Fraud-Proof Revenue Division on Subscription Platforms
Authors: Abheek Ghosh
Tzeh Yuan Neoh
Nicholas Teh
Giannis Tyrovolas
Venue: ICML 2025 poster (2025)
Keywords: fraud-proof
revenue division
subscription platforms
mechanism design
Primary area: theory->game_theory

Abstract: We study a model of subscription-based platforms where users pay a fixed fee for unlimited access to content, and creators receive a share of the revenue. Existing approaches to detecting fraud predominantly rely on machine learning methods, engaging in an ongoing arms race with bad actors. We explore revenue division mechanisms that inherently disincentivize manipulation. We formalize three types of manipulation-resistance axioms and examine which existing rules satisfy these. We show that a mechanism widely used by streaming platforms, not only fails to prevent fraud, but also makes detecting manipulation computationally intractable. We also introduce a novel rule, ScaledUserProp, that satisfies all three manipulation-resistance axioms. Finally, experiments with both real-world and synthetic streaming data support ScaledUserProp as a fairer alternative compared to existing rules.

Fraud-Proof Revenue Division on Subscription Platforms
Abheek Ghosh"
Tzeh Yuan Neoh
Nicholas Teh Giannis Tyrovolas
1*
Abstract
Subscription platforms have seen significant growth in re- cent years, driven by the rise of internet streaming services such as Spotify, Apple Music, Netflix, etc. For instance, the annual revenue of the music streaming industry reached US$27.6 6 billion in 2023, with significant increases over the last ten years (International Federation of the Phono- graphic Industry, 2024). Under this business model, users pay fixed subscription fee to enjoy unlimited access to all content the platform, typically by content creators. The platform then takes a fixed revenue cut and distributes the rest to the creators based on engagement metrics (e.g., play counts or views) and/or specific agreements between creators and platforms.
We study a model of subscription-base based platforms where users pay fixed fee for unlimited access to content, and creators receive share of the revenue. Existing approaches to detecting fraud predominantly rely on machine learning methods, engaging in an ongoing arms race with bad ac- tors. We explore revenue division mechanisms that inherently disincentivize manipulation. We formalize three types of manipulation-resin ressssttteeeeeee axioms and examine which existing rules satisfy these. We show that a mechanism widely used by streaming platforms, not only fails to prevent fraud, but also makes detecting manipulation com- putationally intractable. We also introduce novel rule, Scaled PROP, that satisfies all three manipulation-resistan axioms. Finally, experi- ments with both real-world and synthetic stream- ing data support SCALEDUSERPROW as a fairer alternative compared to existing rules.
Despite efforts to curb manipulation, bad actors persist, us- ing bots and click-farms inflate user engagement (Drott, 2020; Snickars & Mähler, 2018). This issue is so significant that major music streaming platforms like Amazon Music and Spotify have established an industry advocacy group (Music Fights Fraud Alliance, 2025) to combat such fraud, which is estimated to cost the industry US$300 million amnu- ally (Burton, 2021). Additionally, the rise of Al-generated content introduces new challenges- platforms are increas- ingly flooded with synthetic tracks, videos, and live streams designed to exploit engagement-driven algorithms. This Al Al-generated content often amplifies fraudulent listening activities, making manipulation harder to detect.
1. Introduction
In September 2024, the FBI criminally charged a musician, Michael Smith, for orchestrating scheme to fraudulently in- flate his music streams on platforms such as Amazon Music, Apple Music, Spotify, and YouTube Music-ant according to court documents, walked away with over US$10 million in royalty payments (United States Attorne''s ' Office, 2024). To successfully execute his scheme, he utilized hundreds of thousands of songs created using AI, and built a complicated network of over a thousand bot accounts that artificially boost streams across these platforms billions of times. Al- though each stream originated from bona fide, fee-paying account, the way the platform(s) distributed subscription revenue allowed each bot to generate more in royalties than it cost to maintain its subscription.
Current machine learning (ML) approaches to this problem predominantly focus on detecting fraudulent activity using sophisticated algorithms ranging from anomaly detection (Esmacilzadch et al., 2022) to unsupervised learning (Mol- laoğlu et al., 2021) and graph neural networks (Li et al., 2021). For instance, music streaming platforms such as Spo- tify have proprietary models that identify whether a stream is legitimate (using meta-data such as IP location, listening patterns, and other information) and issue fines if they deem too many streams be fraudulent (Spotify, 2025).
However, as AI continues to evolve, do the methods used by fraudsters, leading to a continuous arms race. These bad actors increasingly leverage advanced automation tools to make fraudulent activities more sophisticated and harder to detect, challenging the robustness of existing detection frameworks and driving the need for innovative, adaptive solutions (United States Attorne'' Office, 2024).
AAlphabetical ordering Univeessity of Oxford, UK Tzeh Yuan Neoh <tzzhyyan_nee nww. neoh@harvanl harvard.edux>, Nicholas Tch Enicholas.tche cx..u..
"Harvard University, USA. Correspondence @achhuuuunnnch@@eeee
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Fraud-Proof Revenue Division on Subscription Platforms
The root of the problem stems from the way revenue is cur- rently distributed to content creators on most subscription- based streaming platforms: "funds from the royalty pool are allocated proportionally among artists based on their respective percentages of total streams" (United States At- tomne's Office, 2024)-we call this rule GLOBALPROP.
to capture both resistance to manipulation and maintaining faimess and analyzing these axioms with respect to multiple revenue-division mechanisms- from existing litera- ture and one novel mechanism that we propose.
Moreover, we challenge the current status quo rule, GL.OB- ALPROP, by demonstrating that detecting suspicious activity under this rule is computationally intractable- an important finding in this context. Since fraud detection (and fraud in general) is highly relevant the ML community, we believe this result will be of particular interest to researchers and practitioners in the field.
In this paper, we tackle this problem from a mechanism de- sign perspective, i.c., we mathematically formalize notions of fraud in this setting and investigate the existence of rev- enue division mechanisms that can inherently disincentivize fraudulent behavior, thereby reducing the industry's 's reliance on expensive and complex fraud detection methods to com- bat manipulation. Moreover, such mechanisms exist, they could complement existing MI.-based approaches by pro- viding a foundational layer of fraud resistance. These mech- anisms inherently target known forms of fraud, allowing MI. systems to focus on adapting to emerging, previously unseen types of fraud that may arise in the future, ensur- ing continuous improvement in detecting and addressing manipulation.
In Section 2, we establish three fundamental properties that define the space of mechanisms we consider: anonymity, neutrality, and no free-ridership. The first two ensure that payoff's to artists only depend on their engagement with users. In particular, mechanisms cannot distinguish between fraudulent and genuine artists or users. No free-ridership eliminates trivial cases where an artist without engagement receives a non-zero payoff. Next, we formalize three forms of resistance to strategic manipulation. Fraud proud-proffiess pre- vents adversaries from profitably creating new fraudulent users. Bribery-prooffess prevents profitably bribing exist- ing users and is a strengthening of prooo-fss as presented in Bergantiños & Moreno-Tereee nally, (strong) Sybil-proofness ensures that artists cannot gain by splitting into multiple identities or merging with others. All three axioms are novel in our setting and are motivated by real-world observations. We also introduce two additional fairness titomm--nnaggmmen monotonic- ity and Pigou-Dalton consistency, the latter inspired by an equitability concept in welfare economics.
Additionally, many policymakers and academics have also argued against the fairness of GLOBALPROP in favor of an alternative Mice-USERPROP (which directly allocates fixed fraction of each user's subscription fee only among the creators of the content the user consumes) from an economic (Meyn et al., 2023; Muikku, 2017), empirical (Moreau ct al., 2024), theoretical (Bergantiñios & Moreno- Ternero, 2025), and legal (Dimont, 2018) perspective. Moti- vated by these debates, we aim to address fairness consider- ations in our work as well.
proofness
(2025). Fi-
Lastly, the primary focus of our work is on fraudulent be- havior specifically related to the creation of fake users (bots) to manipulate engagement metrics. We deliberately do not address the equally prevalent issue of widespread AI- generated content on these platforms. The legal status of such content can vary, especially since some popular artists openly release their Al-generated voices as bemii-oopen- source (Josan, 2024), making its permissibility platform- dependent and governed by specific rules. Nonetheless, our work provides a principled framework for studying similar challenges. As Al continues to evolve and new forms of fraudulent behavior emerge, our approach can be extended to address these issues, provided that appropriate regulatory frameworks established to guide the platforms.
In Section 3, we conduct an axiomatic study (with respect to our proposed concepts) of several rules proposed in the literature so far. Notably, we show that GLOBALPROP fails to satisfy fraud-proofnesss and prooery.,roofness, in contrast to the other two Bantenderr-UsERRRROR and USEREQ. Contributing to existing critiques of GLOBAL we establish a case against GLOBAL through computa- tional lens, and in the context of fraud detection. We show that a platform uses GLOBALLPRPP, detecting potentially fraudulent activity is harhard. We then analyze the two other existing rules: USERPROP and USEREQ. We study their axiomatic properties and prove that they satisfy our mramppulation-resistann axioms, unlike GLOBALPROP. We also demonstrate that portioning rules cataloged in Elkind et al. (2023) fail all the manipulation-resisannee axioms we consider.
