Research map / Learning theory and algorithms / Prediction and decision losses
Reaching a Consensus in Predictive Loops
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Proposes a minimal model coupling Friedkin-Johnsen peer opinion dynamics with performative prediction (platform retrains on expressed opinions), showing predictive loops can drive networks to consensus and amplify platform intervention effects.
Problem
Opinion dynamics models treat platforms as static or exogenous, missing that platform predictions retrained on expressed opinions feed back into those same opinions (performativity). The paper asks how this predictive loop changes network equilibria.
Approach
Nested feedback model: platform predictions set initial opinions (weighted by platform susceptibility beta), peers update via Friedkin-Johnsen dynamics (alpha), and the platform retrains on expressed opinions. Equilibrium is performative stability; with perfect prediction and high beta the system reaches consensus even on non-primitive graphs with stubborn agents, and extrapolated predictions crea
Key results
- Theorem: with all platform susceptibilities beta_i -> 1, equilibrium opinions reach consensus even for heterogeneous innate opinions and alpha_i in (0,1).
- Proposition: the variance of equilibrium opinions strictly decreases as platform susceptibility beta grows (under regular graph, homogeneous parameters).
- Simulations on Yelp show opinions converge across retraining steps for perfect, mean, OLS and LightGBM predictors, with variance approaching 0.
Surprising findings
- Consensus can emerge from predictive loops even though classical FJ dynamics on the same graph would lead to disagreement.
- A fully stubborn individual (alpha=0) is still influenced by peers' opinions via platform predictions.
Limitations
- Assumes perfect measurement of opinions and non-parametric (perfect) prediction in theory.
- Self-fulfilling performative effects only; network topology and susceptibilities held fixed.
- Simulations are semi-synthetic, with opinions derived from profile/review data rather than real opinion measurements.
Experimental setup
Datasets: Pokec social network Yelp open dataset
Benchmarks: Pokec (semi-synthetic simulation) Yelp (semi-synthetic simulation)
Metrics: variance of opinions at equilibrium mean opinion deviation of stubborn individual opinion
Baselines: Friedkin-Johnsen model (platform-free) DeGroot model mean estimation ordinary least squares LightGBM
Builds on: Friedkin-Johnsen model DeGroot model performative prediction
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