,t, U.) is defined as
Pe Fia,t 0,) = Tiaat (iaatt)
Pia (1,) (1- (1:)) hhatt -raat Traat
where It., is the current impression count for user-ad pair (i, a), ax is the current click click for (ax)) )) is the expected click probability.
(i,a), a), and (0s) Log (lr,)

---

B
Recommendation procedure
Algorithm 1: Recommendation procedure.
Input parameters. (n, L, m, θ 2, T, {po, oa), uo, {go) na k, A, Co. T)
Initialize users. For each user E [n]] sample:
cookie-cohort pairs (dr, 0²) μ
topic affinities ai LogNormal og,)
consent decision I; Bernoullige.))
Form interim beliefs. For each user E [n]:
x; then
// user provided consent
ia(0)= + Eor 9orm(or,00) 1 E θ
gau(dr.))
else
// user withheld consent
(1-90) En m(
(0) + Eor(1-gu)) Ens' p(o6, 1 E θ
end
Offline responses. Form priors using Lo: 11,0 < Hiss, Lo), i E [n]
Online recommendations.
for / = -......; T do
Define current ad pool Ar by sampling items uniformly without replacement from T // retraining step
mod (t, Tb) = 0 then
Update cohort beliefs: H4,t + f(u,e-,, \ G--n).i ie [n]
Compute weights: Wt,a. Ee 0,)), [n]
Update factor estimates:
(ūt, 6;) argmin (w
EierewwEc (ia Ua r2
> Eie(n |1ull22 Eae(ml [|vall2]
else
Propagate cohort beliefs: Pr + Mz-1 Propagate factor estimates: (ū,, 0t) &- (ú ):-1)
end
Recommend ads: for each E [n]. recommend at di,t via
argmax d. w.p. w.p.
ag = a~ U(Ar)
Append responses: L.+1 Le (ai,s Co.ia} end

---

C Simulator and experiments
Our simulator was built upon RecSim (source code htttp://giithu. com emeemmieehiiii ing cookie- cookie-consent/ consent/). The high-level architecture of our simulator is illustrated in Fig. of Section Additional details (with references to objects in the source code) are provided below.
Advertisement and samplers. The advertisement sampler object (AdverttisementSSample.. defines the distribution of each ad feature, here assumed to simply be the ad's 's topic. Similarly, the user sampler object (iserstateSampler defines the distribution of each user feature, described by the joint cookie-cohort prior, the opt-in distribution, and the statistics of the user's 's topic affinities. The ad sampler and user sampler objects are used to define a gym environment for the recommendation procedure (via whereas users remain fixed for the duration of the episode.
Enveerrmiiirrnrrreeeeoee and RecS RecSimmymin imGymEnv). Ads are resampled in each round
Users and the recommender agent. Each user is described by the class RSUserModel. This class contains the user's choice model, i.e., the logit model dictating the binary click decision given the recommended ad (see the method simulate _essptteeeeeee.e.._______
Given the collections of ads and users, the recommender agent makes recommendations according to an s-greedy bandit (see the pseudocode in Section B
Retraining consists of first updating the cohort beliefs (via the methods and
prw.abiiitiis.s... see Appendix [ for the expressions), updating weights a and recomputing the matrix factor estimates (via get ret_estimated factooss see (2). Estimation is carried out via stochastic gradient descent with learning rate of 0.01, regularization weight of 0.01,
and a stopping threshold on the mean-squared error of Ehresh = 0.001. Latent factors are assumed to be of dimension & = 50.
Experimental setup. Simulations were run Python 3.8 on an Intel(R) Xeon(R) CPU E5-2667 v2 (3.30GHz). Unless otherwise stated, baseline parameters of the simulation environment were as follows: = 1000 users, m 200 ads, ad candidate size 50, batch size T₁ = 1, offline response set Co Ø3 exploration probability 0.1, and binary cookie and cohort spaces. Simulations were averaged over 500 runs/episodes.
The experimental setup can be extended in a variety of directions to investigate additional interesting questions. One direction is extend the feature description the ads (beyond topic) include features that reflect ad quality and location. This would enable studying how the recommender system treats minority populations (compared majority populations). Additionally, augmenting the simulator with the ability to handle a changing user pool would allow for analysis of the cold start problem.
3

