DOI: 10.57760/sciencedb.29411
title: Validation of the Effectiveness of the Range-Fixed Trade-off Method (RFTM)
title: 范围固定权衡法的有效性验证

description: This study aims to test the effectiveness of the Range-Fixed Trade-off Method (RFTM) by comparing the utility functions elicited by it and by the conventional trade-off method. To this end, a within-subjects design was adopted with two sub-experiments: Sub-experiment A used the Range-Fixed Trade-off Method, and Sub-experiment B used the conventional trade-off method. All subjects completed both sub-experiments and produced a standard outcome sequence and a standard probability sequence.In Sub-experiment A, subjects were first asked to choose between the initial prospect R=(6000CNY,0.1;200CNY,0.5;0CNY,0.4) and the prospect S^'=(5000CNY,0.1;x,0.5;0CNY,0.4) constructed using the bisection method based on the initial prospect, where x=(0+m)\/2. If R was chosen, implying x_1∈(x,5000), update x=(x+5000)\/2 and repeat the operation; else, x=(0+x)\/2 and repeat the operation. After 5 iterations, the program then recorded the midpoint of the final interval where x_1 lies as x_1. Update R by replacing x_0 (i.e. 200CNY) with x_1, and continue similarly to elicit x_2 through x_6. Next, elicit q_i (i=1,⋯,5) for indifference between R=(x_6,q_i;x_(0,) 1-q_i ) and S=(x_i,1), using 6 bisection iterations per q_i.In Sub-experiment B, subjects were first asked to choose between the initial prospect S=(200CNY,2/3;100CNY,1/3) and the prospect R^'=(x,,2/3;0CNY,1/3) constructed using the bisection method based on the initial prospect, where x=(200+5000)\/2. If the subject chose prospect S, implying x_1∈(x,200+5000), update x=(x+200+5000)\/2 and repeat the operation; else, x=(200+x)\/2 and repeat the operation. After 5 iterations, the program then recorded the midpoint of the final interval where x_1 lies as x_1. Update S by replacing x_0 (i.e. 200CNY) with x_1, and proceed to elicit x_2 through x_6. Then, elicit q_i (i=1,⋯,5) for indifference between R=(x_6,q_i;x_(0,) 1-q_i ) and S=(x_i,1), with 6 bisection iterations each.As such, eliciting each x_i (i=1,⋯,6) required 5 choices per subject, while each q_i (i=1,⋯,5) required 6 choices. To assess data reliability, after eliciting both standard outcome sequence and standard probability sequence, subjects re-answered the fourth question for each element in both sequences. 
description: This study aims to test the effectiveness of the Range-Fixed Trade-off Method (RFTM) by comparing the utility functions elicited by it and by the conventional trade-off method. To this end, a within-subjects design was adopted with two sub-experiments: Sub-experiment A used the Range-Fixed Trade-off Method, and Sub-experiment B used the conventional trade-off method. All subjects completed both sub-experiments and produced a standard outcome sequence and a standard probability sequence.In Sub-experiment A, subjects were first asked to choose between the initial prospect R=(6000CNY,0.1;200CNY,0.5;0CNY,0.4) and the prospect S^'=(5000CNY,0.1;x,0.5;0CNY,0.4) constructed using the bisection method based on the initial prospect, where x=(0+m)\/2. If R was chosen, implying x_1∈(x,5000), update x=(x+5000)\/2 and repeat the operation; else, x=(0+x)\/2 and repeat the operation. After 5 iterations, the program then recorded the midpoint of the final interval where x_1 lies as x_1. Update R by replacing x_0 (i.e. 200CNY) with x_1, and continue similarly to elicit x_2 through x_6. Next, elicit q_i (i=1,⋯,5) for indifference between R=(x_6,q_i;x_(0,) 1-q_i ) and S=(x_i,1), using 6 bisection iterations per q_i.In Sub-experiment B, subjects were first asked to choose between the initial prospect S=(200CNY,2/3;100CNY,1/3) and the prospect R^'=(x,,2/3;0CNY,1/3) constructed using the bisection method based on the initial prospect, where x=(200+5000)\/2. If the subject chose prospect S, implying x_1∈(x,200+5000), update x=(x+200+5000)\/2 and repeat the operation; else, x=(200+x)\/2 and repeat the operation. After 5 iterations, the program then recorded the midpoint of the final interval where x_1 lies as x_1. Update S by replacing x_0 (i.e. 200CNY) with x_1, and proceed to elicit x_2 through x_6. Then, elicit q_i (i=1,⋯,5) for indifference between R=(x_6,q_i;x_(0,) 1-q_i ) and S=(x_i,1), with 6 bisection iterations each.As such, eliciting each x_i (i=1,⋯,6) required 5 choices per subject, while each q_i (i=1,⋯,5) required 6 choices. To assess data reliability, after eliciting both standard outcome sequence and standard probability sequence, subjects re-answered the fourth question for each element in both sequences.