# How much would people value receiving a \$100 gift

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3 174 JOURNAL OF CONSUMER RESEARCH FIGURE 1 HYPOTHESIZED MAGNITUDE VALUATION, TIME DISCOUNTING, AND PROBABILITY WEIGHTING FUNCTIONS UNDER JE AND SE NOTE. Adapted from figure 3 in Hsee and Zhang implications of the proposition for trade-off preferences, including risk preference and time preference. Why do the JE and SE functions differ? In SE, people are presented with only one value, and they tend to evaluate it by its category rather than by its magnitude because category is generally easier to evaluate than magnitude (Hsee and Zhang 2004, 2010). In JE, people are presented with multiple values and can directly compare and evaluate them by their (relative) magnitude, rather than by just their category. Thus, people in SE are sensitive to the category in which a given value falls and relatively insensitive to its magnitude, whereas people in JE are more sensitive to its magnitude. Suppose that x 1 and x 2 belong to two different categories on a given attribute, and x 2 and x 3 belong to the same category on the same attribute, and objectively x 3 x 2 p x 2 x Then x 1 and x 2 will be evaluated differently in both SE and JE, whereas x 2 and x 3 will be evaluated similarly in SE but differently in JE. Categories depend on salient reference points; in other words, salient reference points on the target attribute divide its values into different categories. In magnitude valuation, the most salient reference point is zero; for example, whether the price of a product involves no (zero) discount or some discount off its manufacturer s suggested retail price (MSRP). Therefore, if one option involves a magnitude of zero and another a magnitude of nonzero (e.g., if one store offers no discount on a certain product and another offers some discount on the same product), the two magnitudes are categorically different and will be evaluated differently in both SE and JE. However, if both magnitudes are nonzero and one is greater than the other (e.g., if one store offers a \$10 discount and another offers a \$20 discount), they are only incrementally different and will be evaluated similarly in SE but still differently in JE. This explains why magnitude valuation functions are similar between SE and JE around zero but different away from zero (fig. 1A). Specifically, we propose the following hypothesis: H1: (concerning magnitude valuation): Around the zero-magnitude point, magnitude valuation functions are as steep (or steeper) in SE as (than) in JE, and away from the zero-magnitude point, magnitude valuation functions are flatter in SE than in JE. We propose that the analysis for magnitude valuation functions applies also to time-discounting and probability weighting functions. In time discounting, the most salient reference point is zero delay (immediate; Scholten and Read 2006). Therefore, if one option involves zero delay and another option involves some delay, the two options are categorically different and will be evaluated differently in both SE and JE. If one option involves a shorter delay and another option involves a longer delay, then the two options are only incrementally different and will be evaluated similarly in SE yet still differently in JE. This leads to our second hypothesis (fig. 1B): H2: (concerning time discounting): Around the zerodelay point, time-discounting functions are as steep (or steeper) in SE as (than) in JE, and away from the zero-delay point, time-discounting functions are flatter in SE than in JE. Likewise, in probability weighting, the most salient reference points are certainty (100%) and impossibility (0%). Thus, if one option is certain (100%) and another option is probabilistic, or one option is impossible (0%) and another is probabilistic, then the two options are categorically different and will be evaluated differently in both SE and JE. If both options are probabilistic, with one being more probable than the other, the two options are only incrementally different, and they will be evaluated similarly in SE (Kunreuther, Novemsky, and Kahneman 2001) yet still differently in JE. This leads to our third hypothesis (fig. 1C): H3: (concerning probability weighting): Around certainty (100%) and impossibility (0%), probability weighting functions are as steep (or steeper) in SE as (than) in JE, and away from certainty and impossibility, probability weighting functions are flatterinsethaninje. Of these three hypotheses, the hypothesis about magnitude valuation (hypothesis 1) has already been suggested in earlier writings (Hsee and Zhang 2004; Hsee et al. 1999). The present research extends the hypothesis about magnitude valuation to time discounting (hypothesis 2) and probability weighting (hypothesis 3) and shows that these three functions behave similarly with respect to JE versus SE. TRADE-OFF PREFERENCES In the previous section, we focused on how people s reactions to a single attribute (magnitude, time, or probability) vary between JE and SE. In this section, we examine how preferences for options involving two attributes vary between JE and SE. For example, between \$100 now and \$150 in a month, which one is more appealing in JE and which is more appealing in SE? Between \$100 for sure and an

