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Conjecture 6.5: Sustained Skepticism

EXPLORED 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: Explored

Explored in the exploratory desire-as-regulariser runs. In those runs the skeptical agent records a lower calibration error than the aligned agent at each horizon tested. The runs cover one belief model and three horizons, so the conjecture remains open.

Evidence Summary

Calibration error is measured as the gap between predicted and observed frequencies. Recorded values:

  • 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 the two errors is roughly constant across the three horizons in this run

The mechanism under test is shrinkage: a prior that pulls the posterior away from the data limits overconfidence at finite sample sizes, in the manner of weight decay. Whether that accounts for the recorded differences, and whether they persist under other belief models and longer horizons, is not established.

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

If the conjecture holds, a permanently contradicting agent is a design option for belief systems. The runs to date are consistent with it at three horizons; establishing it needs more belief models, longer horizons and an account of the mechanism.