# 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 …

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

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 :

```
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 | |||||

σ^{2} |
5470.70 | ||||

τ_{00} _{ID} |
24991.14 | ||||

ICC | 0.82 | ||||

N _{ID} |
214 | ||||

Observations | 427 | ||||

Marginal R^{2} / Conditional R^{2} |
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 | |||||

σ^{2} |
9659.50 | ||||

τ_{00} _{ID} |
4751.64 | ||||

ICC | 0.33 | ||||

N _{ID} |
214 | ||||

Observations | 427 | ||||

Marginal R^{2} / Conditional R^{2} |
0.026 / 0.347 |