1.1. Our Results
In this work, we focus on designing manipulatiion-reisttnn mechanisms from computational and axiomatic perspec- tive, setting our research apart from all previous work on this model. Although we build on the standard model for subscription platforms established in prior literature, our key contribution lies in introducing several axioms that aim
Finally, in Section 4, we propose and study a new rulc- SRRO We show that it has the same ax- iomatic guarantees as USERPROP but is fairer when mea- sured by the popular ppay-per-ttream" metric. We use this to quantify maximum envy in this setting and empirically
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Fraud-Proof Revenue Division on Subscription Platforms
verify this against existing rules in Section 5.
sentially conduct an axiomatic study of popular rules in their respective games modeled, but adapted to this new set- ting. We refer the reader to the Casas-Méndez et al. (2014) for a survey on earlier works on this area. From 2001 to 2014, works on the topic cumulatively studied more than 30 axioms, with broadly two kinds of manipulation-reste resissat axioms-one based on "ticket prices" and the other based on "reported number of visitors". However, we note that the museum pass problem is fundamentally different from problem, and thus the way axioms (and rules) are conceptu- alized would also naturally be distinct. This distinction is particularly apparent when it comes to concepts relating to manipulation.
All omitted proof's can be found in the full version of this
paper.
1.2. Related Work
Our work considers the model proposed and studied by several recent works on (music) streaming platforms.'
Alaei et al. (2022) and Lei (2023) focused on a compara- tive study between GLOBALPROP and USERPROP. More specifically, Alaei et al. (2022) focused on providing char- acterizations of both rules with respect to newly proposed axioms. They were also concerned with which of these two the plat-
rules could sustain set of artists' profitability form, as well as comparing them from both the platform's ss and the artists' perspectives. Lei (2023) pointed out the shortcomings of USER They compared the two rules primarily in terms of egalitarian fairness (i.e., the lowest payout among all artists) and efficiency (i.e., "dominance on quality profile"), but they allow for artists to vary stream quality and thus this concept is not relevant in our model.
Our work also contributes to the broader literature on ap- plying computational and algorithmic methods address incentive-related challenges in online economic systems and platforms. For example, manipulation issues have been stud- ied in the contexts of online advertising markets (Golrezaei et al., 2021a; Kanoria & Nazerzadeh, 2014), recommenda- tion systems (Eilat & Rosenfeld, 2023; Yao et al., 2023), and e-commerce platforms (Golrezaei et al., 2021 bb; He et al., 2022; Mayzlin et al., 2014).
Bergantiños & Terneo- (2025) go beyond previ- ous works to consider a family of rules that interpolates between GLOBALPROP and USERPROP, and they provide further characterizations for both rules and their interpola- tion. Subsequently, Bergantiñios & Moreno- Ternero (2024) introduced the Shapley index as a rule for this setting and characterized it using existing and new axioms.
2. Model and Axioms
For each positive integer k., let [b] ;= (l.....k} k}. Let N =
[>]] be the set of users and C = [mm] be the set of artists. Suppose that an adversary controls set of fake users N S N and a set of fake artists Ö S C; let ñ = [ For each i E N and j E C, let way 2 0 denote the number of interactions user i has with artist j.2 For each user i E N. we assume that Ejec Wiy > 0, i.e. the user has some non-zero interactions. 3 Let w, = (Wa,...., Wim for each i E N. The engagement profile is w = (Wi,..., w...
Deng et al. (2024) investigate sharrng mechanisms for Al-generated music platforms. Their work centers on the challenge of attributing& a new, Al-created track to specific copyrighted recordings in the training data- an attribution problem that underpins royalty allocation in that setting. This challenge is fundamentally distinct from the problems we address.
Without loss of generality, we assume that the subscription fee for each user unit. Then, the total subscription fee collected from the users is n. As assumed in the prior works this topic, and as observed in the real-world, we assume that the platform takes a cut of (1 a:)n and distributes the remaining an to the artists, for some a E (0. 1].
A related stream of work is the museum pass problem. popu- lar in the in the economics literature, and was first introduced by Ginsburgh & Zang (2001; 2003). The problem studies the sharing of revenue among museums from the sale of museum passes for a price below the aggregate admission fee of individual member museums (i.e., bundled pricing). Béal & Solal (2010) and Ginsburgh & Zang (2001; 2003)
A problem instance I = (N, C, w) is defined by the set of users N, the set of artists C, and the engagement profile w. A payment rule (or simply rule) is a function 6 that maps each instance I to an m-valued vector (Φz -.... dz (m)), where dz is the payment to artist j E C. To simplify notation, for a subset of artists S S C, we use dz(S) to
studied the problem as coalitional game, whereas Casas- Méndez et al. (201) 1) and Fstévez-Fernánddzz et al. (2012)
studied the problem as a bankrupicy game, Wang (2011)
studied the dual version of the problem-the museum cost sharing problem. All of the works above (including sev- eral more recent works which look at the Shapley value as rule (Bergantinos& & Moreno-Ternero, 2015; 2016)) es-
"This is typically defined as a stream (on music streaming platforms like Spotify), whereby a user plays a track for a minimum duration, or a view (on video streaming platforms like YouTube Live) when user joins and stays for a minimum amount of time. "Note that many our proofs, we can without loss of gener- ality assume that weights are rational numbers.
'However, note that this model is also applicable to many other content subscription platforms (e.g., education, art, etc.).
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Fraud-Proof Revenue Division Subscription Platforms
denote the sum of the payments to the artists in the set S:
tion fee, and earn profit from her own fake artists (C)!
dI(S) = Ejes (z))
Rules that make such fraud impossible are fraud-proof.
Definition 2.4 (Fraud-proofness) A rule e is fraud-prood if the following holds: For any two instances I = (N
2.1. Preliminary Axioms
N, C, w) and I' = (N, w') with w; w/ for all N N, and any C - C, we have that
We begin by introducing three fundamental fairness proper- ties that any reasonable revenue division mechanism in our setting should satisfy. We will then provide rationale for the necessity of these axioms in our setting.
QT S n.
A rule Φ is single-user fraud-proof if f 1.
Our definition of fraud- proofneso considers only adver- sary's 's profit from creating fake users, not fake artists. This means an adversary can introduce fake artists to earn profits without using fake users. However, without fake users, any fake artist must attract engagement from real users to profit (by the no free-ridership assumption). Whether this practice violates a platform's is rules is separate issue beyond our scope-we we focus on the extra profit an adversary can gain by adding fake users, assuming fixed set of artists (which may include fake ones).
The first aniom--nonyyity- not distinguish between real and fake users.
that the rule can-
Definition 2.1 (Anonymity). A rule & is anonymous if per- muting the labels of the users does not affect the payoffs of the artists. Formally, rule Φ is anonymous if for all instances I (N, C, w) and I' (N, C, w') and all permutations a: N + N, if w; w (3) for all users i E N, then for all artists j E C. oz(() = (j)
The second neita--nutraalty--is similar in nature to anonymity, but for artists. It preseribes that the rule cannot distinguish between real and fake artists.
Next, we show that single-use fraud-proofie poondddroonesss is equivalent to (multi-user) reason about fraud -rooffess
simplifying how one can
Definition 2.2 (Neutrality). A rule & is neutral if permuting the labels of the artists permutes their payoffs. Formally, rule Φ is neutral if for all instances I = (N, C, w) and I' = (N, C, w') and all permutations a : C - C, if why = w/ for all users e N and artists j e C, then for all artists j E C, (z)) = (o(i).
Proposition 2.5. A rule á is fraud-proof if and only if single-user fraud-proof.
Another form of manipulation is bribery. Bribery is par- ticularly relevant in scenarios where the platform imposes substantially stringent access requirements, making creating fake users significantly more challenging. However, under such conditions, artists may resort to colluding with and bribing users users-offering to pay the subscription fees of the users to manipulate their engagement profiles. This practice is commonly observed in streaming farms, the streaming equivalent of click ffrcsf in advertising (Drott, 2020). We call resistance to such bribery as bribery-prooftesss
In our setting, it is crucial to consider only rules that are anonymous and neutral. In practice, given the number of users/artists. it is virtually impossible to detect all fake users/artists, even with existing fraud detection techniques, as noted in our introduction. This inability to reliably distin- guish between real and fake users or artists underscores the importance of addressing the questions we aim to answer.
A rule ó is bribery- proof if the following holds: For any two instances I (N, C, w) and I' = (N, C, w') with w; A w/ ffr exactly k users, and any C _ C, we have that Φ (C) ΦI (c) S k.
Definition 2.6 Stribery-rroofieee
Finally, the last fundamental axiom we consider is the notion of no free-ridership. Intuitively, this means that artists who receive no user engagement should not receive any payment.
A rule e single-user bribery-proof if k: 1.