6 HSEE ET AL. 177 TABLE 1 RESULTS OF ALL OF THE STUDIES INVOLVING A SINGLE ATTRIBUTE Study JE mean (SD) SE mean (SD) Study 1 (willingness to donate to a polar bear rescue program, in \$): 0 and 100 polar bears.66 (5.51) a.81 (3.12) a (26.79) b (26.33) b 0 and 200 polar bears 1.17 (5.48) a.81 (3.12) a (30.03) b (14.87) b 100 and 200 polar bears (18.03) a (26.33) a (27.93) b (14.87) b Study 2 (willingness to tutor for an amount to be paid at various time points, in ): Now (64.34) a (48.13) a 1 month (64.79) b (64.34) b 3 months (64.66) c (68.55) b Study 3a (willingness to wait for a chance to acquire a certificate, in minutes): 100% (42.94) a (40.68) a 90% (39.80) b (35.44) b 80% (41.51) c (37.02) a,b Study 3b (willingness to wait for a chance to acquire a certificate, in minutes): 0%.59 (2.30) a 3.99 (9.74) a 10% (25.45) b (30.84) b 20% (34.28) c (25.17) b Additional study reported in General Discussion (willingness to pay for cactus of various diameters, in \$): Reference p 60 centimeters: 60 centimeters (147.02) a (181.38) a 70 centimeters (157.39) b (222.34) b 80 centimeters (294.80) c (154.57) a,b Reference p 80 centimeters: 60 centimeters (94.65) a (111.89) a 70 centimeters (117.42) b (132.06) a,b 80 centimeters (112.45) c (163.81) b NOTE. The superscripts indicate whether or not means in the same evaluation mode (JE or SE) condition of each study are significantly different from each other. Means with different superscripts are significantly different from each other; means with the same superscript are not. M 0 bear p 1.30, t(218) p 19.83, p!.0001; in JE, M 100 bears p 4.42 vs. M 0 bear p 1.12, t(82) p 20.44, p!.0001). Over the 100-to-200-bear range, desirability ratings increased more in JE than in SE (t(277) p 6.56, p!.0001 using the hybrid t-test); in SE, respondents found the program equally desirable whether it had saved 200 or 100 polar bears (M 200 bears p 4.16 vs. M 100 bears p 4.45, t(204) p 1.42, NS), whereas in JE, respondents found the program more desirable if it had saved 200 polar bears than if it had saved 100 polar bears (M 200 bears p 4.85 vs. M 100 bears p 3.59, t(73) p 11.54, p!.0001). Over the 0-to-200-bear range, desirability ratings also increased more in JE than in SE (t(252) p 3.45, p!.001 using the hybrid t-test); in both evaluation modes, respondents found the program more desirable if it had saved 200 polar bears than if it had saved 0 (in SE, M 200 bears p 4.16 vs. M 0 bear p 1.30, t(170) p 15.12, p!.0001; in JE, M 200 bears p 4.94 vs. M 0 bear p 1.18, t(82) p 22.31, p!.0001). More pertinent to our theory was the relationship between the evaluability ratings and the magnitude variable. Based on our theory concerning the role of the endpoint (zero magnitude), we made two predictions. First, evaluability for zero magnitude (0 bear) would be higher than evaluability for nonzero magnitudes (100 or 200 bears). Second, the difference in evaluability between the zero and nonzero magnitudes would be larger in SE than in JE. Consistent with our first prediction, in both evaluation modes, evaluability ratings were indeed higher for the zero magnitude than for the nonzero magnitude conditions (in SE, M zero mag. p 3.56 vs. M nonzero mag. p 2.90, t(297) p 5.75, p!.0001, by combining the 100-bear-SE and the 200-bear-SE conditions and comparing the combined data with the 0-bear- SE condition; in JE, M zero mag. p 3.48 vs. M nonzero mag. p 3.11, t(165) p 3.19, p!.01, by comparing the zero and the nonzero magnitude results in the 0-to-100-bear-JE and the 0-to-200-bear-JE conditions). Consistent with our second prediction, the difference in evaluability ratings between the zero magnitude and the nonzero magnitude conditions was (marginally significantly) greater in SE than in JE (t(462) p 1.89, p p.059, using the hybrid t-test). These results suggested that it was easier to evaluate the endpoint (zero magnitude) than to evaluate the other values and that joint eval-