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D Sensitivity analyses
Sensitivity analyses on cohort errors were carried out by independently varying the prior batch size
Ti. offline response set Co. and topic affinity means (po: (I) with fixed parameters nt 200 users, m 200 topics, ad pool size / = 50, latent factor dimension = 50, and ( | = 2. Plots illustrate error means and standard deviations (red:
blue f 1, solid: consent group, dashed: non-consent group) over 50 episodes. Baseline parameters are:
0.4
0.1 0.4
T3
Co 2, (po/m, PI pm/m) (0.3, 0.7)
0.1
Prior. The impact of the prior was studied in three cases dictated by the degree of informativeness of the cookie for inferring the cohort.
00.4 0.1
Partially informative: μ =
0.1
0.4
cohort error
cohort error
cohort error
1.0
2.0
1.0
0.0
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10
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20
(q0: Q1.
(0.25, 0.25)
(qu, q1)
(0.25, 0.5)
(g0. 91) = (0.25, 0.75)
0.5
0
Fully informative:
0.5
cohort
cohort erro
cohort error
1.0
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(gu. (1)
(0.25, 0.25)
(go, Q1) (0.25, 0.5)
(go, 91) = (0.25, 0.75)
0.255
0.25
Uninformative: /
0.25
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(go, (1 (0.25, 0.25)
(go, Q1) (0.25, 0.5)
(go. 91) (0.25, 0.75)

---

For partially informative prior (any j that does not have identical rows), knowledge of a user's s cookie partially reveals the user's cohort. The resulting cohort errors are consistent with Fig. of Section 5.1 For the fully informative prior, the agent is completely certain of users' cohorts for users who opted-in (the agree group), but still possesses uncertainty for users who did not opt-in (the disagree group). Lastly, for the uninformative prior, revelation of user's cookie does not inform the user's ' cohort (as the likelihoods of seeing cookie values are identical across cohorts) and the agent must infer cohorts solely from differences in response behavior.
Batch size. The batch size, To. dictates how many responses to collect from each user before retraining. Values for the batch size were varied in the range Tú, E 21,2,10)
TB 1:
conort error
cohort eлro
cohort error
0.6
0.6
0.6
0.4
0.4
0.4
20
(go: ②1) (0.25, 0.25)
(go: 21) (0.25, 0.5)
(g0, 21) (0.25, 0.75)
To = 2:
arror
1.0
1.0
0.6
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(go, (1
(0.25, 0.25)
(go, Q1) (0.25, 0.5)
(go, 91) (0.25, 0.755
TB 10:
cohort error
cohort error
cohort error
1.0
1.0
1.0
0.8
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0.2
0.2
0.2
0.0
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10
29
40
20
20
40
20
(go: (1) (0.25, 0.25)
(90.91)
(0.25, 0.5)
(go, 91) = (0.25, 0.75)
Intuitively, for the same number of observations, cohort estimation errors are the same across various batch sizes (e.g., updates may be less frequent but they contain more data). However, waiting until batch update (T3 >> 1) results in more interactions where the users face greater disparate estimation errors (compared the T3 case).
5

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Size of offline response set. The offline response set, Lu. is set of recommendation respoossss that are available before the online recommendation process. Recommendations in the offline set, Lo. were generated uniformly at random with responses generated by the users' choice models. Simulations were run for [ = (0,1,5), differing in the number of offline responses assumed available from each user.
[Co 0:
cohort eптОг
cohort eπoо
cohort error
1.0
1.0
1.0
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(go, Q1
(0.25, 0.25)
(20.q1)
Q1) ) (0.25, 0.5)
(g0, (1) = (0.25, 0.75)
Col
cohort error
cohort arror
cohort error
1.0
1.0
1.0
0.0
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0.0
0.6
0.4
0.2
0.2
6.0
0.0
0.0
[go, Q1 (0.25, 0.25)
(20, 21) (0.25, 0.5)
(g0, Q1) = (0.25, 0.75)
Col
cohort error
cohort arror
cohort error
1.0
1.0
1.0
0.0
0.8
0.0
0.4
0.2
0.2
0.0
0.0
0.0
20
(go: Q1
(0.25, 0.25)
(90. 91) (0.25, 0.5)
(90.91) = (0.25,.0.75
The impact of the offline response set does not appear to have significant effect on the evolution of the cohort errors.