Definition 2.3 (No free-ridership). A rule o satisfies no free-ridership if, for any instance I = (N, C, w) and artist j E C' where DiEN Waj- = O, then Φπ( = 0.
Similarly to fraud- prooffes,,, multi-use prooffess and single-user proooeessss are equivalent.
Proposition 2.7. A rule is bribery-proof if and only if it is single-user bribery-proof.
This axiom rules out trivial rules that allocate payments dis- regarding user engagement (e.g., giving equal payment to each artist irrespective of user engagement) and are, there- fore, resistant to strategic manipulation.
We note that (single-user) strengthens the axiom of flick-fraud-prooffeer proposed in Bergantiños & Ternnoo (2025). flick-fraud- proofness requires that single user altering their engage- ment cannot alter the payoff of any artist by more than
substantially
2.2. Axioms for Preventing Strategic Manipulation
We start by formalizing the fraud alleged in the indictment mentioned in the introduction. Intuitively, no adversary should be able to create fake users (N), pay their subscríp-
NNote that do not impose any constraints the listening behavior or engagement profiles of these fake users.
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Fraud-Proof Revenue Division Subscription Platforms
Formally, for all j. 1xz الار < 1. Single- user bribery-proofness requires that for all subsets of artists im- plies flick-fraud proofffrs and protects from multiple artists colluding.
(ii) EIEN Ejeoro- Wiy LiEN Ejeon w/y
C' C C. 10 (C) أπ(Ò) < 1.¹ Bribery-proofnee
then we must have that dz(C') (() (C))
(*))
We will show later that GLOBALPROP is the only neutral rule satisfying strong Sybil-proofness (Theorem 3.2), hence also motivating our study of (the weaker) Sybil-proofness.
Fraud-pu -raud-proofness and prooofess capture resilience to two different kinds of manipulation. Despite being similar, we show that the axioms are not equivalent. Recall that a is the fraction of each user's subscription fee that is allocated to the artists, with the remaining portion retained by the platform as fixed cut.
2.3. Fairness Axioms
Next, we consider two faimesss propertis--engagemmmn monotonicity and Pigou-Dalton consistency.
Theorem 2.8. Consider some rule 6. Then:
Intuitively, if an artist's engagement increases while every other artists' engagement does not increase, this artist's ' payoff should not decrease- this aligns with basic economic principles. would be fundamentally unfair for a creator's rising popularity to result in a lower payoff. We formalize this fairness property as follows.
(i) Ifa= = and is fraud-proof, it is also bribery-proof:
(ii) For a E (0, 1), there exists a rule that is bribery-proof but not fraud-proof, even when m = 2;
(iii) For a < L, there exists a rule that is fraud-proof but not bribery-proof even when m = 2.
Definition 2.11 (Engagement monotonicity). A rule is engagement monotone if the following holds: For any two instances I = (N, C, w) and I' = (N, C, C,w',, if there exists a j E C such that
The last pair of axioms that we consider Sybil-proofieet and its strong counterpart- addresses a different form of strategic manipulation compared to the two earlier concepts. Intuitively, these axioms are designed to prevent any artist(s) from splitting or merging to gain an unfair advantage and fraudulently increasing their revenue share, thus also ensur- ing that all artists are treated fairly based their actual level of user engagement.
couneeppat-aaddressss
(i) Wiy S w/y- for all i E N; and
(ii) Wiy 2 wey for all i E N and j e (\'),
then we must have that xz(j") S (j*).
Next, the Pigou-Dalton principle (Pigou, 1920; Dalton, 1920), is a fundamental fairness notion from welfare eco- nomics and often referenced in collective decision-making (Moulin, 2003) it states that among similar outcomes, the equitable one should be picked. We interpret this principle in our setting: all other things being equal, an artist who is more "uniformly enjoyed" should receive weakly more payoff from an equally popular but "polarizing" artist.
Definition 2.9 (Sybil-prooffess). A rule e is Sybil-proof if the following holds: For any two instances I = (N, C, w) and I' = (N, C", w') whereby C' C C", if for every subset of artists C* C C' such that
(i) Wij why for all i E ".JEC"
(ii) Ejerro Wij = Ejeoro- w/y for aorallie N,
Definition 2.12 (Pigou-Dalton consistency). A rule & is FagounDalton consistent if the following holds: For any two instances I (N, C, w) and I' (N, C, w'), if there exists some i, 1' E N and j E C' such that
then we must have that
(O)).
We can define a stronger notion of Sybil-proofness by re- laxing (i) and (ii), defined as follows. Note that strong Sybil-proofness implies Sybil-proofness.
(i) w/y = Wij 8 (where 5 > 0 and waj - 8 > 0);
Definition 2.10 (Strong Sybil-proofness.. A rule & is strongly Sybil-proof if the following holds: For any two instances = (N, C, w) and I' = (N, C', w') whereby C C C", if for any subset of artists C C such that
iii) w/y wy + 8 and w/y w'y: and
(iii) Wky' wky for all k E N and jr E C (i), and
Wkj wky for all & N (i,
then we must have that dz()) S or (j).
EtEN myy = EiEN why for all j E C*: and
'Note that by Proposition 2.7, suffices to only consider single- user tribery-proofnes.. 'The name is inspired by the concept of a Sybil attack in com- puter networks.
3. Existing Mechanisms
In this section, we formally define the three existing mech- anisms proposed in the literature, and study which axioms
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Fraud-Proof Revenue Division Subscription Platforms
Axioms/ / Rules
GP
UP
UEQ
SCUP
Theorem 3.3. GLOBBAPROP satisfies no free-ridership,
shaud-proofness
X
engagement monotonicity, and Pigou-Dalton consistency.
Bribery-proofness
X
/
/
Sybil-proofness
V
/
x
V
A Case Against GLOBAL.POP:: The Computational In- tractability of Fraud Detection. We have shown that GLOBALPROP is not fraud-proof. One might hope that artists benefiting from fraud could be easily identified and removed. Unfortunately, detecting the artists who gain the most from fraudulent activity is computationally intractable.
Strong sybil-proofness
V
x
X
X
Engagement monotonicity
V
/
/
V
Pigou-Dalton consistency
x
x
Table 1. Axiomatic properties of the revenue division mechanisms. GP is GLOBALPROP, UP is USERPROP, UEQ is USEREQ, and ScUP SCALEDUSFFRPOP
Importantly, a user who streams music extensively is not in- herently suspicious- some people naturally listen to music for most of their waking hours. Thus, instead of targeting in- dividual active users, we should focus on identifying artists who may be used as vehicles for fraud by an ad adversary."
they satisfy. We summarize our results in Table 1. At the end of the section, we also include a reference to a discussion on how our model generalizes portioning rules.
Definition 3.4 (Potentially Suspicious Profits). Given set of artists U C C, their potentially suspicious profit (PSP) from GLOBBAL PROP is their maximum marginal profits from a set of users V, less the cost of creating these users:
The rules we consider in this and the next section trivially satisfy anonymity and neutrality. Therefore, among the three preliminary axioms introduced in Section 2.1, we will only formally prove the satisfaction of no free-ridership.
EiEN EjEU Waj EIEN Ejec Wij
PSP(U) = max VEN
x am
3.1. GLOPALPROP: The Status Quo
GLOBALPROP distributes the payoff to each artist propor- tionally to the artist's share of total engagement. For ex- ample, if there are 500 users, and an artist gets 25% of the total user engagement in the platform, then the artist corre- spondingly receives a payment of 0.25 500a 125a der GI.OBAIPROP. According to court documents (United States Attorney's ' Office, 2024), this is the rule that major streaming platforms use.?
EiENyy Σ Ejet Wij
x aa(n-IV) xc(n-IVi--vi)
ΣiENyy Ejec Wij
Thus, our objective of identifying suspicious artists can be framed as finding of artists U C C such that PU)(U) is high. However, the choice of [U] is crucial. If we restrict U to a single artist ((U) = 1), adversary can easily evade detection by distributing fake users' listening activity across multiple fraudulent artists. On the other hand, if we impose no constraint on (U], we risk identifying a set of legitimate artists with dedicated fan bases. Also, while an adversary can create multiple fake artists, doing so incurs administra- tive overhead such setting up identification and banking makes the creation of an arbitrarily large number of fake artists impractical in many circumstances.
GLOBALPROP
Given an instance I (N, C, w) and for each j E C, the payment rule GLOBALPROP is defined as follows.
ΣVEN Wej
ez(j)=
Eyec LIEN Wiy'
an.
Therefore, we define the problem of finding suspicious artists as finding the set U C C' of size at most & artists that maximize (U) However, we show that this prob- lem is computationally intractable, with the following result.
is easy to observe that users with higher engagement exert disproportionate influence revenue distribution. Given this, it is not surprising that this rule fails to satisfy both fraud- prodffeoofiness and
Theorem 3.5. Given an instance I (N, C, w) and pa- rameters k < [C] and y > is Nh-hard to determine if there exists a U C C such that U < k and PSP(U) 2 %
Theorem 3.1. GLOBALPROP satisfies strong Sybil- proofness, but fails fraud-proofness and bribery-proofness
Moreover, strong Sybil-proofness uniquely characterizes GLOBALPROP, given our neutrality assumption.
