This page presents the data used in

[94.8] Wakker, Peter P., Ido Erev, & Elke U. Weber (1994), “Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories,” Journal of Risk and Uncertainty 9, 195-230.

PRINTING THIS PAGE: When printed, the data come out best in nonproportional fonts such as Courier.

FILLER STIMULI: This page only presents the data used in the analysis of the paper. Filler stimuli were also used. For their results, click here.

1. The Stimuli

There are six “sets.” Each set consists of four gamble pairs. Hence, there are 24 gamble pairs in total. Subjects chose their preferred gamble from each gamble pair. Hereafter, (p1, $x1; p2, $x2; p3, $x3) denotes a gamble yielding $x1 with prob. p1, $x2 with prob. p2, and $x3 with prob. p3. The safer of the two choice options is always presented first, and in gambles the “common outcome” is always presented first.


       
SET 1 (Fig. 3.1 in Wakker et al.)
                
1st pair: (.55, $0.5;  .25, $6.0;  .20, $7.0) (safe) versus
          (.55, $0.5;  .25, $4.5;  .20, $9.0) (risky) 

2nd pair: (.55, $3.5;  .25, $6.0;  .20, $7.0) (safe) versus
          (.55, $3.5;  .25, $4.5;  .20, $9.0) (risky)   

3d  pair: (.55, $6.5;  .25, $6.0;  .20, $7.0) (safe) versus
          (.55, $6.5;  .25, $4.5;  .20, $9.0) (risky) 

4th pair: (.55, $9.5;  .25, $6.0;  .20, $7.0) (safe) versus
          (.55, $9.5;  .25, $4.5;  .20, $9.0) (risky) 

 
SET 2 (Fig. 3.2 in Wakker et al.)
                  
1st pair: (.65, $0.5;  .20, $3.5;  .15, $5.5) (safe) versus
          (.65, $0.5;  .20, $3.0;  .15, $6.0) (risky) 

2nd pair: (.65, $2.5;  .20, $3.5;  .15, $5.5) (safe) versus
          (.65, $2.5;  .20, $3.0;  .15, $6.0) (risky) 

3d  pair: (.65, $4.5;  .20, $3.5;  .15, $5.5) (safe) versus
          (.65, $4.5;  .20, $3.0;  .15, $6.0) (risky) 

4th pair: (.65, $6.5;  .20, $3.5;  .15, $5.5) (safe) versus
          (.65, $6.5;  .20, $3.0;  .15, $6.0) (risky) 


SET 3 (Fig. 3.3 in Wakker et al.)
                  
1st pair: (.40, $0.5;  .40, $2.5;  .20, $6.0) (safe) versus
          (.40, $0.5;  .40, $1.5;  .20, $7.5) (risky) 

2nd pair: (.40, $3.0;  .40, $2.5;  .20, $6.0) (safe) versus
          (.40, $3.0;  .40, $1.5;  .20, $7.5) (risky) 

3d  pair: (.40, $5.5;  .40, $2.5;  .20, $6.0) (safe) versus
          (.40, $5.5;  .40, $1.5;  .20, $7.5) (risky) 

4th pair: (.40, $8.0;  .40, $2.5;  .20, $6.0) (safe) versus
          (.40, $8.0;  .40, $1.5;  .20, $7.5) (risky) 


SET 4 (Fig. 3.4 in Wakker et al.)
                  
1st pair: (.70,  $2.5;  .10, $5.5;  .20, $10.5) (safe) versus
          (.70,  $2.5;  .10, $3.5;  .20, $12.5) (risky) 
                       
2nd pair: (.70,  $6.0;  .10, $5.5;  .20, $10.5) (safe) versus
          (.70,  $6.0;  .10, $3.5;  .20, $12.5) (risky) 

3d  pair: (.70,  $9.5;  .10, $5.5;  .20, $10.5) (safe) versus
          (.70,  $9.5;  .10, $3.5;  .20, $12.5) (risky) 

4th pair: (.70, $13.0;  .10, $5.5;  .20, $10.5) (safe) versus
          (.70, $13.0;  .10, $3.5;  .20, $12.5) (risky) 


SET 5 (Fig. 3.5 in Wakker et al.)
                  
1st pair: (.50, $0.0;  .10, $2.0;  .40, $2.0) (safe) versus
          (.50, $0.0;  .10, $0.0;  .40, $3.0) (risky) 

2nd pair: (.50, $2.0;  .10, $2.0;  .40, $2.0) (safe) versus
          (.50, $2.0;  .10, $0.0;  .40, $3.0) (risky) 

3d  pair: (.50, $4.0;  .10, $2.0;  .40, $2.0) (safe) versus
          (.50, $4.0;  .10, $0.0;  .40, $3.0) (risky) 

4th pair: (.50, $6.0;  .10, $2.0;  .40, $2.0) (safe) versus
          (.50, $6.0;  .10, $0.0;  .40, $3.0) (risky) 


SET 6 (Fig. 3.6 in Wakker et al.)
                  
