Team Bachelor Autumn 2022

Dominik Basler
Luca Burkart
Sabrina Clement
Tanja Erni
Dunia Lemqadem
Venusza Sivaramalingam

Original work

Rottenstreich, Y., & Hsee, C. K. (2001). Money, kisses, and electric shocks: On the affective psychology of risk. Psychological science, 12(3), 185-190. DOI

Abstract

Prospect theory’s S-shaped weighting function is often said to reflect the psychophysics of chance. We propose an affective rather than psychophysical deconstruction of the weighting function resting on two assumptions. First, preferences depend on the affective reactions associated with potential outcomes of a risky choice. Second, even with monetary values controlled, some outcomes are relatively affect-rich and others relatively affect-poor. Although the psychophysical and affective approaches are complementary, the affective approach has one novel implication: Weighting functions will be more S-shaped for lotteries involving affect-rich than affect-poor outcomes. That is, people will be more sensitive to departures from impossibility and certainty but less sensitive to intermediate probability variations for affect-rich outcomes. We corroborated this prediction by observing probability-outcome interactions: An affect-poor prize was preferred over an affect-rich prize under certainty, but the direction of preference reversed under low probability. We suggest that the assumption of probability-outcome independence, adopted by both expected-utility and prospect theory, may hold across outcomes of different monetary values, but not different affective values.

Replication

Does affect change the way we evaluate choice options? To answer this question we run a direct replication and extension of Rottenstreich & Hsee (2001).

Demographics

We sample 214 Swiss participants (58.41% female, 1 non-binary and 2 missing) with an average age of M = 26.01 years (SD = 9.44).

Experiment 1

In experiment 1 Rottenstreich et al. explored the difference between participants making choices in an affect-poor or affect-rich condition between certain and uncertain (riksy) choices. One alternative had “the opportunity to meet and kiss your favorite movie star” or USD 50.- in cash for certain as the options. The other had “the opportunity to meet and kiss your favorite movie star” or a 1% chance of winning USD 50.- in cash. The interaction between these affect and money options was the central test for their argument.

Looking back at Rottenstreich et al.’s (2001) (see Figure 1) results we see that the authors find quite a strong interaction effect with differences between the 1% and 100% option of more than 30 percentage points in the choices …

Figure 1: Results Rottenstreich et al. Exp 1

Inspecting our results we see the interaction effect but, in comparison, weaker with differences of roughly 20 percetage points.

Figure 2: Interaction between responses in emotional (kiss) vs. money option (cash).

This is also shown in a Chi^2 test to compare choice proportions. But hey - different times, different country - there is something there to work with … lets move to Experiment 2 an see whether making the context of choices more concrete (from kisses to travel) and switching from choice to willingness to pay (WTP - for our economist friends) will change something in the results and replication.


    Pearson's Chi-squared test

data:  Exp1_calc$response and Exp1_calc$Sicherheit
X-squared = 4, df = 1, p-value = 0.05

Experiment 2

In the original study different student groups were used for each experiment - in our study we chose a withing subjects design and randomized position of the different tasks, hence the subject pool for this task is the same as before.

But first some housekeeping: the plot function from Base R is super useful to quickly get an overview of the values of a variable - so for our WTP responses (which were unrestricted in the questionnaire, we just checked that a number larger or equal to zero was entered) we quickly see that there is one response that stands out. Most outlier definitions (and there are plenty) would flag this response (> 9000) so for our analysis we will take out this one response, and go from Figure 3 :

To this Figure 4 :

Figure 4: WTP after removing outlier > 9000.

                     Df   Sum Sq Mean Sq F value  Pr(>F)    
condition             1  1553141 1553141   50.97 4.1e-12 ***
emotional             1       30      30    0.00    0.98    
condition:emotional   1      274     274    0.01    0.92    
Residuals           423 12888296   30469                    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear mixed model fit by REML ['lmerMod']
Formula: value ~ condition * emotional + (1 | ID)
   Data: Exp2_WTP

REML criterion at convergence: 5350

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-5.077 -0.152 -0.031  0.004  6.220 

Random effects:
 Groups   Name        Variance Std.Dev.
 ID       (Intercept) 24991    158     
 Residual              5471     74     
Number of obs: 427, groups:  ID, 214

Fixed effects:
                              Estimate Std. Error t value
(Intercept)                      20.19      16.87    1.20
conditioncertain                119.02      23.86    4.99
emotionalUSA                     -1.07      10.11   -0.11
conditioncertain:emotionalUSA     4.45      14.33    0.31

Correlation of Fixed Effects:
            (Intr) cndtnc emtUSA
conditncrtn -0.707              
emotionlUSA -0.300  0.212       
cndtncr:USA  0.211 -0.299 -0.706

	value
Predictors	Estimates	CI	Statistic	p	df
(Intercept)	20.19	-12.97 – 53.36	1.20	0.232	421.00
condition [certain]	119.02	72.12 – 165.93	4.99	<0.001	421.00
emotional [USA]	-1.07	-20.95 – 18.81	-0.11	0.916	421.00
condition [certain] × emotional [USA]	4.45	-23.72 – 32.62	0.31	0.756	421.00
Random Effects
σ²	5470.70
τ₀₀ _ID	24991.14
ICC	0.82
N _ID	214
Observations	427
Marginal R² / Conditional R²	0.108 / 0.840

Experiment 3

                   Df  Sum Sq Mean Sq F value Pr(>F)   
Sicherheit          1    1996    1996    0.14 0.7100   
Punish              1  151515  151515   10.51 0.0013 **
Sicherheit:Punish   1    9145    9145    0.63 0.4262   
Residuals         423 6097471   14415                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Linear mixed model fit by REML ['lmerMod']
Formula: value ~ Sicherheit * Punish + (1 | ID)
   Data: Exp3_WTP

REML criterion at convergence: 5245

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-2.522 -0.287 -0.026  0.074  7.364 

Random effects:
 Groups   Name        Variance Std.Dev.
 ID       (Intercept) 4752     68.9    
 Residual             9659     98.3    
Number of obs: 427, groups:  ID, 214

Fixed effects:
                        Estimate Std. Error t value
(Intercept)                 8.71      11.61    0.75
SicherheitU                 5.00      16.41    0.30
PunishShock                46.91      13.44    3.49
SicherheitU:PunishShock   -18.54      19.03   -0.97

Correlation of Fixed Effects:
            (Intr) SchrhU PnshSh
SicherheitU -0.707              
PunishShock -0.579  0.409       
SchrhtU:PnS  0.409 -0.578 -0.706

	value
Predictors	Estimates	CI	Statistic	p	df
(Intercept)	8.71	-14.10 – 31.52	0.75	0.453	421.00
Sicherheit [U]	5.00	-27.26 – 37.26	0.30	0.761	421.00
Punish [Shock]	46.91	20.50 – 73.32	3.49	0.001	421.00
Sicherheit [U] × Punish [Shock]	-18.54	-55.95 – 18.87	-0.97	0.331	421.00
Random Effects
σ²	9659.50
τ₀₀ _ID	4751.64
ICC	0.33
N _ID	214
Observations	427
Marginal R² / Conditional R²	0.026 / 0.347