---

Similarity of topic affinities. The sensitivity to similarity of topic affinities was studied by increasing similarities the synthetic affinities via means (normalized by topic count m) (po/m, P1 /1/m) {00.3, 0.7), (0.4, 0.6), (0.5, 0.5)}.
(Po/m, P1 m) (0.3, 0.7):
cohort error
cohort error
cohort error
1.0
1.0
1.0
0.0
0.8
0.0
0.2
0.2
6.0
0.0
0.0
10
20
20
(40: ②1 (0.25, 0.25)
(90. q1)
(0.25, 0.5)
(90. (1).91) = (0.25,0.75
(Po/m, m. P1 m)) (0.4,
cohort enror
cohort error
cohort error
1.0
1.0
1.0
0.8
0.8
0.8
19
0.2
0.2
0.2
6.0
0.0
0.0
10
30
20
20
(go: Q1) (0.25, 0.25)
(90, (1) (0.25, 0.5)
(90.91) = (0.25, 0.75)
(pn/mo mm p1 mm) (0.5, 0.5):
cohart error
cohort arror
cohort error
10
1.0
1.0
0.8
0.8
0.8
0.2
0.2
0.2
0.0
0.0
0.0
30
30
20
20
[go: Q1) (0.25, 0.25)
(90.91) (0.25, 0.5)
(g0. = (0.25,0.75
The agent's ability distinguish users based their responses depends on the similarities of affinities across users different cohorts. Intuitively, as the topic affinities across cohorts become more similar, the agent requires more responses to reach the same level of estimation error (since users from different cohorts behave more similarity as topic similarity grows). The extreme case of identical statistics of users' affinities across cohorts (po/m,, m)) = (0.5, 0.5)) results in the agent being unable to resolve any uncertainty over users' cohorts (since user responses are uninformative for their cohort).


