Bayesian Optimization for Building Social-Influence-Free Consensus

TL;DR

The paper tackles social influence in collective decision-making by introducing Social Bayesian Optimization (SBO), which jointly learns a hidden social graph and de-biases feedback to recover social-influence-free utilities. An impossibility result shows that no aggregation rule can be groupthink-proof under noisy feedback alone, motivating a dual voting scheme that leverages cheap public votes and costly private votes. SBO uses optimistic MAP to learn a graph-convolution model v=Au and to bound uncertainty, enabling efficient convergence to the true social-influence-free consensus while reducing private-query costs. Across diverse real-world tasks, SBO achieves fast convergence with sublinear private-vote usage, demonstrating practical impact for group decisions in domains such as thermal comfort, team-building, and energy trading.

Abstract

We introduce Social Bayesian Optimization (SBO), a vote-efficient algorithm for consensus-building in collective decision-making. In contrast to single-agent scenarios, collective decision-making encompasses group dynamics that may distort agents' preference feedback, thereby impeding their capacity to achieve a social-influence-free consensus -- the most preferable decision based on the aggregated agent utilities. We demonstrate that under mild rationality axioms, reaching social-influence-free consensus using noisy feedback alone is impossible. To address this, SBO employs a dual voting system: cheap but noisy public votes (e.g., show of hands in a meeting), and more accurate, though expensive, private votes (e.g., one-to-one interview). We model social influence using an unknown social graph and leverage the dual voting system to efficiently learn this graph. Our theoretical findigns show that social graph estimation converges faster than the black-box estimation of agents' utilities, allowing us to reduce reliance on costly private votes early in the process. This enables efficient consensus-building primarily through noisy public votes, which are debiased based on the estimated social graph to infer social-influence-free feedback. We validate the efficacy of SBO across multiple real-world applications, including thermal comfort, team building, travel negotiation, and energy trading collaboration.

Figures (9)

• Figure 1: A dual voting system: the difference in public and private votes can identify the social influence. Once identified, social-influence-free consensus can be estimated only from noisy public votes, thereby reducing the total cost.
• Figure 2: Pareto frontier corrupted by the social influence can exclude the true consensus $x^\star$.
• Figure 3: The dotted and solid lines represent the ground truth $u, v$ and estimated utilities $\tilde{u}, \tilde{v}$, respectively, with the shaded area indicating the confidence interval. Dots mark the queried points, where $|\mathcal{Q}^u_t|=10$ and $|\mathcal{Q}^v_t|=20$. Since utility values are not directly observable, the dots are for visual guidance. The acquisition function $\alpha(\cdot, x_{t-1})$ represents the upper confidence bound of improvement from the previous query $x_{t-1}$, with its argmax determining the next query $x_t$ (red vertical line). While the independent model assumes no relationship between $u, v$, the graph convolution model enforces a linear constraint $v = A u$. This yields a tighter predictive interval, resulting in a next query closer to the true consensus $x^\star$ (black vertical line).
• Figure 4: Robustness analysis was conducted using the function shown in Fig. \ref{['fig:visual_exp']}. The lines and shaded areas represent the mean $\pm$ 1 standard error. The cumulative regret $R_T$ reaches a plateau, confirming the no-regret property, while the cumulative queries $|\mathcal{Q}^u_t|$ demonstrate sublinear convergence.
• Figure 5: Real-world experiments with varying number of agents $n$ and aggregation rule $\rho$

Theorems & Definitions (57)

• Definition 2.3: Aggregation function
• Proposition 2.4: Proposition 1 in sim2021collaborative
• Definition 2.5: Social influence
• Definition 3.1: Groupthink-proof
• Definition 3.2: Trivial social consensus
• Theorem 3.3: Impossibility of groupthink-proof aggregation
• Theorem 3.5: Regret bound
• Theorem 3.6: Graph identification
• Definition A.1: Invertibility
• Definition A.2: Identifiability