Estimating peoples’ dilution of responsibility through delegation: Theory and experimental evidence

2024-08-12

2025-12-31

There are two kinds of primary outcomes:

Primary outcome I: Does the frequency of subjects with a positive willingness to pay differ with and without delegation.
We use the following measures:
Ia) In (Ia), we consider only the first decision of each subject in order to exclude that results are partially driven by the subjects’ preferences for consistent behavior (between-subject analysis). We use a Chi2-test and a linear probability model (OLS) with our control variables. In the linear probability model, the dependent variable takes the value 1 (0) if subjects announce a positive (no) willingness to pay in their first decision. The main independent variable takes the value 1 (0) if a subject’s first decision is with (without) delegation.
Ib) In (Ib), we examine the same question as above and consider both decisions of each subject. We use a Mc Nemar-test and a linear probability model (OLS) with our control variables. In the linear probability model, there are now two main independent variables, the dummy for delegation and a dummy that accounts for order effects. Standard errors are clustered at the subject level.

Primary outcome II: Does the amount offered by subjects differ with and without delegation.
We use the following measures:
IIa1) Similar to (Ia), we consider only the first decision of each subject. We use a Mann Whitney Wilcoxon test and an OLS regression with our controls and the amount as dependent variable. The main independent variable takes the value 1 (0) if a subject’ first decision is with (without) delegation.
IIa2) (IIa2) is identical to (IIa1) except that we exclude observations where subjects have zero willingness to pay in at least one stage. We do that to analyze if the amounts differ for subjects who have always a positive willingness to pay.
IIb1) and IIb2): Identical to IIa except that we now consider both decisions of subjects. We use a Wilcoxon signed rank test and an OLS regression. with our controls and the amount as dependent variable. The main independent variable is again takes the value 1 (0) if a subject’ fist decision is with (without) delegation. In the regression, there are now two main independent variables, the dummy for delegation and a dummy that accounts for order effects. Standard errors are clustered at the subject level.
For all primary outcomes in II), we also use a Kolmogorov-Smirnov-test to see if the distributions of the willingness to pay differ between the decisions with and without delegation.

By regression analysis, we analyze how the willingness to pay with and without delegation is partially correlated with personal controls.

Online experiment. Within- and between-subject design.

The experiment consists of five stages.

Stage 1: Subjects are asked to choose between two divisions of 6 GBP between themselves and another participant they are randomly paired with. In the equitable division E, both subjects get 3 GBP. In the selfish division S, the dictator gets 5 GBP and the passive recipient they are paired with gets 1 GBP. Stage 1 differs from a standard dictator game in two respects: First, dictators need to buy the right to implement the selfish payoff division. Second, buying this right does not ensure that allocation S is implemented, but only increases the probability from zero to 36%. We use an incentive compatible price list approach to elicit the dictators’ willingness to pay.

The probability of 36% is identical to the frequency of dictators in a preceding study who chose S. This previous study was run only for getting this frequency. With the counter-probability of 64%, the allocation will be E even when dictators pay for increasing the probability that S is implemented.

Stage 2: The incentive structure of the dictator game is identical to stage 1, but dictators can now increase the probability that S is implemented by buying the right to be randomly matched with one of the subjects in the previous experiment. Before eliciting their willingness to pay, dictators are informed that the frequency of dictators who chose S in the preceding experiment was 36%.
50% of our subjects will first play stage 1, and the other 50% will first play stage 2.

Stages 3 and 4: Subjects now take the role of passive players for stages 1 and 2, and one of the four stages will randomly be paid out.

Stage 5: Subjects are incentivized for guessing how many of 10 randomly chosen subjects in the experiment have a positive willingness to pay. 50% of subjects each are asked for the stage with and without delegation. We also ask all subjects about their risk attitudes, their feeling of responsibility when making/delegating a decision that harms a third person.

The study will be conducted on Prolific. Subjects registered on Prolific platform can take part in our experiment. To ensure high data quality, we require subjects to be fluent in English, to reside in either UK or USA, be at least 18 years old, and to have an approval rate of at least 95%. In addition, we will ask four control questions in the first part of the experiment and two control questions in the second part. If subjects answer more than two questions in the first part incorrectly, they cannot proceed to the decision stage, have to leave the study, and do not receive a bonus. Similarly, it they answer both questions incorrectly in the second part, they cannot proceed to the decision stage of the second part, have to leave the study, and do not receive a bonus. Data already collected for subjects who have to leave the study will be excluded from the analysis.

Not available

Computer (online experiment)

Experimental session for which stage is played first, stage 1 or stage 2.

No

A total number of 780 subjects: 390 subjects playing stage 1 first; 390 subjects playing stage 2 first.

A total number of 780 subjects. Each subject makes two decisions on willingness to pay, so we have a total number of 1,560 observations (willing-to-pay price).

390 subjects playing stage 1 first; 390 subjects playing stage 2 first.

Given that the between-subject comparisons (only considering each subject’s first decision) have a lower power compared to the within-subject comparisons, we base our power calculation on the between-subject comparison for our primary outcome Ia. Using a Chi2-test, we require a total of 780 subjects for detecting a difference in proportions of 10 percentage points with a power of 80% and an alpha-level of 5% based on the most unfavorable case where the frequency of subjects with a positive willingness to pay is 50% in one group. Given this sample size of 780 subjects and using a Mann Whitney Wilcoxon test for our primary between-subject outcome IIa1, we have a minimum detectable effect size d=0.2 with a power of 80% and an alpha-level of 5%. All tests are two-sided.