Reviews:
[{"review_id": "EeZIAGG1bg", "reviewer": "Reviewer_iC41", "summary": "This paper investigates the influence of varying consent rates on the accuracy of estimation. The paper utilizes a simulation-based approach, in which the decision to share cookies plays a significant role.\nThe findings reveal interesting patterns that can contribute to the development of more refined fairness metrics, taking into account the individual's choice to share information.\n", "questions": "Q1: Can the observations in Fig.2 at t=0 be simply demonstrated by your calculated prior $\\mu_{i,0}^{-}$? Is there a significant difference between the priors $\\mu_{i,0}^{-}$ without the recommendation simulation and $\\mu_{i,0}$ with the offline responses?\n\nQ2: The demographics and cookies are set to a specific number of 2. If the attribute number is changed (e.g., to 3, 4, etc.), do the observations still hold?\n\nQ3: What is the trend of cohort-dependent consent rates on cohort beliefs $\\mu$, and weights W? Could you provide a similar illustration as in Fig.2 for estimation errors?\n", "limitations": "See weaknesses and questions", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1.The paper presents an intriguing explanation of the observed phenomena in the simulation experiment, particularly the behavior of low-agree individuals (such as older people) choosing not to share information, which instead results in a lower estimation error for the agent in a cold-start setting. \n\n2.The author's discuss on how these results can guide future directions to enhance the consistency of fairness evaluations.\n", "weaknesses": "1.The study's conclusions are based solely on a simple simulation experiment. There is a lack of discussion or testing on whether these observations would hold or approximately hold in real-world datasets. This limits the generalizability of the findings and their applicability to practical scenarios. Please correct me if I missed the details.\n\n2.The observations (1 and 2) seem like they could be derived from trivial calculations using the prior $\\mu_{i,0}^{-}$ without the need for simulation. (See Questions)\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. We've provided some answers to your questions below.\n\nThe need for simulations:\n\n- While the priors do indeed dictate the relative accuracy disparities across cohorts and user consent decisions, the evolution of these errors as a consequence of the recommendation process is not straightforward. We’ve run some additional simulations to emphasize this point. In particular, see the plots in the 1-page attachment studying the resulting CTRs (under the caption “Impact on recommendation quality”) as well as how the cohort belief errors behave for an increased number of cookies/cohorts (\"Effect of model size parameters\").\n\n- Generally, there does seem to be an impact of consent on recommendation quality, however, the specific nature of the impact is not clear. We were originally planning on including these results in the initial submission, however, given that we lack a clear “observation” of the impact of consent on recommendation quality, we decided to instead present our findings on the impact of consent on estimation accuracy (we can however include these in the supplemental material for completeness). We feel that the impact on accuracy is a sufficiently interesting observation to encourage the community to investigate this issue further (in both simulated and real-world settings).\n\nImpact of number of cookies/cohorts:\n\n- Our additional simulations in the attachment illustrate the behavior of the model under both $c=d=3$ and $c=d=4$\n\n- The primary observations still hold as the number of cookies and cohorts increases. See the section \"Cookie and cohort model\" in the global response section for a more detailed description (as this query was raised by another reviewer as well).\n\nRelationship between consent rates and cohort beliefs and weights:\n\n- The impact of consent rates on cohort beliefs can be derived directly from the Bayes update equations. Generally, higher consent rates for a particular cohort will increase the belief (higher confidence) that users are from that cohort if they opt-in, with lower consent rates having the opposite effect. Similarly, given that the weights are the expected binomial probability of the current response counts, a higher consent probability will lead to a higher weight (reflective of a higher confidence for the given counts).\n"}, {"review_id": "4ALdoUtjVm", "reviewer": "Reviewer_cPvy", "summary": "This paper simulates a recommendation system that is aware of and responds to users decision to share cookies, along with data from users' clicks. In this simulation, the paper finds that the recommendation accuracy could be higher for users who do not consent to provide cookies under certain conditions. The paper empirically analyzes these conditions along various dimensions.", "questions": "See weaknesses above", "limitations": "The paper does not discuss any limitations. I think discussing the limitations is important, given the assumptions made in the simulation.", "rating": 7, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The paper is very well written, and the presented result is novel to the best of my knowledge. The paper has a high potential to spur future work on the interplay between cookie consent decisions and recommendation accuracy.", "weaknesses": "**Strong claim in the title**\n\nThe key finding is via simulations. The title makes it seem like the result of a randomized field experiment. I think it is possible to temper the title to reflect this.\n\n**Complex simulation setup, results possibly driven by unrealistic recommendation model*\n\nThe simulation setup is not parsimonious, which makes it hard to see the key drivers of the result.\n\n   a. Why is the ad pool sampled in each round and not deterministic?\n   b. Why does the cookie contain demographic information, and not contain user click/navigation history information?\n   c. The recommendation model is designed to be click-maximizing for the given user model. In practice, the recommendation system has no idea about the user model and likely just performs matrix factorization (with or without exploration) to generate recommendations. This modeling choice for the recommendation model is a large deviation from practice; what happens to the results if the recommendation model is just user model-agnostic matrix factorization?