1st pair: (.50, $2.0;  .10, $4.0;  .40, $4.0) (safe) versus
          (.50, $2.0;  .10, $2.0;  .40, $5.0) (risky) 

2nd pair: (.50, $4.0;  .10, $4.0;  .40, $4.0) (safe) versus
          (.50, $4.0;  .10, $2.0;  .40, $5.0) (risky) 

3d  pair: (.50, $6.0;  .10, $4.0;  .40, $4.0) (safe) versus
          (.50, $6.0;  .10, $2.0;  .40, $5.0) (risky) 

4th pair: (.50, $8.0;  .10, $4.0;  .40, $4.0) (safe) versus
          (.50, $8.0;  .10, $2.0;  .40, $5.0) (risky)

The data were presented under four different conditions:

Condition collapsed (C, 22 subjects)
Condition not collapsed (N, 21 subjects)
Condition verbal (V, 20 subjects)
Condition graphical (G, 21 subjects)

2. The Data

The following four matrices (one for each condition) give the individual data. The subjects had to make each choice twice. For each gamble pair we counted the number of risky choices. Thus, we have the following scores:

2: The subject consistently chose risky, i.e., chose the risky gamble both times.
1: The subject was inconsistent, i.e, chose risky once and safe once.
0: The subject consistently chose safe, i.e., chose the safe gamble both times.

In the matrices, each row gives the scores of a subject. Column 1 gives subject nr, the other colums belong to gamble pairs. Column 2 corresponds with the first gamble pair of set 1, ..., column 5 corresponds with the fourth gamble pair of set 1, ...., column 22 corresponds with the first gamble pair of set 6, ..., column 25 corresponds with the fourth gamble pair of set 6.


 ------------------Condition Collapsed (C)-----------------
 
        set 1    set 2    set 3    set 4    set 5    set 6    
 
 C01   1 1 0 0  0 2 1 1  0 1 1 1  2 1 2 2  0 1 0 1  0 2 1 0  
 C02   1 1 2 0  1 2 2 1  0 2 1 1  2 2 1 1  2 2 2 0  1 0 0 0   
 C03   1 2 2 2  1 0 1 0  2 2 2 2  2 2 2 2  0 0 0 0  0 0 0 0   
 C04   1 0 1 1  1 2 0 0  0 1 1 0  2 2 2 2  2 2 1 1  2 1 0 1   
 C05   0 0 1 2  0 2 2 0  0 0 0 0  0 0 1 1  1 0 0 0  0 0 0 1   
 C06   1 1 2 2  2 2 2 0  1 1 1 2  2 1 2 2  0 0 0 0  1 0 0 0   
 C07   1 0 0 0  0 0 0 1  0 0 0 1  2 2 2 1  1 0 0 0  2 0 0 0   
 C08   2 2 2 1  1 2 0 1  1 1 0 1  2 2 2 1  2 0 1 0  2 1 0 1   
 C09   0 1 0 0  0 0 0 0  1 1 1 1  2 2 2 2  2 2 1 2  1 2 2 2   
 C10   0 0 0 0  1 0 1 0  1 0 0 0  2 1 2 2  0 1 1 1  2 2 1 2   
 C11   2 0 1 0  1 2 1 1  2 1 1 0  1 1 1 1  2 0 0 1  2 0 0 0   
 C12   0 1 1 0  2 1 2 0  1 1 1 1  1 1 2 2  2 0 0 0  0 0 0 0   
 C13   1 2 1 0  2 2 2 2  1 2 2 1  1 1 1 1  0 1 1 0  2 2 2 2   
 C14   0 0 0 0  0 0 1 1  0 0 0 1  1 0 1 1  0 1 0 0  2 1 1 0   
 C15   2 1 0 1  2 2 2 2  0 0 0 0  0 0 0 0  0 0 0 0  1 0 0 0   
 C16   1 1 1 0  1 2 2 1  2 1 1 1  0 0 1 0  1 0 0 0  2 1 0 0   
 C17   2 2 2 2  1 0 0 0  1 1 2 0  2 2 2 2  2 2 1 1  2 0 1 2   
 C18   0 2 1 0  2 1 2 2  2 1 2 1  2 1 1 1  2 0 0 0  1 1 0 0   
 C19   0 2 1 2  0 2 1 1  1 1 1 0  0 1 1 1  1 0 0 1  1 0 0 0   
 C20   1 1 1 2  2 1 1 2  1 1 0 0  1 0 0 1  2 1 0 0  2 1 2 1   
 C21   1 1 1 1  0 1 1 1  1 0 1 0  2 2 1 2  2 2 2 1  1 1 0 1   
 C22   2 1 2 2  2 2 2 2  1 2 1 2  2 1 2 1  1 0 0 0  2 1 0 1   




