二分法與適測性心理物理方法於偏好研究中無異點估計之比較

Abstract

二分法(the bisection method)被應用於所謂的權衡法(trade-off paradigm, Abdellaoui, 2000; Wakker and Deneffe, 1996)，以測量決策理論中評估效用的無異點。然而其精確度可能受到兩項因素的影響：一是參與者選擇反應中的隨機性，二是二分演算法本身的邊界設定規則。本研究旨在檢驗二分法(包含其簡化版本 SimpBisection)之有效性，並探討其他適測性心理物理學方法，如 ASA、PEST 與 MOBS，作為估計無異點的可能替代方法。 本研究進行了兩項模擬實驗，採用 Abdellaoui et al. (2016) 中用以測量價值函數的實驗設計，比較各種無異點估計方法的表現。模擬結果顯示，在相同終止準則下，所有方法的估計大致不偏。然而，若邊界設定不當，二分法可能會產生有偏估計。在測試的方法中，ASA 有最高的效率性，但通常需要較多次的迭代數。當迭代次數有限(但非極少)時，對選擇行為較為確定的參與者而言，採用固定初始邊界的二分法與 SimpBisection 均能展現良好的效率性。相對地，對於選擇行為較隨機性的參與者，ASA 與 SimpBisection 則為較佳的選擇。鑑於實際實驗常見參與者異質性及限制迭代次數的情況，SimpBisection 可視為各方法間的良好折衷方案。

The bisection method has been implemented within the so-called trade-off paradigm (Abdellaoui, 2000; Wakker and Deneffe, 1996) to elicit indifference points for utility assessment in decision theory. However, its precision may be affected by two factors: response randomness in participants' choices and the boundary determination rules inherent in the bisection algorithm. This study aims to evaluate the validity of the bisection method --- including a simplified version, SimpBisection --- and to explore adaptive psychophysical methods such as ASA, PEST, and MOBS as potential alternatives for eliciting indifference points. Two simulation studies were conducted to compare the performance of these elicitation methods under the experimental design of Abdellaoui et al. (2016) for measuring the value function. The simulation results show that, under the same stopping criterion, all methods are largely unbiased. However, the bisection method can produce biased estimates if the boundary settings are poorly chosen. Among the tested methods, ASA demonstrates the highest efficiency, although it typically requires more iterations to complete the procedure. When the number of iterations is limited (but not too small), both the bisection method (with fixed initial boundaries) and SimpBisection perform efficiently for participants exhibiting more deterministic choice behavior. For participants with greater choice randomness, ASA and SimpBisection offer better alternatives. Given the prevalence of participant heterogeneity and practical constraints on iteration counts in real experiments, SimpBisection appears to be a reasonable compromise.