\n\n**Cookie-cohort dependency and cookie model assumptions**\n\nThe cookie in the user model is designed to have the sole function of being a proxy for the user's cohort. Specifically, it is not \"contaminated\" by what the user actually clicks on, which deviates from reality (cookies track clicks and navigation history to some extent). Combined with the demographic disparity in consent rates, this turns the presence or absence of cookies (and the cookies themselves) into unrealistically strong correlates of the cohort of an individual.\n\nHow do the results change if the cookies also stored some sort of \"average empirical topic preferences\" over the users' last N clicks? This reduces their strength as a prior and makes them less useful, since they reflect data that the recommendation model has already seen. However, I think this is more realistic.\n\n**Theoretical explanations for the empirical observations**\n\nHow do the observations deviate from theoretical predictions?\n\nSpecifically, Bayes' rule can be used to show that a demographic demographic disparity in consent rates will increase the accuracy of predicting a user's cohort from their consent decision. Further, the cohort with a higher consent rate will provide more data to estimate that cohort's topic preferences accurately in each round. These two factors combined will influence the overall recommendation accuracy until the recommendation system has collected enough clicks from both cohorts.\n\nAs such, Observation 1 and 2 seem to say that the outlier groups in each cohort (with respect to the consent decision) have a higher estimation error. Does Figure 3 contradict this explanation?\n\nMy low overall rating is primarily a function of the lack of theoretical explanations.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your detailed review of our paper. We’ve responded to each of your queries (either in this response or in the global rebuttal).  \n\nResponse to: \"Complex simulation setup, results possibly driven by unrealistic recommendation model\":\n\n- Practically, the set of recommendable ads may be fixed, (re)sampled, or generated by some other process (e.g., via some auction process); see a discussion in the simulation framework upon which our code is based [Ie et al., 2019]. We chose a resampled ad pool because we felt that it was more realistic than a fixed ad pool (real-world ads are continually coming and going). Additionally, from an algorithmic perspective, a resampled ad pool helps with inference/learning due increased diversity of ads across a given episode. We’ve included a plot in the one-page attachment to illustrate the effect of a deterministic/fixed ad pool.\n\n- Your comment regarding the nature of information contained in the cookie was raised by another reviewer as well. Please see the global rebuttal (under \"Cookie and cohort model\") for our response.\n\n- We would like to address your comment that “in practice, the recommender system has no idea about the user model.” While we agree that most recommender systems may not have access to an explicit user model, the system is not blind to user behavior/preferences. Real-world recommender systems base recommendations on learned user preferences (from vast amounts of user-item interaction data) in order to maximize the some measure of engagement (e.g., clicks, shares, watch time, etc.). These data-driven models serve as models of user behavior, even if implicit. Consequently, we argue that no recommendation model is completely model-agnostic, but we would be happy to discuss more on some model variants we can investigate.\n\n\nResponse to: \"Cookie-cohort dependency and cookie model assumptions\":\n\n- We appreciate your comment regarding incorporating click behavior into the description of the user’s cookie. Under your proposed modification, a cookie would be represented as a pair (cookie value, empirical topic preferences). Given that both the consent rate and a user’s tastes are cohort-dependent, we feel that incorporation of average empirical topic preferences into a dynamic component of the cookie would still exhibit strong cohort-dependence (rather than be contaminated by user behavior). We’d like to incorporate this into the paper but given the time constraints of the rebuttal period we were unable to include this modification. \n\n\nResponse to: \"Theoretical explanations for the empirical observations\":\n\n- Regarding your comment on theoretical explanations for the empirical observations, observation 1 states that, in the case of cohort-dependent consent rates, users who disagree (to sharing their cookie) experience a lower estimation error only if they belong to the lower consent rate population (the intuitive non-consent leading to higher errors only holds for the higher consent rate population). Note that this effect holds purely due to the difference in the consent rates between the two cohorts, and is not dictated by the relative size of the agree vs disagree groups in each cohort in general (in response to your statement on “outlier groups”). In other words, even in the case where both cohorts have more users that disagreed vs agreed (see the case where $q_0=0.1$ and $q_1=0.3$). Observation 2 explains how two users from different cohorts fare when making a given consent decision. These observations appear consistent with the figure.\n\nOther comments:\n\n- We’re currently discussing some modifications to the title without deviating too much from the main finding of our experiments (disparate impact of consent). \n\n- We've also included a summary of the limitations of our paper in the global rebuttal section.\n\n- Lastly, while we agree that our paper is empirical in nature, we feel that this brings sufficient value due to the potential to encourage additional conversations (and experimentation) in this space, even in the absence of theoretical explanations."}, {"review_id": "e2y1EsfI8Q", "reviewer": "Reviewer_S9vB", "summary": "* This paper aims to investigate the effect of cookie consent (as mandated by GDPR, ePD), on the accuracy of recommendation algorithms using a simulation study.\n* Model:\n  * Each advertisement $a$ is characterized by a topic $\\tau \\in \\mathcal{T} \\cong [m]$.\n  * Each user $i\\in[n]$ described by a cookie $\\phi_i \\in \\Phi \\cong [c]$, a demographic $\\theta_i \\in \\Theta \\cong [d]$, and vector of topic affinities $\\alpha_i \\in \\mathbb{R}_+^m$. \n  * Prior $\\mu\\in\\Delta(\\Phi\\times\\Theta)$ is assumed over cohort-cookie pairs. Users from cohort $\\theta$ reveal their cookie with independent probability $q_\\theta$. User preferences $\\alpha_i$ are multivariate log-normal.