A Log-Linear Evaluation Model: From Psychological Operators to Kalman Filtering

This work proposes the Log-Linear Evaluation Model (LLEM), a unified theoretical framework for understanding human evaluation. The LLEM formalizes everyday psychological operations—addition, multiplication, subtraction, division, thresholds, saturation, and comparison—and shows that these inherently non-linear evaluative processes become linear when expressed in logarithmic space. This transformation naturally connects classical psychological laws, such as Fechner’s logarithmic law and Wundt’s apperception theory, with modern statistical methods including exponential-family modeling, least-squares estimation, Bayesian inference, and Kalman filtering. The model provides a mathematically coherent explanation for well-known psychological phenomena such as the asymmetry between trust loss and trust recovery, the pratfall effect, and context-dependent evaluation shifts (e.g., ingroup/outgroup differences). By expressing evaluation as a log-linear state-space model, the LLEM enables sequential inference through the Kalman filter and its non-linear extensions, offering a principled account of dynamic trust updates and impression formation. Beyond psychology, the LLEM has applications in narrative theory and character design, allowing phenomena such as “weakness → empathy → attractiveness” to be represented quantitatively. Despite its concise form, the model integrates insights from psychology, cognitive science, statistics, control engineering, and creative studies, providing a compact but powerful foundation for future interdisciplinary research.