Sync or Sink: Bounds on Algorithmic Collective Action with Noise and Multiple Groups

TL;DR

This work addresses the problem of algorithmic collective action when coordination noise and multiple groups shape the data distribution. By introducing a multi-distribution model with $\mathcal{P}_0$, $\mathcal{P}_1$, and $\mathcal{P}_2$ and mixtures $\mathcal{P} = \sum_i \alpha_i \mathcal{P}_i + (1-\alpha)\mathcal{P}_0$, it derives lower bounds on the success $S(\alpha_1)$ for both feature-label and feature-only strategies, with key terms including cross-signal overlap $\mathcal{P}_2(\mathcal{X}_1)$ and suboptimality gaps $\Delta^j_i(y^*)$. The theoretical results are complemented by empirical evaluation on a resume-classification task using DistilBERT, showing that noise can dramatically reduce performance from near $100\%$ to below $60\%$ and that trade-offs between group size and coordination quality can determine which strategies prevail. The findings have practical implications for designing robust systems and understanding the nuanced dynamics of strategic behavior in ML pipelines, highlighting when smaller, well-coordinated collectives may outperform larger, noisier ones. Overall, the paper provides formal guarantees for multi-distribution collective action and demonstrates the tangible impact of coordination noise on downstream outcomes.

Abstract

Collective action against algorithmic systems provides an opportunity for a small group of individuals to strategically manipulate their data to get specific outcomes, from classification to recommendation models. This effectiveness will invite more growth of this type of coordinated actions, both in the size and the number of distinct collectives. With a small group, however, coordination is key. Currently, there is no formal analysis of how coordination challenges within a collective can impact downstream outcomes, or how multiple collectives may affect each other's success. In this work, we aim to provide guarantees on the success of collective action in the presence of both coordination noise and multiple groups. Our insight is that data generated by either multiple collectives or by coordination noise can be viewed as originating from multiple data distributions. Using this framing, we derive bounds on the success of collective action. We conduct experiments to study the effects of noise on collective action. We find that sufficiently high levels of noise can reduce the success of collective action. In certain scenarios, large noise can sink a collective success rate from $100\%$ to just under $60\%$. We identify potential trade-offs between collective size and coordination noise; for example, a collective that is twice as big but with four times more noise experiencing worse outcomes than the smaller, more coordinated one. This work highlights the importance of understanding nuanced dynamics of strategic behavior in algorithmic systems.

Figures (5)

• Figure 1: Relationship between $\Delta_2^1(y_1^*)$, $\mathcal{P}_2(\mathcal{X}_1)$ and success bound. We fix $\alpha_1 + \alpha_2 = 0.3$ and vary the proportion $r$. We fix $\epsilon_1 = 0$, $\Delta_0^1 = 0.01$, and $\mathcal{P}_0(\mathcal{X}_1) = 0.01$
• Figure 2: Comparison of different noise variations for different collective sizes. The x-axis here is the total collective size, measured by the percentage of the total population is participating. The $y$-axis is the success rate of causing resumes with the "true" signal to be classified to the target class. The black dashed line represents success rate without noise. The strategy is feature-label where noise is only applied to the features. We observe that making more characters for mistakes leads to lower success (Random-Subset vs Random-Full and Displaced-Original vs Displaced-Full)
• Figure 3: Impact of noise (Random-Subset) on different strategies. We consider various levels of noise for differing levels of participation. Each curve represents a fixed level of participation. The x-axis is the percentage of that group subject to noise. The left represents the feature-label strategy subject to noise on both the features and the labels. The middle represents the feature-label strategy where only the features are subject to noise. The right figure shows the feature-only strategy. We find that when noise affects both the feature and label, the decline in success is significant - especially at lower levels of participation. When noise just affects the inputs, the declines are more modest.
• Figure 4: Interaction between underlying frequency and susceptibility to noise (Random-subset) for feature-label strategy. Here we see for moderate levels of participation ($0.25\%$ and above), the low baseline scenario is more robust to noise.
• Figure 5: Impact of noise (Random-subset) on the feature-only strategy. Compared to the feature-label strategy, both the high and low frequencies cases are impacted by noise across differing participation levels. The high frequency case, however, sees more gradual declines in the success rate compared to the low frequency case.

Theorems & Definitions (13)

• Theorem 1: Feature-label
• Theorem 2: Feature-only
• Theorem 3: Feature-label with two distributions
• Corollary 3.1
• Theorem 4: Feature-only with two distributions
• Theorem
• proof
• Theorem : Feature-only with two distributions
• proof
• Theorem 5