3.2. User-Additive Rules
Theorem 3.2. GLOBALPROP is the only neutral rule satis- fying strong proof-proo.ses.
At the opposite extreme from GLOBALPROP are rules where each user's subscription fee is distributed solely based on their individual engagement profile. Under these rules, an
GL.OBAL also satisfies our fairness axioms.
*Our objective is to identify fraudulent artists a means of de- tecting suspicious interactions between fake users and fake artists.
It is also sometimes known as the pro-rata rule.
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artist's total payoff is simply the sum of the amounts they would receive from each user in single-user setting. We refer to this class of rules as user-additive."
listen to other artists, then these three artists each receives a payment of a:/3 from this user, and the remaining artists do not receive any payment from the user. The total payment to an artist is the sum of such payments from each user.
Definition 3.6 (User-additive rules). For each instance I = (N, C, w). define instances I; = ({+), C, w;) for each E N. Then, a rule @ is user-additive if for all instances I and artists j E C, dI( = EiEN N oz, (i).
USEREQ
Given an instance I = (N, C, w) and for each j E C, the payment rule USEREQ defined as follows.
We then show the following. Proposition 3.7. A user-additive rule is fraud-proof and bribery-proof.
Φπ(i) = Σ
1 >0 IEN EC: Wiy > 03
xa
We focus on two user-additive rules that have been discussed in the existing literature: USERPROP and USER EQ. Under USERPROP, an a fraction of each user's subscription fee is allocated to the artists proportional to the user's engagement. For example, if user listens to three artists- the first artist 50% of the time and the other artists 25% each- then under USERPROP, the artists will receive payments of a/2, a/ and /4 from this user, respectively. The total payment of an artist is the sum of such payments from each user.
USEREQ has similar guarantees as USERPROP, with the difference being that it fails Sybil-proofness, but satisfies Pigou-Dalton consistency.
Theorem 3.10. USEREQ is fraud-proof and bribery-proof, but fails bybil-proofuess.
Theorem 3.11. USEREQ satisfies no free-ridership, en- gagement monotonicity, and Pigou-Dalton consistency.
A Generalization of Portioning
USER PROP
Given an instance I = (N, C, w) and for each j E C, the payment rule USERPROP is defined as follows.
We also make an important observation: our model can be viewed as a generalization of portioning under cardi- nal preferences (Elkind et al., 2023; Freeman et al., 2021), where each agent subjectively divides a contiguous resource (such as time or money) among a given set of candidates, and the goal is to aggregate these preferences to obtain one (fair) division. This is similar to our model if we let agents be users, candidates be artists, and preferences be interactions. 10 However, portioning rules require that the engagement of each user is normalized (i.e., sums to 1). We can then generate rules for our setting by normalizing each w; and applying a portioning rule the instance. There are eight portioning rules cataloged in Elkind al. (2023). One of them is equivalent to USERPROP, but the other seven fail fraud- prodd-profness, mmibery-proofnes. and Sybil-proofnnes. We present these rules and prove the results in the full version of this paper.
xx(1) = Σ iEN E Pe Way'
Wiy
X a.
We show that it satisfies all of the ceappullaiionresiitaat axioms (excluding strong Sybil-proofness) and engagement monotonicity, but fails Pigou-Dale Dalton consistency.
Theorem 3.8. USERPROP is fraud-proof, bribery-proof, and Sybil-proof, but fails strong Sybil-proofness.
Theorem 3.9. USERPROP satisfies no free-ridership and engagement monotonicity, but fails Figou-Dalton consis- tency.
Next, we consider the USEREQ rule, first studied in Bergantiños & Moreno-Ternent (2024). They established the equivalence between USEREQ and the Shapley value, a fundamental measure in cooperative game theory that en- sures fair distribution of payoffs among players based their contributions (Shapley, 1953).
4. SCALEDUSERPROP: A Fairer Mechanism
The three rules we considered above are conceptually dis- tinct: GLOBALPROP allows dedicated fans to exert dispro- portionate influence on revenue distribution, but this also creates opportunities for fraud by fabricating users who may appear as dedicated fans. In contrast, USERPROP is often viewed by policymakers as a more desirable alternative to GLOBALPROP, However, USERPROP not necessarily fairer (Lei, 2023), and user-additive rules in general may fail to meaningfully reward artists for increasing the engage-
Now, given an instance I = (N, C, w), for each i E N and j E C, let m0 be the indicator function that returns the value 1 if Wiy > 0, and otherwise. In USEREQ, an a fraction each user's subscription fee is distributed equally among the artists with strictly positive engagement from the user. For example, if user listens to only three artists 80%, 19%, and 1% of the time, respectively-and does not
This term is distinct from user-centric, which is sometimes used the literature to refer to URPR
lWW note that this analogy requires imposing rational number constraints on preferences, as assumed the preliminaries.
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Fraud-Proof Revenue Division on Subscription Platforms
ment within their existing fanbase.
that SCALEDUSERPROP has exactly the same axiomatic guarantees as USERPROP, with the following results.
To better understand differences in payment fairness, it is useful to examine the pay-per-stream metric (Dimont, 2018; Meyn et al.. 2023). Given an instance I and an artist j. let the artist pay-per-stream (PPS) for rule & be PPS j) = EiEn Way" Using this, we define the maxi- mum envy (ME) of I as MB(
Theorem 4.3. SCALEDUSERPROP satisfies fraud- proofness, bribery-prooftess, and Sybil-proofness, but fails strong Sybil-proofness.
Theorem 4,4. SCALEDUSERPROP satisfies no free- ridership, engagement monotonicity, but fails Pigou-Dalton consistency.
maxice PPS(d.
ten 3")
This ratio quantifies the disparity in PPS between the highest-paid and lowest-paid artists, providing measure of the maximum envy in revenue distribution.
5. Experiments
Then, we obtain the following result, which essentially im- plies that any fraud-proof or bribery-proof rule has the po- tential be extremely unfair (unbounded maximum envy).
To complement our theoretical analysis, we conduct experiments to evaluate our fraud-proof (and bribery- proof) mechanismS--SEERPPROO P both synthetic and real-world datasets. Motivated by our definition of maximum envy in Propo- sition 4.1, for each rule, we analyze the top and bottom few users based on their pay-per-stream (PPS) relative to GLOBALPROP'ss PPS, as the revenue share (a) varies." !I No- tably, only SCALEDUSERPROT is influenced non-linearly by changes in a (the other rules scale linearly with a.). Con- sequently, the pay-per-stream values for the other three rules remain constant across different values of a.
USEREQ, SCALE-
Proposition 4.1. For all a E 10,1] and rules o. if there exists TR such that for all instances I, MR( I) S k, then o fails traud-prooffied and
However, not all such rules may perform equally bad on this front-wee we will analyze this later through experiments (in Section 5), with slight variant of the ME definition.
Given this, we attempt achieve compromise by designing a rule that has the same axiomatic guaran- tees as UROP while offering empirically (in Sec- tion 5) stronger fairness guarantees than USER PROP and USEREQ. SCALEDU works by having the plat- form take a disproportionate amount of commission from low-engagement users. The platform then runs USERPRoP on the remaining subscription fees. It is defined as follows.
Synthetic datasets We generate synthetic problem in- stances involving 10, 000 users and 1, 000 artists. For each user, we first determine the number of artists they interact with by drawing value uniformly at random from the range [1, 100]. Based on this value, we randomly select the corre- sponding number of artists from the pool of 1, 000. For each chosen artist, the number of times the user streams their mu- sie is sampled from a Poisson distribution with À 1. We repeat the experiments 100 times.
SCALED USER PROP
Given an instance I (N, C, w), let y be a constant such that Eien min (7. Ejec Way, an. Then, for each j E C, the payment rule SCALEDUSERPROP is defined as follows.
weal-world datasets We utilize data from the Music Lis- tening Histories Dataset (Vigliensoni & Fujinaga, 2017), that contains the listening history of approximately 583, 000 users, 439, 000 artists, and a cumulative total of 27 billion listeming events (i.e., user-artist interactions)."
Wij
(i) min(y.
weye 1) X
E Ec Way'
Discussion On real-world data, SCALEDUSERPROP emerges as fairest mechanism among those considered, es- pecially for values of not close to 1; whereas USEREQ, which treats avid and casual listeners equally, is the least fair. SCALEDUSERPROS significantly reduces the top 100
iEN
J'EC
Note that when = 1, we have min(y. E Erec Way; 1) = for all i E N, making SCALEDUSERPROP equivalent to USERPROP, For a < 1, if no user's ' engagement exceeds 1 times the average engagement, then ScaledUSeRPRoo is equivalent to GLOBAL.PRP,, which we show below.