 ----------------Condition Not collapsed (N)---------------
  
        set 1    set 2    set 3    set 4    set 5    set 6    
 
 N01   2 0 0 1  1 1 0 1  2 0 0 0  2 0 0 1  0 0 0 0  0 1 0 0   
 N02   1 1 0 0  0 1 1 0  1 1 0 0  2 2 1 2  0 1 0 1  2 0 0 2   
 N03   2 1 1 1  0 0 1 1  1 1 1 0  2 2 2 2  0 0 0 0  1 1 1 1   
 N04   2 2 2 2  0 0 0 0  0 0 0 0  2 2 2 2  0 1 1 2  2 2 1 2   
 N05   2 2 0 2  1 2 1 2  0 1 0 0  2 2 2 2  0 0 0 0  2 2 1 1   
 N06   1 1 1 2  1 2 2 0  1 1 0 1  1 1 2 1  0 0 0 0  1 0 0 0   
 N07   0 0 0 0  0 0 0 0  0 0 0 0  2 2 1 2  2 0 0 0  2 1 2 1   
 N08   0 1 2 1  0 1 1 1  1 1 1 1  0 1 0 1  1 1 2 1  1 1 1 1   
 N09   1 0 2 1  0 0 0 1  0 0 0 0  2 1 2 2  0 2 1 1  2 2 2 2   
 N10   2 0 1 1  2 2 2 1  1 2 2 1  2 1 1 2  0 0 1 1  1 0 2 0   
 N11   2 1 2 2  2 2 2 1  2 1 0 0  2 2 1 1  0 0 0 0  0 1 0 1   
 N12   1 0 2 2  2 2 2 2  0 2 1 1  1 0 1 1  0 0 0 0  0 0 0 0   
 N13   1 1 0 0  1 1 2 2  0 1 0 0  2 2 1 2  0 0 2 2  2 1 1 0   
 N14   1 1 0 2  1 1 2 1  1 0 0 0  1 1 2 2  0 1 1 0  0 0 0 0   
 N15   2 1 1 2  1 2 1 1  0 1 2 0  2 1 1 2  0 0 0 0  0 2 0 1   
 N16   0 0 1 0  1 0 1 1  0 0 0 1  2 2 2 1  0 0 0 0  2 1 2 2   
 N17   2 2 2 2  1 0 0 1  0 0 0 0  2 2 2 1  1 2 2 2  1 2 2 2   
 N18   2 1 2 1  1 2 1 2  1 0 1 0  1 2 1 2  0 0 0 0  0 0 0 0   
 N19   0 2 1 2  2 2 2 1  1 1 0 0  2 2 2 2  0 0 0 0  2 1 1 1   
 N20   1 0 2 0  1 1 0 1  0 0 0 0  1 2 1 1  0 1 0 0  1 0 1 0   
 N21   1 0 1 0  1 1 2 1  0 0 0 1  1 1 0 1  1 0 0 1  2 2 1 1   




