On Path Dependence in the Even-Swap Decision-Making Method

The even-swap method builds the dominance relations between alternatives based on trade-offs between criteria. This dominance relation is affected by the order (i.e., the decision path) in which decision makers put alternatives and criteria into trade-offs. Such a phenomenon is referred to as path dependence. Although some psychological factors contributing to path dependence have been identified, studies on the causes and conditions that lead to path dependence are still lacking, making it difficult to quantify the influence of decision path on dominance relations. This paper reveals that the trade-off process in the even-swap method resembles the matching process used to generate indifference curves. Inspired by this finding, indifference curves are used to analyze the trade-off process and obtain trade-off curves. Based on these trade-off curves, a mathematical definition of path dependence is proposed, which serves as the occurrence condition of path dependence in the even-swap method. A sensitivity analysis is conducted to examine the effects of risk attitude, loss attitude, and inconsistent reference points on path dependence. The results reveal two interdependent necessary conditions for path dependence: (1) the presence of kinks in the utility function and (2) the use of inconsistent reference points across trade-offs. Furthermore, path dependence is found to be more likely when both evaluation distances are less than 1 and evaluation gap ratios approach 1. Finally, two practical insights are provided to help avoid path dependence.

Funding: This research was supported by the Sichuan Science and Technology Program [Grants 2025NSFSC1961, 2025NSFJQ0072], the National Natural Science Foundation of China [Grants 72171158, 72371173], and the Team Development Program at Sichuan University.