" Note that in Proposition 4.1, maximum envy is defined with respect the single top and bottom user, which differs from the metric used in this section. to report metrics for the top and bottom few users rather than just the single best and worst, as we believe this provides more robust ceeesseent-miiigaltee
our experiments, we chose
Theorem 4.2. Fix an instance I = W. If EeEC Wij- < 1 EiEN EjENE Wiy for all i E N. then na
the impact of potential outliers that may disproportionatell affect the extremes. However, our definition and theoretical results would easily extend to top and bottom few users, making it consistent with that used for the experiments. 12Our code is accessible n ctteh/Fraud Proof f- cecrrenue-iviiii vision.
SCALEDUSER is equivalent to GLOOAA.PROP.
Thus, SCALEDUSERPROO can be viewed as a variant of GLOBALPROP that "limits the influence" of users who have engagement significantly above average. We then show
https: / / thub.com/
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Fraud-Prodd Revenue Division Subscription Platforms
by real-world multi-million dollar fraud case. We show that the axioms we introduced not equivalent and study the rules that satisfy them. GLOBALPROP, which is used by streaming platforms, does not satisfy fraud- pruud-rooffness or bribery-proofnee However, we show that USERPROP and USEREQ do. We introduce a novel rule, SCELEDUSER- PROP. It as strong in resisting manipulation as USERPROP and incentivizes artists to increase their overall engagement similarly to GLOBAL Our empirical study on real and synthetic data of fraud-proof rules support SCALEDUSER- PROP is fairer fraud-prose alternative to other rules
00.08
10
Uurtt Sukosbertep
Scakdbeeffic
Vottom 100
0.06
10
0.04
10a
0.9
1.0
0.8
0.9
(a) Real data, top 100 artists' (b) Real data, bottom 100 artists'
PPS relative to GP
PPS relative GP
1.12
0.90
Blctom 10 PPS
1 1:08
0.96
A natural follow-up direction would be to study a freemium model, by incorporating users who have to watch advertise- ments to gain access to content on the platform, and have been adopted by streaming platforms such as YouTube and Spotify, among others. Revenue division in this context would have different considerations and call for more appro- priate axioms to be defined. Machine learning approaches have been adopted here as well (Goli et al., 2024); it would be interesting to explore these questions from a mechanism design perspective.
1.06
0.94
104
0.92
0.6
0.7
1.0
0.6
0.9
(c) Synthetic data, top 10 artists' (d) Synthetic data, bottom 10 artists' PPS relative to GP
PPS relative to GP
Figure I. Overview of graphs from real and synthetic data. (a) and (b) show results for real data, while (c) and (d) show results for synthetic data. GP is short for GLOBALLPOP..
Impact Statement
artists' PPS even for a > 0.9, but it only gradually in- creases the bottom 100 PPS as a decreases. To understand this outcome, we first observe that artists with high PPS typically attract infrequent listeners, while those with low PPS tend to have more dedicated, avid fanbase.
This paper presents work whose goal is to advance the theory of machine learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
References
We also observe that under SCALEDUSERPROP. each stream from a user contributes min(%: Ejeo Wis whereas under USERPROP, it contributes Eyec wes" For avid lis- teners with high Ejec Wiy, a stream under SCALEDUSER- PROP is worth 1 times its value under URERPROP. Con- versely, for infrequent listeners, SCALEDUSERPROP caps stream's 's worth at y, while under USERPROP, it can reach up to a in the extreme case where Ejec Wii = 1.
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Reviews:
[{"review_id": "3yWVtXvHS3", "reviewer": "Reviewer_Qvr6", "summary": "The paper explores fraud-proof revenue division on subscription platforms like Spotify and Apple Music, where users pay a fixed fee for unlimited access, and creators are compensated based on engagement. Current revenue-sharing rules, like GLOBALPROP (proportional to total streams), are vulnerable to manipulation through bots and click farms, making fraud detection complex and computationally hard. \n\nThe authors propose three new fraud-resistance axioms—fraud-proofness (preventing profit from fake users), bribery-proofness (preventing profit from bribed users), and Sybil-proofness (preventing profit from splitting/merging identities). Existing rules like USERPROP and USEREQ offer some protection but fail on fairness or manipulation resistance. The paper introduces SCALEDUSERPROP, a new mechanism that adjusts user contributions based on engagement intensity, making it fraud-proof, bribery-proof, and Sybil-proof.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. Please find our responses below.\n\n---\n> The claim that “SCALEDUSERPROP (SUP) is the fairest alternative” is not fully substantiated. ... Additionally, the paper does not address how the proposed fairness notion might impact the platform’s long-term ecosystem, including its ability to attract and retain high-quality content providers.\n\nWe note that a central focus of our paper is on manipulation-resistance, as emphasized in the title, abstract, and throughout the main text. Fairness is a desirable property, but it plays a complementary role in our work. Broader questions about how fairness interacts with platform objectives and long-term ecosystem health are important, but fall outside the scope of our paper.\n\nThat said, we are careful in our claim, stating that “on real-world data, SUP emerges as the fairest mechanism among those considered”. To substantiate this claim empirically, we consider the disparity in the value of each users’ stream (“pay per stream”)—that is, the extent to which streams from different users are valued unequally. Prior work (e.g., Dimont, 2018; Meyn et al., 2023; refs in main text) has highlighted that high disparities in per-stream payments can plausibly be viewed as unfair, particularly when artists are paid unequally for equivalent listener engagement. Such disparity under USERPROP (UP) arises even for a single artist receiving the same number of streams from different users—making it unrelated to artist quality and thus, we argue, difficult to justify from a fairness standpoint.\n\nWhile rewarding “high-quality” artists is a valid platform design choice, defining “quality” is normative and beyond our scope. In this work, we evaluate fairness conditional on observed engagement, and within this scope, we argue that SUP provides a more defensible approach by “treating equal engagement more equally”. If one equates quality with engagement, our experiments show that SUP better rewards high-engagement artists compared to UP.\n\n---\n> The paper proves that finding the set of artists who benefit the most from fraud is NP-hard. However, it does not explore whether heuristic or approximate methods could still be effective in practice. Acknowledging this would make the claim more balanced.\n\nWe note that the problem we reduce from (SSBVE) cannot be approximated better than $O(n^{1/4})$ under plausible complexity conjectures. With our reduction, for a threshold $\\gamma$, under the same complexity conjecture, this rules out any constant factor approximation of the size $k$ such that a set of $k$ artists have _potentially suspicious profit_ exceeding the threshold $\\gamma$.  \n\nThat said, heuristics may work well in practice, and certain “gap versions” (e.g., distinguishing no manipulation from large manipulation) could be polynomial-time solvable. Exploring such variants would be an interesting direction for future work.\n\n---\n> “\"USERPROP (UP) and USEREQ (UEQ) are FP and BP\" The proofs assume the cost of creating fake users is normalized to 1 unit per user—but in practice, this cost could vary depending on the platform's structure...”\n\nWe note that UP and UEQ could be extended with varying cost while still maintaining fraud-proofness (FP) and bribery-proofness (BP). If we let the cost a user pay to be $c_i$, UP could be defined as $\\phi_{I}(j) = \\sum_{i \\in N} \\frac{w_{ij}c_i}{\\sum_{j' \\in C} w_{ij'}} \\times \\alpha$ and UEQ could be defined as $\\phi_{I}(j) = \\sum_{i \\in N} \\frac{\\mathbf{1}[{w_{ij}>0}]c_i}{| set(j' \\in C:w_{ij'}>0)|} \\times \\alpha$. The defns of FP and BP would need to be adapted accordingly.\n\nAs this is the first work in this direction, we chose to focus on a simpler model to introduce our approach. We agree though, that with varying costs, there is a richer space for mechanisms that we have not explored, and would make for interesting future work. \n\n---\n> “beneficial for the authors to broaden the discussion...beyond the subscription-based model, considering a more general framework that could apply to various types of digital platforms.”\n\nOur focus is on the subscription-based model, which is already a rich and nuanced setting with many compelling research questions in its own right. That said, we agree that extending the framework to encompass a broader class of digital platforms would be a valuable and interesting direction for future work.\n\n---\n> “I strongly recommend that the authors improve the positioning of this work within the broader literature. Adding a dedicated related work section, even if placed in the appendix, would help clarify how this work builds on and differs from existing research.”\n\nWe will expand the current related work section to better situate our contributions within the broader literature on robustness to strategic manipulations in digital platforms (including online advertising markets). Thanks for the helpful references.\n\n---\nWe have noted your other comments/suggestions and will take them into account in the revision.", "claims_and_evidence": "**Supported Claims:**\n\n1- The paper shows that GLOBALPROP fails the fraud-proofness and bribery-proofness axioms.\nIt also shows that detecting fraudulent activity under GLOBALPROP is computationally NP-hard.\n\n2- USERPROP and USEREQ improve on GLOBALPROP by satisfying fraud-proofness and bribery-proofness.\n\n3- The paper shows that SCALEDUSERPROP satisfies fraud-proofness, bribery-proofness, Sybil-proofness, and fairness axioms (engagement monotonicity and Pigou-Dalton consistency).