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Algebraic reproduction and comparative evaluation of egalitarian, utilitarian, and triage decision making based on simple heuristics of boolean multivalued logic

artificial-intelligence
data-mining-and-machine-learning
optimization-theory-and-computation
theory-and-formal-methods
neural-networks

Abstract

Purpose: This study aims to elucidate the fundamental differences among three typical decision-making models—Egalitarian, Utilitarian, and Triage (which integrates both ethical perspectives)—addressing the pressing ethical dilemma of establishing treatment priorities in disaster medicine. Methods: We executed a computer simulation to rank treatment for three victims (one severely injured and two lightly injured). Employing multivalued logic derived from Boolean algebra, we tackled a quasioptimization problem based on five atomic logical formulas. The constraints incorporated the pre- and post-treatment survival probabilities of the victims, the conditions surrounding treatment resources, and the various decision-making models. We performed a statistical analysis on the solutions of the quasioptimization problem and the inference outcomes to compare the differences among the three decision-making frameworks. Results & Discussion: The chi-square test yielded statistically significant differences between Egalitarian and Utilitarian (p = 3.64 ×10−23), as well as between Egalitarian and Triage (p = 6.73 ×10−30). This illustrated the divergent treatment policies: while Egalitarian tends to favor treating the severely injured victim, both Utilitarian and Triage lean toward prioritizing treatment for the two lightly injured victims. Furthermore, for the logical formulas comparing the Utilitarian and Triage models, where no significant difference was noted in the chi-squared test, the Mann–Whitney U test indicated statistically significant differences in three logical formulas. First, concerning the atomic logical formula representing “survival,” Triage exhibited a significantly higher truth value compared to Utilitarian (p = 0.020 < 0.05). This noteworthy finding implies that Triage can enhance the expected number of survivors more effectively than Utilitarian. Second, for the logical formula representing “one is a heavily injured victim,” Triage demonstrated a significantly lower truth value than Utilitarian (p = 0.044 < 0.05). This suggests that Triage shows a reduced subconscious bias toward heavily injured victims compared to Utilitarian, leading to a preference for treating the two lightly injured victims. Lastly, the truth value of the logical formula stating “everyone should be treated and survive as possible under conditions where they would not survive without treatment” was found to be significantly higher for Triage than for Utilitarian (p = 0.001 < 0.05). This finding indicates that Triage benefits from a synergistic effect between the commitment to active treatment and the aim of maximizing expected survivors. Conclusion: The Egalitarian and Utilitarian approaches are shown to be compatible under certain conditions, and it has been demonstrated that Triage can serve as a more efficient decision-making process for maximizing the expected number of survivors compared to the Utilitarian model.
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