\nProbability of user $i$ clicking ad $a$ (denoted $c_{i,a}=1$) is $p_{i,\\tau}$, depending on the the utility and on a “no-click-mass” parameter $p_0$.\n  * Upon observing the user's cookie (or lack of consent), the system constructs a posterior belief on their cohort $\\bar{\\mu}{i,0}\\in\\Delta(\\Theta)$. Items are recommended by an $\\varepsilon$-greedy policy, and the model is retrained at each time step $t$ using regularized least squares.\n* In the main experiment, the authors simulate the environment using the Recsim framework, for a population with two cohorts, two types of cookies, $n=200$ users, and $m=200$ topics.\n  * Section 5.1 demonstrates disparate impact of consent - Errors are symmetric in the case of homogeneous consent, and disparate in the case of heterogeneous consent.\n  * Section 5.2 aims to demonstrate amplification effects, showing the gap in consent rates serves as an amplifier for an individual’s consent decision.\n* Finally, the authors discuss in detail the possible implications of such effects on popular notions of fairness, and the effect of cookie of consent on the industry.\n", "questions": "* What is the effect of the recommendation algorithm on such accuracy disparity effects? Do recommendation algorithms that are indifferent to cookie consent amplify or diminish disparity? (e.g matrix factorization with uniform weights instead of uniform, KNN, etc.)\n* What is the motivation behind the modeling of cookies as a low-dimensional categorical variable ($\\phi \\in \\Phi \\cong [c]$)? How does it reflect the common structure of tracking cookies in practice? As far as I understand, cookies contain unique identifiers that track users across visits, and are therefore unique to every user. Moreover, users can store multiple types of cookies, and not just one.\n* How does the model behave when there are more than 2 cohorts? How does it behave when more than 2 categorical cookie types?\n* In which ways does the synthetic simulation differ significantly from practical settings? Do we expect the magnitude of disparity effects to increase or diminish when discussion moves to practical settings? Why, and is it possible to support the claim with experiments?\n* Can similar disparity effects be derived from simpler principles? (i.e the “Missing at Random” model from survey statistics causing bias when unaccounted for?)\n", "limitations": "I feel that the authors did not discuss limitations to a sufficient extent. Claimed effects are only demonstrated in a synthetic simulation with a non-standard recommendation algorithm. Even though I strongly agree that discrepancy effects may occur in practice to some extent, the analysis does not indicate whether their magnitude is significant in practical settings.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 1, "strengths": "* Problem is novel and well-motivated.\n* Model is outlined clearly.\n* Documented code is provided, and sensitivity analysis was conducted on the provided model.\n", "weaknesses": "* Paper only analyzes the behavior of a specific, non-standard recommender in a fully-synthetic environment. It is not clear from the analysis whether such effects are significant compared to other factors which are currently ignored in practice.\n* Disparity between the consent group vanishes as $t$ grows, raising concerns about the significance of the claimed effects in practice\n* Experiments compare relatively simple populations: Only two populations, with relatively low dataset sizes (fixed pool of $n=200$ users). Such experiments can be complemented either by theoretical analysis or experiments on real-world data, but neither are provided in the paper.\n* Minor technical remark: The letter $a$ is used to denote both ads (e.g in section 4), and “agreement to collect cookies” (e.g in section 5.2), which caused confusion. The notation $\\bar{\\mu}$ is not referred to in the algorithm.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your careful review. We hope that our responses below resolve some of your concerns.\n\nImpact of recommendation algorithm on accuracy disparity:\n\n- The impact of different recommendation algorithms on the observed disparity differs depending on how the algorithm deals with missing information. Generally, algorithms that are indifferent to consent would treat all users identically (ignoring the cookie information of consenting users). Matrix factorization with uniform weights is one such algorithm — all user-item interactions would be weighed the same likely leading to lower disparity. For KNN, the situation is more complex, where depending on how many “neighbors” a user has (dictated by the consent decision) it could be possible that disparity would be amplified as the measure of similarity becomes less reliable. In general, whether an algorithm diminishes or amplifies disparities depends on how it deals with the user’s missing cookie information (in the case of non-consent). \n\nModeling of cookies: \n\n- We agree that our cookie model is simplified. In practice, cookies generally contain both static information (e.g., user’s region) that is informative for their demographic/cohort as well as dynamic/behavioral information (e.g., click and browsing behavior). As part of our initial investigation, we’ve decided to focus on just the static component. \n\n- While we haven’t included behavioral information into a user’s cookie for the purposes of this paper, this is certainly an interested direction. As an initial thought, given the essentially unique cookie value for each user, revealed cookies would provide a significant amount of information on the identity of the user, potentially increasing the gap in treatment between consenting and non-consenting users. This is certainly a topic that we would like to investigate in follow-up work.\n\n\nModel behavior for more than 2 cohorts/cookies:\n\n- We’ve run additional simulations in response to your question (see the attached pdf). Explanation of the results for an increased number of cookies and cohorts can be found in the global rebuttal (under “Cookie and cohort model”) as it was raised by another reviewer.\n\n\nDifferences between simulation and practical settings:\n\n- Our model differs from practical settings in multiple ways. As discussed in the global rebuttal section, our model is intentionally simplified in order to isolate the effects of cohort-dependent consent rates without the noise or confounding factors present in practical settings (factors that would mask our ability to detect such disparities but may still exist). We do not know with certainty how the degree of disparity would change in practice (it’s possible that disparities may increase with dynamic information as discussed above). We argue that the findings from our simplified setting should at least provide some motivation for investigating if these issues also exist in practice.