Asymptotic (1-AUC) floor model selection: Psi floor <= 0.10 vs Galesic/Jain-Singh floors >= 0.10/0.08 with crossing point n* in [10^4, 10^5]

Imagine you're trying to track how people's beliefs shift over time — say, measuring public sentiment about a political issue or how trust spreads through a social network. Researchers have built several types of mathematical detectors to do this, each making different assumptions: one treats beliefs like a smooth, flowing landscape (kernel density estimation, or KDE), another treats them like particles in a physics simulation snapping between fixed states (a Boltzmann model), and a third tracks each individual's beliefs changing according to rules about trust (an ODE model). The question is: which one is actually best? This hypothesis proposes a clever new way to answer that question — by asking what happens to each model's error rate as you throw more and more data at it. Every model has a theoretical 'floor': a minimum error it can never get below, no matter how much data you collect. The KDE approach, it turns out, has a floor that shrinks all the way to zero with enough data, because it makes fewer rigid assumptions. The physics and trust-dynamics models, however, are stuck with permanent blind spots (estimated at 8–10% irreducible error) because their mathematical structure can never fully capture the messy, continuous nature of real human beliefs. There's also a twist: at smaller dataset sizes (roughly 1,000 to 10,000 data points), the more rigid models might actually perform better, before the flexible KDE model eventually wins out. This matters because it reframes model comparison not as 'which model fits the data today?' but as 'which model is fundamentally capable of the task?' — borrowing an idea similar to AIC/BIC model selection criteria used widely in statistics, but applied to this specific domain of belief-tracking.

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