Trust via Reputation of Conviction

Abstract

The question of \emph{knowledge}, \emph{truth} and \emph{trust} is explored via a mathematical formulation of claims and sources. We define truth as the reproducibly perceived subset of knowledge, formalize sources as having both generative and discriminative roles, and develop a framework for reputation grounded in the \emph{conviction} -- the likelihood that a source's stance is vindicated by independent consensus. We argue that conviction, rather than correctness or faithfulness, is the principled basis for trust: it is regime-independent, rewards genuine contribution, and demands the transparent and self-sufficient perceptions that make external verification possible. We formalize reputation as the expected weighted signed conviction over a realm of claims, characterize its behavior across source-claim regimes, and identify continuous verification as both a theoretical necessity and a practical mechanism through which reputation accrues. The framework is applied to AI agents, which are identified as capable but error-prone sources for whom verifiable conviction and continuously accrued reputation constitute the only robust foundation for trust.

Figures (4)

• Figure 1: The four mechanisms for establishing truth, organised by reproducibility (rows: repetitive vs. one-time) and number of independent sources (columns: one source vs. multiple sources).
• Figure 2: Full source-model chain for a specific claim $\gamma$. Claim space ($\mathcal{N}$, above the separator): The latent claim $\gamma$ (green) is mapped by source $\sigma$ to its perception $\Gamma_\sigma(\gamma)$ (red); together they generate three collections of samples from other sources --- direct perceptions $\Gamma_1^n(\gamma)$, the joint perceptions $\Gamma_1^n(\gamma,\Gamma_\sigma(\gamma))$, and derived perceptions $\Gamma_1^n(\Gamma_\sigma(\gamma))$. Truth-assessment layer (below separator): Each collection yields individual assessments $\{\Theta_i(\Gamma_i(\cdot))\}_{i=1}^n$, aggregated via $\bigvee$ into finite-sample estimates $\hat{\Theta}_n(\cdot)$. Asymptotic layer: As $n\to\infty$ (in probability), these converge to the objective truths $\hat{\Theta}(\gamma)$, $\hat{\Theta}(\gamma,\Gamma_\sigma(\gamma))$, and $\hat{\Theta}(\Gamma_\sigma(\gamma))$. The latent truth $\Theta(\gamma)$ (green, solid arrow from $\gamma$) and the source's subjective assessment $\Theta_\sigma(\Gamma_\sigma(\gamma))$ (red, solid arrow from $\Gamma_\sigma(\gamma)$) are shown alongside, as the targets that the estimation chain approximates.
• Figure 3: The four notions of truth and their six bilateral interactions. Solid arrows: interactions among the three notions that exclude $\hat{\Theta}(\gamma)$ (Faithfulness, Conviction, Transparency). Dashed arrows: interactions that directly involve $\hat{\Theta}(\gamma)$ (Correctness, Neutrality, Redundancy).
• Figure 4: Classification of source behaviour by the objective truth of the original claim $\hat{\Theta}(\gamma)$ (horizontal axis) versus the joint objective truth after incorporating the source's perception $\hat{\Theta}(\gamma, \Gamma_\sigma(\gamma))$ (vertical axis). The dashed diagonal is the line of no influence. Parallel offset lines delimit the four regions.

Theorems & Definitions (11)

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