\n\n\nDisparity effects from simpler principles:\n\n- Your question regarding the “Missing at Random” model is interesting, however, we feel that this is a different setting from our cohort-dependent consent setting. The MAR model assumes that the probability that a value is missing is related to the observed data but is independent of the unobserved data. Mapping this to our consent setting, this would imply that a user’s consent decision is based solely on observed quantities, without any influence from the underlying unobserved quantities (e.g., cohort). Our model specifies that consent is dictated by the unobserved quantity (cohort), which differs from the MAR model.\n\nOther comments:\n\n- Regarding your comment on the disparity vanishing as the number of interactions grow, this occurs after a relatively high number of interactions, with the disparity present for a significant number of interactions (upwards of 20 interactions). We lack precise data on the average number of sequential interactions that a user makes with a given website (or an ad serving platform), however, there are many reasonable scenarios where a user will only interact with a website a handful of times before navigating elsewhere (not to mention users periodically clearing their cookies, restarting the interaction counter as a result). \n\n- While we did not run simulations on a dynamic user pool due to the time constraints for the rebuttal, we would imagine that the impact of a such a modification may further amplify the observed disparities. The reason for this is because the gap in estimation accuracy between consenting and non-consenting users is greatest when the interaction count is low; when the user pool is changing, there will be more fresh users in the user pool who, by definition, have zero interactions with the recommender system.\n\n- We've included a summary of the limitations of our paper in the global rebuttal section.\n"}, {"review_id": "ZdPm344qZx", "reviewer": "Reviewer_WBi3", "summary": "Cookies enable accurate identification and tracking of user behavior, leading to personalized ads and better ad campaign performance. However, this raises privacy and fairness concerns. This study investigates the impact of user consent on a recommender system's ability to learn about users' demographics and preferences. It reveals that when consent rates are demographically dependent, a user's choice to not share their cookie can paradoxically lead to the recommender system knowing more about them. Moreover, the gap in consent rates between demographics amplifies estimation errors. As the system receives more user responses, the effects of consent decisions diminish. The findings highlight the need for new fairness notions that promote consistency between users' privacy choices and the accuracy of the recommender system's estimations.", "questions": "1. User grouping/clustering is a common practice in industry. Estimating effects of cookie consent stuff with real-world dataset is more meaningful. I would suggest analyze performance and consent rate with the external grouping info ", "limitations": "N/A since the authors didn't propose new methods.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper studied a practical topic which is valuable to the community. The paper is also clearly written and easy to follow. ", "weaknesses": "1. The work seems incomplete. With a simulation experiment and an analysis, there's no solution to the observed issues.\n2. The simulation setting is a bit simplified, introducing inductive bias to the results. Concretely, matrix factorization only mimics user behaviors (e.g., click), ignoring the user/item features. To be honest, matrix factorization is not the mainstream technique in industry. It is tree model and deep model. These model will be affected by user consent decision since user features will be unavailable, which will pose challenges to model training and serving, and then model performance and subsequent fairness, privacy issues. It will be more attractive if authors consider this setting.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for the review.\n\n- Regarding your comment that our paper does not contain a solution, our view is that there is value in drawing attention to an issue without necessary having a fix. We’ve proposed changes to industry practice that should be made, along the lines of ensuring that how much a system knows about a user is consistent with their privacy decision, but we feel that by no means is the solution trivial. It will likely require deliberate loss of user information, which in turn will require the design of incentives to do so. The goal of our paper is to present an interesting observation related to the fairness of consent with the hopes of seeding further conversation on the topic.\n\n- In response to your comment on the simplicity of the simulation setting, we agree that it would be interesting to investigate the impact of user consent in the context of more realistic recommender system algorithms, however, we would like to note that (while a simple algorithm) matrix factorization does form the basis for many more modern recommender algorithms (hybrid and embedding-based methods). The goal of our paper was to illustrate the disparate impact of consent for a simple foundational algorithm such that these insights would encourage broader discussion in the community (and, to your point, investigation into if these effects also exist in more complex systems). Additional discussion on the simulation setting can be found in the global rebuttal section under “Real-world relevance of the studied model.” \n\n- Lastly, grouping or clustering of users is done in practice to aid with scalability — clustering reduces the effective dimension of the recommendation task by making group-level recommendations (generally at the cost of recommendation accuracy). While this is an important algorithmic step for practical recommender systems, the focus of our paper is on the impact of user-level consent decisions. Our understanding of your comment is to extend this study to include alternative grouping structures (not necessarily dictated by the user’s cohort), which is certainly an interesting direction, but we feel falls outside the main message of our paper."}]