8 HSEE ET AL. 179 they were less sensitive in SE than in JE to how big the chance was. STUDY 3B Methods Study 3b was identical to study 3a except that it examined the impossibility (0%) end of probability with three chance (probability) levels: 0%, 10%, and 20%. Participants were 336 students, of whom 182 (50% female) were from the University of Miami and 154 (48% females) from Shanghai Jiaotong University in China. As in study 3a, we performed two hybrid t-tests, one for 0% versus 10% and one for 10% versus 20%. According to the first hybrid t-test, respondents were similarly sensitive in JE and in SE to whether the probability was 0% or 10% (t(250) p 1.31, NS); in both evaluation modes, respondents were willing to wait longer in the 10% probability condition than in the 0% probability condition (in SE, M 10% p vs. M 0% p 3.99, t(164) p 6.55, p!.0001; in JE, M 10% p vs. M 0% p.59, t(86) p 6.14, p!.0001). According to the second hybrid t-test, respondents were more sensitive in JE than in SE to whether the probability was 10% or 20% (t(245) p 3.07, p!.01); in SE, respondents were willing to wait as long in the 20% probability condition as in the 10% probability condition (M 20% p vs. M 10% p 26.69, t(159) p.09, NS), whereas in JE, respondents were willing to wait longer in the 20% probability condition than in the 10% probability condition (M 20% p vs. M 10% p 17.31, t(86) p 8.14, p!.0001). Consistent with hypothesis 3, these results suggested that the respondents were similarly sensitive in SE and JE to whether there was a chance to acquire a certificate, yet when there was a chance, they were less sensitive in SE than in JE to how big the chance was. Put together, the results of the studies reported so far supported our proposition that, in JE, people are similarly sensitive to categorical and incremental differences whereas, in SE, people are more sensitive to categorical differences than to incremental differences. Studies 1 3b tested hypotheses 1 3, each concerning a single attribute; the remaining studies tested hypotheses 4 7, each concerning a trade-off between two attributes. STUDY 4 Methods Study 4 tested hypothesis 4 concerning time preferences involving a trade-off between immediacy and magnitude. It examined respondents willingness to pay for either a slower but immediately available Internet service (smaller immediate gain) or a faster but not immediately available Internet service (larger delayed gain). Participants were 96 students (54% female) from Shanghai Jiaotong University in China. In a questionnaire, they were asked to imagine that they planned to subscribe to a 1-year Internet service plan. There were two options: one featured a 2 megabyte per second speed and would be installed immediately, and the other featured a 4 megabyte per second speed and would not be available for installation until 3 months later. In either case, the subscription fee had to be paid up front. Participants were randomly assigned to one of three conditions: one JE and two SE. Those in the JE condition saw both service options (presented side by side, order counterbalanced) and indicated their willingness to pay for each option. Participants in each SE condition saw only one of the two service options and indicated their willingness to pay for that option. According to hypothesis 4, relative to larger delayed gains, smaller immediate gains will be favored more in SE than in JE. The results, summarized in table 2, indeed exhibited this pattern. A hybrid t-test revealed a significant JE-SE preference reversal (t(93) p 2.56, p!.05). In JE, respondents were willing to pay more for the delayed 4- megabyte service (M del. 4MB p vs. M immed. 2MB p , t(29) p 2.24, p!.05) whereas, in SE, respondents were willing to pay somewhat (not significantly) more for the immediate 2-megabyte service (M del. 4MB p vs. M immed. 2MB p , t(64) p 1.63, NS). Methods STUDY 5 Study 5 sought to replicate the finding of study 4 in a real rather than hypothetical decision context. It examined students willingness to participate in two upcoming studies, one offering a smaller immediate payment and the other a larger delayed payment. Participants were 68 students (56% female) from Shanghai Jiaotong University in China. They were randomly assigned to one of three conditions: one JE and two SE. Those in the JE condition were approached at public places on campus by a research assistant who was recruiting students to participate in two upcoming 10-minute paper-and-pencil studies on stress management. One of the upcoming studies would pay each participant 10 immediately afterward; the other upcoming study would pay each participant 25 but the payment would not be delivered until 2 months later. The participants were asked to indicate their willingness to participate in each of the upcoming studies by drawing a vertical line on a 5-inch scale anchored by not willing at all (left) and very willing (right). Responses were later converted into numbers; for example, if a participant drew a vertical line 2.5 inches from the left end of the scale, her response would be coded as 2.5. Participants in each SE condition received the same information except that they were told about only one of the upcoming studies and asked