 -------------------Condition Verbal (V)-------------------
 
        set 1    set 2    set 3    set 4    set 5    set 6    
  
 V01   1 0 1 0  0 1 1 0  0 0 0 0  2 1 1 2  0 0 0 0  0 0 0 0   
 V02   2 2 2 2  2 2 2 2  1 1 0 1  2 1 2 1  0 0 0 0  1 1 2 0   
 V03   0 0 0 1  0 1 1 1  2 0 1 0  0 0 0 0  0 0 0 0  0 0 0 0   
 V04   2 2 2 2  1 1 1 1  0 0 0 0  0 2 0 1  0 0 0 0  0 1 0 0   
 V05   2 1 2 2  1 1 0 1  0 0 0 0  2 1 2 2  0 0 0 0  1 1 2 2   
 V06   0 1 0 0  2 0 1 2  2 0 0 0  1 0 0 1  0 0 0 0  1 0 2 1   
 V07   2 2 0 1  0 2 1 1  2 2 0 0  1 0 1 0  0 0 0 0  0 1 1 1   
 V08   2 0 2 2  2 2 1 2  2 0 1 2  2 1 1 2  0 0 1 0  1 1 1 1   
 V09   0 2 1 2  2 1 2 2  0 1 0 1  1 1 1 1  0 0 0 0  0 0 0 1   
 V10   2 1 2 2  1 1 0 2  2 2 1 0  2 2 0 1  0 0 0 0  0 0 0 0   
 V11   1 2 2 2  1 2 1 1  1 2 2 0  1 0 1 0  0 0 0 0  1 0 0 1   
 V12   2 2 2 2  1 1 1 2  2 1 1 2  1 0 1 1  0 0 0 0  1 0 1 0   
 V13   1 1 2 1  2 1 1 2  1 0 1 0  1 0 0 2  0 0 0 0  2 0 1 0   
 V14   2 1 1 0  1 2 2 2  0 0 0 0  1 0 0 0  0 0 0 0  0 0 0 0   
 V15   1 2 1 2  1 0 2 1  1 1 0 1  1 1 2 2  0 1 0 0  0 0 1 0   
 V16   2 1 2 2  0 2 1 2  2 2 1 1  1 2 2 1  0 0 0 0  1 0 0 1   
 V17   2 1 0 1  1 2 0 1  0 1 1 0  2 2 2 2  0 1 0 0  2 2 0 1   
 V18   1 1 1 0  1 1 1 1  1 1 0 1  2 2 1 2  1 0 0 2  1 1 2 2   
 V19   0 1 0 0  0 0 0 0  0 0 0 0  1 2 2 2  0 2 2 1  2 2 2 2   
 V20   2 1 2 2  0 1 2 2  0 0 1 0  1 1 2 2  0 0 0 0  1 0 0 2


 ------------------Condition Graphical (G)-----------------
 
        set 1    set 2    set 3    set 4    set 5    set 6    
 
 G01   0 0 2 1  1 0 0 1  0 1 1 1  2 2 2 2  1 2 1 1  2 2 2 1   
 G02   0 0 1 0  0 2 1 1  0 0 0 0  1 0 1 0  0 0 0 0  0 0 0 0   
 G03   2 2 2 2  2 1 2 2  2 2 2 2  2 2 2 2  1 0 1 0  1 1 0 0   
 G04   2 1 0 1  1 0 1 2  0 0 0 0  1 1 2 2  0 0 0 0  0 1 0 1   
 G05   1 2 1 1  1 2 1 2  2 2 2 2  2 2 2 2  0 1 1 0  2 2 1 2   
 G06   1 1 2 2  2 0 0 0  1 1 2 0  2 1 2 2  0 0 0 0  0 1 1 2   
 G07   2 2 2 2  2 2 1 2  2 2 2 2  1 2 1 1  0 1 2 0  2 2 1 0   
 G08   2 2 1 1  2 2 2 1  2 2 2 2  1 2 1 2  1 0 0 0  2 2 2 1   
 G09   1 2 1 2  0 1 1 0  0 2 1 1  2 2 2 2  0 0 0 1  1 0 0 1   
 G10   2 1 0 1  1 1 2 1  1 0 0 0  2 0 1 2  0 0 1 0  1 1 0 0   
 G11   2 2 2 2  2 1 2 2  2 2 1 1  2 2 2 1  0 0 0 0  2 0 0 1   
 G12   2 0 0 1  2 1 1 1  1 0 1 0  2 2 2 2  0 0 0 1  2 1 2 2   
 G13   2 2 1 2  1 0 1 0  0 1 0 0  1 2 2 2  0 0 0 0  2 2 1 2   
 G14   1 1 2 1  0 2 2 1  1 0 2 0  2 2 2 2  0 0 0 0  2 1 0 2   
 G15   2 0 1 2  1 2 2 2  0 2 0 1  1 2 2 1  0 0 0 0  1 0 1 0   
 G16   1 2 1 1  1 0 2 1  0 0 1 1  2 1 1 1  0 0 0 0  0 0 0 0   
 G17   2 2 2 2  2 2 1 2  1 2 2 2  2 2 2 2  0 0 0 0  1 0 2 0   
 G18   2 1 1 1  1 2 1 1  1 2 1 1  1 1 0 1  1 1 1 2  0 2 2 1   
 G19   2 1 2 2  0 0 1 0  0 1 1 2  2 2 2 2  0 2 1 0  1 1 1 1   
 G20   0 0 1 0  0 0 0 0  0 0 0 0  2 2 2 2  0 0 1 0  2 1 2 2   
 G21   2 1 1 0  2 1 0 2  0 0 0 0  1 1 2 2  0 0 0 0  1 1 1 1