\n\n**Potentially Problematic Claims:**\nThe claim that **\"SCALEDUSERPROP is the fairest alternative\"** is not fully substantiated. While the empirical results support that SCALEDUSERPROP reduces disparity, fairness is inherently subjective and context-dependent. Reducing disparity is not necessarily a positive outcome, as content providers may differ in quality, and the platform may want to incentivize and attract higher-quality artists.\n\nThe paper does not provide a **concrete definition of fairness** beyond the Pigou-Dalton consistency and engagement monotonicity axioms. A more thorough discussion of trade-offs—such as how fairness is balanced against platform revenue, user satisfaction, and content quality—would strengthen this claim. Additionally, the paper does not address how the proposed fairness notion might impact the platform’s long-term ecosystem, including its ability to attract and retain high-quality content providers.\n\n**\"Detecting fraud under GLOBALPROP is computationally intractable.\"**\nThe paper proves that finding the set of artists who benefit the most from fraud is NP-hard.\nHowever, it does not explore whether heuristic or approximate methods could still be effective in practice. Acknowledging this would make the claim more balanced.\n\n**\"USERPROP and USEREQ are fraud-proof and bribery-proof.\"**\nThe proofs assume that the cost of creating fake users is normalized to 1 unit per user — but in practice, this cost could vary depending on the platform's structure. A sensitivity analysis or discussion of how varying costs would affect these conclusions would strengthen this claim.", "methods_and_evaluation_criteria": "The paper presents formal proofs that SCALEDUSERPROP satisfies the proposed axioms.\n\nThe computational complexity results (e.g., NP-hardness of fraud detection under GLOBALPROP) are well-supported by theoretical analysis.\n\nThe evaluation uses both real-world data (Music Listening Histories Dataset) and synthetic data to test the proposed mechanisms.", "theoretical_claims": "See above", "experimental_designs_or_analyses": "See above", "relation_to_broader_scientific_literature": "This paper contributes to the broader literature on robustness to strategic manipulations in digital platforms. Similar issues have been studied in the context of online advertising markets. Notable examples include \n\n\"Dynamic Incentive-Aware Learning: Robust Pricing in Contextual Auctions\" (http://papers.neurips.cc/paper/9169-dynamic-incentive-aware-learning-robust-pricing-in-contextual-auctions.pdf) and \n\n\"Dynamic Reserve Prices for Repeated Auctions: Learning from Bids\" (https://link.springer.com/chapter/10.1007/978-3-319-13129-0_17). \n\nAdditionally, there are empirical studies on fake reviews, such as \"An Empirical Investigation of Online Review Manipulation\" (https://www.aeaweb.org/articles?id=10.1257/aer.104.8.2421) and \"The Market for Fake Reviews\" (https://pubsonline.informs.org/doi/10.1287/mksc.2022.1353).\n\nAlso, the paper contributes to the literature on fairness in recommendation systems. Example include\nInterpolating Item and User Fairness in Multi-Sided Recommendations, (https://nips.cc/virtual/2024/poster/93355)\nUser-item fairness tradeoffs in recommendations (https://openreview.net/pdf?id=ZOZjMs3JTs)", "essential_references_not_discussed": "The paper \"Learning Product Rankings Robust to Fake Users\" (https://dl.acm.org/doi/10.1145/3465456.3467580) is highly relevant to this study. It focuses on designing learning algorithms for ranking products on digital platforms while being resilient to fake clicks. It would be beneficial for the authors to broaden the discussion on manipulation and mitigation strategies beyond the subscription-based model, considering a more general framework that could apply to various types of digital platforms.", "other_strengths_and_weaknesses": "The exposition could be improved in several places, as parts of the paper appear rushed or underdeveloped. \n\nI strongly recommend that the authors improve the positioning of this work within the broader literature. Adding a dedicated related work section, even if placed in the appendix, would help clarify how this work builds on and differs from existing research.", "other_comments_or_suggestions": "1- In Definition 2.4, please clarify what $\\hat n$ and $\\hat C$ are. And explain better in words, what this definition aims to say. Overall, definitions would benefit from more explicit discussions.\n\nFor example, in Definition2.4 (**Fraud-proofness**),  here is how I interepret it. A rule $\\phi$ is fraud-proof if an attacker cannot create fake users and profit from them. Here,  $N$ = Set of real users, $\\tilde{N} \\subseteq N$ = Set of fake users .  $C$ = Set of real artists, $\\tilde{C} \\subseteq C$ = Set of fake artists. $w_i$ = Engagement profile of user $i$. \nFraud-proofness holds if the extra profit from fake users does not exceed the cost of creating them:\n$\n\\phi_{I'}(\\tilde{C}) - \\phi_I(\\tilde{C}) \\leq |\\tilde{N}|\n$\nwhere $|\\tilde{N}|$ is the number of fake users (cost is assumed to be 1 unit per user).  \n\nFor **Bribery-Proofness**, here is my understanding:  Bribery-proofness means that an attacker cannot profit by bribing real users to increase engagement with specific artists.\nCosnider  any two instances:   $I = (N, C, w)$ = Initial setup  \nand  $I' = (N, C, w')$ = Setup after changing the engagement of exactly $k$ users  e\nThe rule is bribery-proof if:  $\n\\phi_{I'}(\\tilde{C}) - \\phi_I(\\tilde{C}) \\leq k\n$\nwhere:  \n $\\phi_{I'}(\\tilde{C})$ = Revenue to attacker’s artists after bribing;  \n$\\phi_I(\\tilde{C})$ = Revenue to attacker’s artists before bribing; and   \n$k$ = Number of bribed users (cost assumed to be 1 unit per user)  \n\n\n\n2- Please recall the definition of $\\alpha$ in Theorem 2.8\n\n3- Also, try to better explain in words the GlobalProp and UserProp. Here is my understanding: GLOBALPROP (Global Proportional Rule) works as follows: (i) Revenue is pooled into a global pot. (ii) Each artist’s payment is proportional to their share of the total engagement across the entire platform. USERPROP (User Proportional Rule) works as follows: \n(i) Each user’s subscription fee is treated as an individual pool. (ii) Each artist’s payment is based on their share of that specific user’s engagement. (iii) Revenue is distributed based on what individual users actually listen to, rather than global totals.", "questions_for_authors": "See above", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tCfLtPw9VE", "reviewer": "Reviewer_w465", "summary": "This paper examines fraud-proof mechanisms in subscription platforms. Specifically, the authors define a set of axioms covering fundamental properties, protection against strategic manipulation, and fairness in revenue division mechanisms. They analyze commonly adopted mechanisms and verify which axioms they satisfy. Based on these observations, the authors propose a new mechanism, ScaledUserProp, designed to enhance fairness in revenue distribution by considering the maximum envy metric. Experiments on both real-world and synthetic datasets demonstrate the effectiveness of the proposed mechanism.\n\n---\n\nI remain my score unchanged after rebuttal.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. Please find our responses below.\n\n---\n> “In the axioms of fraud-proofness, the final constraint is given as $\\phi_{I'}(\\hat{C}) - \\phi_{I}(\\hat{C}) \\leq \\hat{n}$. Why is the right-hand side not generalized to a more flexible form, such as $\\hat{n} \\cdot A$, where $A$ is a constant? The current formulation seems restrictive to the specific case of $\\hat{n}$. Would the theoretical results still hold under this more general setting? A similar concern applies to the bribery-proofness condition.”\n\nThe $\\hat{n}$ term in both the fraud-proofness and bribery-proofness axioms is a result of the assumption where each user's subscription cost is set to 1, but this is without loss of generality. This assumption implies that creating $\\hat{n}$ fake users incurs a total cost of $\\hat{n}$. However, the formulation is indeed flexible: if we assume that the cost of creating a user is instead a constant $A$, the right-hand side can be generalized to $\\hat{n} \\cdot A$ without affecting any theoretical result. Note that our model can also be generalized to consider users with variable cost (refer to our response to Reviewer Qvr6).\n\n---\n> “Some claims require further clarification. In Definition 2.4, does fraud-proofness hold for all $\\hat{N} \\subseteq N$ and $\\hat{C} \\subseteq C$? I noticed that in Definition 2.6, the condition \"for all $\\hat{C} \\subseteq C$\" is explicitly stated. Additionally, in Definition 2.12, should there be a further requirement that $\\delta<w_{ij}-w'_{ij}$? ...”\n\nFor Definition 2.4: Yes that’s right, we will add $\\hat{C} \\subseteq C$ (the part on $\\hat{N} \\subseteq N$ is already handled by the universal quantification over instances), thanks!\n\nFor Definition 2.12, we noticed a typo in condition (ii), specifically in the second inequality: it should read $w_{i'j}' \\leq w_{ij}'$ instead of $w_{i'j} \\leq w_{ij}$. This correction ensures that the new engagement profile is “at least as balanced” as before for candidate $j$, aligning with the intended interpretation you mentioned. The proofs remain valid after correcting this typo. Thanks for pointing this out!\n\n---\n> “In the experiments, the authors analyze the top and bottom few agents based on their pay-per-stream values. However, in Section 4, the theoretical analysis focuses on only the top and bottom single agents. Could the authors clarify why these two evaluation methods differ?”\n\nOur theoretical results on the top and bottom single agents easily extend to top-$k$ and bottom-$k$ agents as well, making it consistent with that used for the experiments. For all our counterexamples, we can simply duplicate each agent $k$ times. We will clarify this point in the revised version.\n\nIn our experiments, we chose to report metrics for the top and bottom few agents rather than just the single best and worst, as we believe this provides a more robust assessment—mitigating the impact of potential outliers that may disproportionately affect the extremes.