Author rebuttal:
Real-world relevance of the studied model:

- We appreciate the reviewers’ concerns regarding the relevance of the model to real-world settings. We’d like the emphasize that the goal of this investigation is to present an intentionally simplified model in order to isolate and understand the effects of specific model aspects (i.e., impact of different user consent rates) without the additional noise and confounding factors present in real-world settings. 

- That being said, we were careful when designing our model to ensure that it captured the core aspects of real-world recommender systems, namely confidence weights [Hu et al., 2008; Koren et al., 2009] and continual/online update of factor estimates via online methods [Wang et al., 2017]. These seminal papers form the foundation of many (more complex) models deployed in practice. As such, a primary takeaway of our paper is that there is at least a cause for concern that our findings may also exist in production-level recommender systems that are based on these fundamental algorithms. We will include a segment on this discussion in the revised paper.

- We feel that this philosophy (of gaining insights for a simplified version of a model) is a powerful approach to research in complex AI systems, as many negative effects can be hidden in the complexity of real-world models, but still present under the surface. 


Cookie and cohort model:

- A couple of reviewers have raised questions on the choice of representing cookies as static quantities. We agree that in reality cookies contain both static information (e.g., location information) and dynamic information (e.g., user click and browsing behavior). Our decision to model user cookies as only containing static information (as a proxy for user cohort) was an intentional simplification to isolate the effects of cohort-dependent consent rates (which users are more or less likely to provide their consent) on the recommendation process and investigate the potential fairness issues on specific user groups. In practice, the user profile (as opposed to the actual cookie value) is what drives recommendations — we abstract this by representing cookies as proxies for the user’s core identity (cohorts/demographics).

- Regarding the impact of a larger number of cookies/cohorts, we’ve run some additional simulations under two cases: i) $c=d=3$, and ii) $c=d=4$, each under a variety of cohort-dependent consent rates. Please see the attached pdf under the caption “Effect of model size parameters.” As seen from the plots, the primary observation still holds, with a necessary modification: non-consenting users in any cohort that is not the maximal consent-rate cohort experience lower estimation errors for disagreeing (non-consent) than agreeing (consent). We will augment the observations in the paper to include this generalization.


In response to the reviewer’s comments, we’ve consolidated the limitations of our approach (to be included as a limitations section of the revised paper):

- Our findings on the disparate impact of consent should be interpreted with the understanding that our model necessarily has some limitations. Broadly, our model uses a simplified definition of cookies in which cookies serves as a proxy for the users’ cohorts. While the reason for this simplicity is to extract insights that depend directly on the user’s cookie consent decisions, extending the definition of a cookie to more realistic settings by including user click/behavioral information would likely generate additional insights. Secondly, to capture the core aspects of recommender systems, our recommendation model is based on foundational recommendation algorithms (namely online + confidence-weighted matrix factorization). While these algorithms form the basis for modern recommender systems, it would be worthwhile to see how the insights extend to more general algorithms. Lastly, we consider a fixed user pool; consideration of a more realistic dynamic user pool could influence the findings.

References (for both global rebuttal and individual rebuttals):

- [Hu et al., 2008] Yifan Hu, Yehuda Koren, and Chris Volinsky. "Collaborative filtering for implicit feedback datasets." In 2008 Eighth IEEE international conference on data mining, pp. 263-272. IEEE, 2008.

- [Ie et al., 2019] Eugene Ie, Chih-wei Hsu, Martin Mladenov, Vihan Jain, Sanmit Narvekar, Jing Wang, Rui Wu, and Craig Boutilier. "Recsim: A configurable simulation platform for recommender systems." arXiv preprint arXiv:1909.04847 (2019).

- [Koren et al., 2009] Yehuda Koren, Robert Bell, and Chris Volinsky. "Matrix factorization techniques for recommender systems." Computer 42, no. 8 (2009): 30-37.

- [Wang et al., 2017] Huazheng Wang, Qingyun Wu, and Hongning Wang. "Factorization bandits for interactive recommendation." In Proceedings of the AAAI Conference on Artificial Intelligence, vol. 31, no. 1. 2017.

Meta-review: I am recommending an acceptance after a careful reading of the paper, reviews, and author rebuttal. In short, this is a well-written paper with sound results and a clear message – i.e., that refusing cookie consent makes it easier to infer demographics. My views on the submission broadly align with Reviewer [cPvy](https://openreview.net/forum?id=dFtpRphNb3&noteId=4ALdoUtjVm) who has recommended acceptance. I also share some (but not all) of the concerns raised by the other reviewers, and I would encourage the authors to address these issues in their revisions. 

Looking forward, I would like to draw special attention to two particular concerns that multiple reviewers raised:

1. The fact that the paper supports their claim through a simple simulation model. In this case, the authors are correct that using a "real - model" would make it difficult to isolate effects. I would encourage the authors to explicitly discuss the inherent value of their approach in their revision as future readers will share it. I would also encourage the authors to include a discussion on their results to generalize to "real-world" recommender systems (which could include the experiments conducted during the rebuttal phase if need be).

2. The fact that the paper studies a problem but does not propose a concrete way to solve it. In this case, the authors are correct that it is worth drawing attention to problems that might not be easy to solve. This is a claim that does not merit special attention – though it does signal the need for a broader discussion on what can be done to resolve this issue.
Decision: Accept (poster)