9 180 JOURNAL OF CONSUMER RESEARCH TABLE 2 RESULTS OF ALL STUDIES INVOLVING TRADE-OFFS ALONG TWO ATTRIBUTES Study Options JE mean (SD) SE mean (SD) Study 4 (willingness to pay for an Internet service, in ) Larger, delayed (159.16) a (137.55) a Smaller, immediate (88.41) b (176.45) a Study 5 (willingness to participate in a study, on 0 5 scale) Larger, delayed 3.31 (1.06) a 2.24 (1.44) a Smaller, immediate 3.09 (.99) a 3.34 (1.30) b Study 6 (willingness to pay for a rescue program, in million ) Larger, risky (26.51) a (28.02) a Smaller, riskless (30.07) b (24.66) a Study 7 (willingness to participate in a study, on 0 5 scale) Larger, risky 2.69 (1.38) a 2.29 (1.30) a Smaller, riskless 2.47 (1.26) a 2.82 (1.07) b Study 8 (willingness to pay for a repair service, in ) Less delayed; risky (81.24) a (77.94) a More delayed; riskless (90.55) a (134.78) b Study 9 (willingness to participate in a study, on 1 7 scale) More likely; delayed 5.97 (1.17) a 4.10 (2.07) a Less likely; immediate 5.35 (1.25) b 5.13 (1.61) b NOTE. The superscripts indicate whether or not means in the same evaluation mode (JE or SE) condition of each study are significantly different from each other. Means with different superscripts are significantly different from each other; means with the same superscript are not. to indicate their willingness to participate in that study. All participants were told that those who expressed the greatest willingness would be contacted first to participate and that, if contacted, they would be obligated to participate. About 10 participants in each condition who expressed the strongest willingness to participate in that study were indeed contacted later and paid accordingly after their participation. The results, summarized in table 2, replicated those of study 4. A hybrid t-test revealed a significant JE-SE preference reversal (t(65) p 2.80, p!.01). In JE, respondents were somewhat (not significantly) more willing to participate in the upcoming study that offered a larger delayed payment (M del. 25 p 3.31 vs. M immed. 10 p 3.09, t(25) p 1.02, NS) whereas, in SE, respondents were more willing to participate in the upcoming study that offered a smaller immediate payment (M del. 25 p 2.24 vs. M immed. 10 p 3.34, t(40) p 2.62, p!.05). Together, studies 4 and 5 supported hypothesis 4, showing that, relative to an incremental difference in the magnitude of an outcome, a categorical difference in delay has a greater impact in SE than in JE. Method STUDY 6 Study 6 was designed to test hypothesis 5 concerning risk preference involving a trade-off between certainty and magnitude. It examined respondents willingness to fund two disaster prevention programs, one expected to protect a smaller number of people for sure (smaller riskless gain) and the other expected to protect a larger number of people with uncertainty (larger risky gain). Participants were 81 students (33% female) from Shanghai Jiaotong University in China. In a questionnaire, they were asked to assume the role of a government official in charge of disaster prevention programs. They were then asked to imagine that a major flood was about to occur around the Yellow River and that tens of thousands of residents in the region would be affected. Two alternative prevention programs had been proposed. If one program was implemented, 20,000 residents would be protected from the flood. If the other program was implemented, there was a 90% chance that 40,000 residents would be protected and a 10% chance that none would be protected. Participants were randomly assigned to one JE condition or one of two SE conditions. Those in the JE condition were presented with both options (side by side, order counterbalanced), told that government funding was highly limited, and asked to indicate the maximum amount they would pay for each program by circling one of 10 options ranging from 10 million to 100 million. Respondents in each SE condition received the same instructions, except that they were presented with only one of the two programs and indicated their willingness to pay for that program. According to hypothesis 5, relative to larger risky gains, smaller riskless gains will be favored more in SE than in JE. The results, summarized in table 2, were consistent with this prediction. A hybrid t-test revealed a significant JE-SE preference reversal (t(78) p 2.38, p!.05). In JE, respondents would pay more for the risky program (M risky p vs. M riskless p 58.33, t(29) p 2.03, p p.05); in SE, re-

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