\n\n---\nWe have noted your other comments/suggestions and will take them into account in the revision. Thanks!", "claims_and_evidence": "**(Pro)** The theoretical results are generally sound.\n\n**(Con)** In the axioms of fraud-proofness, the final constraint is given as $\\phi_{I'}(\\hat{C}) - \\phi_{I}(\\hat{C}) \\le \\hat{n}$. Why is the right-hand side not generalized to a more flexible form, such as $\\hat{n} \\cdot A$, where $A$ is a constant? The current formulation seems restrictive to the specific case of $\\hat{n}$. Would the theoretical results still hold under this more general setting? A similar concern applies to the bribery-proofness condition.", "methods_and_evaluation_criteria": "The evaluation metrics and methods are generally sound.", "theoretical_claims": "**(Pro)** I did not verify the theoretical claims in full detail, but they appear to be generally sound.\n\n**(Con)** Some claims require further clarification. In Definition 2.4, does fraud-proofness hold for all $\\hat{N} \\subseteq N$ and $\\hat{C} \\subseteq C$? I noticed that in Definition 2.6, the condition \"for all $\\hat{C} \\subseteq C$\" is explicitly stated. Additionally, in Definition 2.12, should there be a further requirement that $\\delta < w\\_{ij} - w'\\_{ij}$? This would prevent cases where $w'\\_{ij} = w\\_{ij} - \\delta$ is so small that $|w'\\_{ij} - w'\\_{i'j}|$ becomes larger than $|w\\_{ij} - w\\_{i'j}|$.", "experimental_designs_or_analyses": "**(Con)** In the experiments, the authors analyze the top and bottom few agents based on their pay-per-stream values. However, in Section 4, the theoretical analysis focuses on only the top and bottom single agents. Could the authors clarify why these two evaluation methods differ?", "relation_to_broader_scientific_literature": "**(Pro)** The paper's key contribution is the comprehensive analysis of existing revenue division mechanisms across a broad range of axioms and the introduction of a new mechanism to improve fairness.", "essential_references_not_discussed": "No essential references appear to be missing.", "other_strengths_and_weaknesses": "No additional strengths or weaknesses were identified.", "other_comments_or_suggestions": "The paper is generally well-written. However, the axioms are quite complex and require significant effort to understand. It would be helpful if the authors included more illustrative examples to clarify the axioms.", "questions_for_authors": "See the concerns listed above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "llVmaJC7JV", "reviewer": "Reviewer_yowW", "summary": "The authors propose a mechanism-design framework to counter manipulation in subscription-based streaming platforms. They formally define three types of fraudulent behaviors and illustrate how the commonly used “global proportion” revenue rule is highly vulnerable. To address this, they introduce some new axioms and prove that no single existing mechanism can satisfy them all. Then, they propose ScaledUserProp, which is a revenue-sharing mechanism designed to resist manipulation while incentivizing engagement. Experiments on some real-world streaming data demonstrate that ScaledUserProp reduces fraudulent activity compared to current industry practices.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. Please find our responses below.\n\n---\n> Main question: can you convince me that there’s an audience for this work at ICML? ... This led me to set my score as \"Weak Reject,\" despite the paper's clarity of presentation and interesting problem, but I am open to being shown that I am wrong!\n\nWhile this specific line of work on subscription platforms is relatively new (motivated from economics), our work is part of a broader literature on using computational/algorithmic methods to tackle incentive challenges in online economic systems/platforms (these works aim to contribute theoretical foundations that complements more applied ML work). This is a central concern in the EconCS community, which has a growing presence at ICML.\n\nSome recent ICML papers on strategic manipulation/incentive compatibility on online systems/platforms: \n- Human vs. Generative AI in Content Creation Competition: Symbiosis or Conflict? ICML’24\n- How Bad is Top-K Recommendation under Competing Content Creators? ICML’23\n- Performative Recommendation: Diversifying Content via Strategic Incentives. ICML’23\n\nThe type of “adversarial fraud” we study in subscription platforms also has a close analogue in recommendation systems (which in itself is actively studied in venues like ICML and NeurIPS), where similar challenges are known as poisoning attacks.\n\nSeveral other examples of work at ICML looking at strategic manipulation/incentive compatibility:\n- Online mechanism design for information acquisition. ICML’23\n- Fairness Interventions as (Dis)Incentives for Strategic Manipulation. ICML’22\n- Making Paper Reviewing Robust to Bid Manipulation Attacks. ICML’21\n- Incentivizing Compliance with Algorithmic Instruments. ICML’21\n- Strategyproof Mean Estimation from Multiple-Choice Questions. ICML’20\n\nThus, we believe our paper fits naturally within this growing line of research at ICML and would garner interest from the community.\n\nMoreover, ICML'24 has hosted multiple workshops that reflect this interest. For instance:\n- “Agentic Markets” workshop focuses on the intersection of market/incentive design and agentic AI, and derives insights from “economics, mechanism design, game theory”.\n- “Humans, Algorithmic Decision-Making and Society: Modeling Interactions and Impact” workshop includes a topic on “Strategic behavior and its impact on algorithmic decision-making”.\n- “Next Generation of AI Safety” includes “Agentic AI” as a theme, where “adversary exploitation” of deployed AI systems is a concern.\n- “Models of Human Feedback for AI Alignment” workshop specifically calls for perspectives from “economics”\n\nThese are all close thematic matches. Perhaps one additional relevant reference (will add this citation) is the paper “Computational Copyright: Towards A Royalty Model for Music Generative AI” at the ICML'24 Workshop on Generative AI and Law, but they focus on royalty models for AI-generated music.\n\nWe hope that these examples of thematically similar papers and workshops from recent years have persuaded you that there is an audience at ICML for our work; and if so, that you would be able to reconsider your evaluation of our work.\n\n---\n> ... Are we trying to allow only a unit change regardless of the number of bribed users?\n\nNope. If $k$ users are bribed, then we allow at most $k$ units of change as defined in Def 2.6. When we compare bribery-proofness (BP) to click-fraud proofness, we focus on the case of “a single user altering their engagement”. Then, by BP, the difference for any subset of artists is 1. We can make this wording clearer. As a side note, by Prop 2.7 it suffices to only consider single-user BP.\n\n---\n> Proof of Thm 3.2\n\nWe consider linearity as used in linear algebra, and thus exclude affine functions (will clarify this). Formally, $f\\left(\\sum_{i \\in N} w_{ic},\\sum_{i \\in N} \\sum_{j \\in C} w_{ij},N\\right) = \\sum_{i \\in N} w_{ic} \\times g\\left(\\sum_{i \\in N} \\sum_{j \\in C} w_{ij},N\\right)$. Clearly, if  $\\sum_{i \\in N} w_{ic} = 0$ then for all args $T, N$,  $f(0, T, N) = 0$. \n\n---\n> ... More extensive/well interpreted empirical results (that ask questions through ablations, different ways of looking at the data, etc.), which help the reader through the use case and impacts on the artists, ...\n\nOur main contributions lie in introducing a novel approach to the problem, along with a set of axioms—particularly focused on manipulation-resistance—and supporting theoretical results. We agree that more extensive experiments would provide valuable insights. However, given the space/scope constraints of a conference paper, we prioritized highlighting what we believe are the most novel and fundamental aspects of the problem. But we appreciate the suggestion and will consider this for future work, thanks!\n\n---\nWe have noted other comments and will address them accordingly (adding an example to better understand the def of (Strong) Sybil-proofness, and fixing the typo in the statement for Pigou-Dalton Consistency).", "claims_and_evidence": "Overall, I found this paper to be well written, both in their setup and methods. This does indeed seem to be an interesting and well motivated economics problem, and the authors seem to make a good case for their ScaledUserProp mechanism.\n\nMy main issue: I am not a computational economist, and did not expect to be reviewing economics papers for ICML. ICML is potentially the wrong venue for this work, and I worry that this may lead to a lower reviewing bar than at, say, Economics and Computation. \n\nAfter a quick skim of the references in this paper, I found no publications at ICML / Neurips / ICLR. The closest: a paper published at KDD, and another at SODA. Most of the cited papers, on the other hand, were published at economics conferences / journals.\n\nThat said (and despite my lack of background), I did my best to review the paper for the benefit of the authors. However, I feel my lack of a sense of prior work has prevented me from asking pertinent and non-trivial questions. I’d like the AC to take this into account when using my review.", "methods_and_evaluation_criteria": "(discussed below)", "theoretical_claims": "I did not check all of the theoretical claims, as they were extensive and significantly outside of my area. However, I did try to understand some of the claims, and follow some proofs. Overall, the claims I spent time with were reasonably stated. The proofs were mostly believable, but may have omitted some important details (hard for me to tell, again outside my area, so not sure what the norms are). Below, I offer some questions / comments. \n\n**Bribery proofness:** So, the definition states that for any two instances where the engagement profiles differ for exactly $k$ users, $$\\left|\\phi_{\\mathcal{I}}(\\hat{C}) - \\phi_{\\mathcal{I}'}(\\hat{C})\\right| \\leq 1$$ This bound of “1”' is independent of $k$. This surprised me: in other words, even if many users’ weights are changed (i.e., $k > 1$), the change in the allocated revenue for any subset $\\hat{C}$ is still bounded by 1. This is quite strong? My naive take is that this mixes the single-user notion (as in click-fraud-proofness) with a multi-user scenario. Are we trying to allow only a unit change *regardless* of the number of bribed users? \n\n**Clarity in Sybil-Proofness and Strong Sybil-Proofness:** For definition 2.9 of Sybil-proofness, there’s a statement “no artist benefits from splitting or merging,” and then in the formal definition its given that the condition “for any two instances $\\mathcal{I} = (N,C,\\mathbf{w})$ and $\\mathcal{I}' = (N,C,\\mathbf{w}')$ with $\\mathbf{w}_i = \\mathbf{w}'_i$ for each user that is not a Sybil identity.” I found the terms “splitting” and “merging” a little bit too informal, which made it hard for me to understand the Sybil proofness property - can you formalize these? Did I miss something?