← All Conjectures

Conjecture 6.5: Sustained Skepticism

VALIDATED Misaligned desires improve belief calibration at ALL observation horizons, not just short-term.

Statement

An agent whose desire \( d \) partially contradicts the evidence stream \( e \) will maintain superior calibration compared to an aligned agent at every observation horizon \( T \), from \( T = 1 \) to \( T \to \infty \).

Status: Validated

This is one of the strongest results in the framework. The skeptical agent outperforms the aligned agent at every single horizon tested, with the calibration gap remaining stable or increasing over time.

Evidence Summary

The skeptical agent achieves 31% better calibration than the aligned agent, measured as the gap between predicted and observed frequencies. Key findings:

  • At \( T = 10 \): skeptic calibration error 0.042, aligned error 0.061
  • At \( T = 100 \): skeptic 0.018, aligned 0.031
  • At \( T = 1000 \): skeptic 0.006, aligned 0.009
  • The ratio of errors remains approximately constant: the skeptic never loses its advantage

The mechanism is Bayesian regularisation: the misaligned desire acts as an informative prior that prevents overconfidence, analogous to weight decay in neural networks. This was formalised in Theorem 7.

Relevant Experiments

  • exp_skeptical_annealing.sx — head-to-head comparison across horizons
  • exp_anima_deep.sx — deep belief calibration with skeptical agents
  • exp_anima_correlated.sx — skepticism across correlated evidence streams

What This Means

Sustained skepticism is the empirical foundation for the adversarial regularisation principle. The finding that partial opposition is always beneficial — not just during exploration — was unexpected and has far-reaching implications. It suggests that systems should be designed with built-in contrarians: agents whose goals intentionally conflict with the main objective, providing a permanent calibration benefit.