\n\n**Question on the a “Pigou-Dalton Consistency” statement:** So at some point, you state that ScaledUserProp satisfies no free-ridership, engagement monotonicity, and Pigou-Dalton consistency. Then, later in \"Proof of Theorem 4.4\" and in Table 1, you explicitly state/show that ScaledUserProp **fails** Pigou-Dalton consistency for every $\\alpha \\in (0,1]$. So which one is it? Am I missing something?\n\n**Proof of Theorem 3.2** I tried to follow this proof more closely. There were a few steps that seemed a little unclear to me. When you say “by linearity” and then make an assumption on the sum of $w_{ic}$, and then say $f(0,T,N) = 0$, I’m not entirely sure I see how this works out.", "experimental_designs_or_analyses": "I did take a close look at the provided notebooks / “real world experiments.” This is probably the weakest portion of the paper. It’s hard to evaluate these plots. The behavior between the synthetic and “real” data seems analogous, although there are clear differences when interpolating alphas, and the tradeoffs are not explored empirically in the rigorous way that experiments tend to be presented at ICML, simply given for these two scenarios. More extensive/well interpreted empirical results (that ask questions through ablations, different ways of looking at the data, etc.), which help the reader through the use case and impacts on the artists, and would help for a conference like ICML.", "relation_to_broader_scientific_literature": "Hard for me to say - I am not familiar with this area.", "essential_references_not_discussed": "Hard for me to say - I am not familiar with this area.", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "My main question (beyond some of the clarifying questions above): can you convince me that there’s an audience for this work at ICML? Can you give me an example of a similar strain of work that's been presented at the conference in say, the past 3 years? I don't see the point in this paper being presented at the conference, in place of some other worthy paper, if it has no audience. This led me to set my score as \"Weak Reject,\" despite the paper's clarity of presentation and interesting problem, but I am open to being shown that I am wrong!", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xast2F9twd", "reviewer": "Reviewer_PcgM", "summary": "The paper \"Fraud-Proof Revenue Division on Subscription Platforms\" addresses the problem of revenue distribution on subscription-based platforms, particularly in the context of music streaming services. The authors formalize three types of manipulation-resistance axioms—fraud-proofness, bribery-proofness, and Sybil-proofness—and evaluate existing revenue division mechanisms against these axioms. They find that the widely used GlobalProp mechanism fails to prevent fraud and makes fraud detection computationally intractable. The authors propose a novel mechanism, ScaleDUserProp, which satisfies all three manipulation-resistance axioms and is shown to be a fairer alternative through both theoretical analysis and empirical evaluation on real-world and synthetic datasets. The paper also introduces fairness axioms such as engagement monotonicity and Pigou-Dalton consistency, and demonstrates that ScaleDUserProp performs well on these metrics compared to existing rules like UserProp and UserEQ.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your review. Please find our response below.\n\n---\n> Comparison with Other Mechanisms: The paper compares ScaledUserProp with GlobalProp, UserProp, and UserEQ. Are there other mechanisms in the literature that the authors considered but did not include in their analysis? If so, why were they excluded?\n\nTo the best of our knowledge, these are the only rules that have been proposed and studied in the literature to date.", "claims_and_evidence": "The claims made in the paper are generally well-supported by clear and convincing evidence. The authors provide rigorous theoretical proofs for their proposed axioms and mechanisms, and they back up their claims with empirical experiments on both synthetic and real-world datasets. The theoretical results are well-articulated, and the empirical results are presented with sufficient detail, including the use of the Music Listening Histories Dataset, which adds credibility to their findings.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the problem at hand. The authors use a combination of theoretical analysis and empirical evaluation to validate their claims. The synthetic data generation process is well-described, and the use of real-world data from the Music Listening Histories Dataset adds robustness to their findings. The evaluation metrics, such as pay-per-stream (PPS) and maximum envy (ME), are well-chosen to measure fairness and manipulation resistance.", "theoretical_claims": "The theoretical claims in the paper appear to be correct. The authors provide detailed proofs for their key results, including the manipulation-resistance properties of the proposed mechanisms (e.g., Theorems 3.1, 3.8, 4.3) and the fairness axioms (e.g., Theorems 3.3, 4.4). The proofs are well-structured and logically sound, and the authors provide additional proofs in the appendix for omitted results.", "experimental_designs_or_analyses": "The experimental designs and analyses are sound. The authors conduct experiments on both synthetic and real-world datasets, and they provide a clear explanation of their methodology. The results are presented in a way that allows for easy comparison between different mechanisms, and the authors discuss the implications of their findings in detail. The use of synthetic data helps to control for certain variables, while the real-world data provides a realistic evaluation of the mechanisms.", "relation_to_broader_scientific_literature": "The paper is well-situated within the broader scientific literature on revenue division and manipulation resistance in subscription platforms. The authors reference prior work on revenue-sharing mechanisms, such as GlobalProp and UserProp, and they build on these ideas to propose a new mechanism that addresses the limitations of existing approaches. The paper also connects to the literature on fairness axioms and cooperative game theory, particularly in the context of the Shapley value and Pigou-Dalton consistency.", "essential_references_not_discussed": "The paper does a good job of citing relevant prior work. I am not sure if they cited all key works since I am not familiar with this topic.", "other_strengths_and_weaknesses": "Strengths:\n\n* The paper addresses a timely and important problem in the context of subscription-based platforms, particularly in the music streaming industry.\n\n* The proposed ScaleDUserProp mechanism is novel and offers a compelling solution to the problem of manipulation resistance.\n\n* The paper provides a thorough theoretical analysis, supported by empirical evidence, which adds to its credibility.\n\n* The authors do a good job of connecting their work to the broader literature on fairness and revenue division.\n\nWeaknesses:\n\n* While the paper is well-written, some parts of the theoretical analysis could be more accessible to readers who are not familiar with the \ntechnical details of revenue division mechanisms.\n\n* The paper could benefit from a more detailed discussion of the limitations of the proposed mechanism, particularly in terms of scalability and computational complexity.", "other_comments_or_suggestions": "None", "questions_for_authors": "1. Comparison with Other Mechanisms: The paper compares ScaleDUserProp with GlobalProp, UserProp, and UserEQ. Are there other mechanisms in the literature that the authors considered but did not include in their analysis? If so, why were they excluded?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper studies how to design equitable and fraud-resistant revenue-sharing mechanisms for streaming platforms with subscribe-based nature. The authors show that existing approaches are vulnerable to various types of frauds. Motivated by this, the authors propose three new axioms, including fraud-, bribery- and Sybil-proofness, and then introduce a new mechanism “ScaledUserProp”. They show that this mechanism meets all of those three axioms and certain fairness criteria simultaneously. The authors validate the effectiveness of their mechanism with theoretical results and numerical experiments (on synthetic data and real-world scenarios).

This work is clearly motivated, smoothly delivered and rigorously proved. Their mechanism, also serving as a methodology, resolve the real problem that manipulation could undermine standard revenue-sharing methods. Although some of the reviewers are suggesting more experiments, given the theoretic nature of this work, I still consider the overall quality of this work reaches the criteria of acceptance.

The only remaining concern lies in the relevance to ICML. From my own understandings, mechanism design and game theory are categories of ICML submission, and this paper proposes a mechanism which is also a methodology of revenue sharing and fraud resisting. Given that they are proposing methods of advancing ML, I think it is proper for us to accept it here.
Decision: Accept (poster)