Risky Prospect Experiment: Choose Your Preferred Option

1. Explanation of Experiment ⅓ €10 €8 ⅔ • Welcome! • You will be asked to choose between two risky prospects. • An example of a (risky) prospect: This prospect gives: €10 with probability ⅓; €8 with probability ⅔. There are no right or wrong answers.Please, choose what you yourself (subjectively) prefer most. That is what we are interested in, and what we want to investigate.

2. 2 Procedure You will fill in three questionnaires with instructions (for us; explained later). 1 of every 10 of you, selected randomly, will receive a prize, ranging from €0 to >€3000. How? Explained later. Average (expected) prize if you are selected for a prize, and if you choose completely at random: €53.27. (But you will choose better than random!)

3. 3 Envelopes We have 100 envelopes, numbered 1 to 100.10 of you are now asked to verify this. Now that this has been verified:Each of you is asked to randomly select one of the envelopes.(Sneakily taking more envelopes brings no advantage but does risk exclusion.) DO NOT OPEN YOUR ENVELOPE! Otherwise: exclusion from prize.

4. 4 Contents of the Envelopes • Each envelope contains two risky prospects. • If prize at the end: you receiveone of the two prospects from your envelope. • Your goal (obviously): • receive the prospect from your envelope that you prefer most. • During the experiment you give us instructions about which prospect we should select from your envelope. • If (unlikely case) your instructions do not specify the choice from your envelope: • then you can choose from the envelope on the spot.

5. 5 Recommendation Give all instructions according to yourtrue feelings. If wrong instructions, and if they concern your envelope, then you get the dispreferred prospect. If correct instructions, then you get the preferred prospect both: • if your instructions concern your envelope (obvious); • if they don’t (also obvious; then you choose on the spot). • So • wrong instructions may give you wrong result. • correct instructions surely give you best result.

6. 6 Contents of the Envelopes • There are 12 types of envelopes; accordingly, 12 experimental questions. Each type occurs several times among the 100 envelopes. • Probability that an experimental instruction you give will be implemented at the end > 1/100. Everything we say is true and completely verifiable.At the end you will get a list describing the contents of all 100 envelopes, and calculations confirming that  average = €53.27  there are prizes > €3000. We will then ask each of you to check your envelope. Now comes practice questionnaire to explain procedures.

7. Participant name ... TO 0.0 Instructions for Choice from Envelope x1 = €. ... First value x2 = €. ... Second value x3 = €. ... Third value x4 = €. ... Fourth value

8. TO 0.1 Determining first number x1 Left prospect ½ ½ ½ ½ Right prospect €10 €X €300 €11 €1 €8 Your envelope may contain two prospects of the above form. (Not only for these two, but) for each nr. X, instruct which prospect you want to be taken from your envelope if its content is as above. What would you choose if X = 300? What would you choose if X = 11? • For small values of X you prefer the right prospect. • For large values of X you prefer the left prospect. • For some value of X, which we call x1, your preference switches. • Fill this switching value in below, and then on page TO 0.0. x1 = ...

9. TO 0.2 Determining second number x2 First substitute your value x1 here. ... ½ ½ €1 €8 ½ ½ €X Recall: Instructing according to your true preference surely delivers your most preferred prospect from your envelope. Wrong instructions can give you the less-preferred prospect from your envelope. Note that: The content of your envelope has already been determined. You cannot influence its content by reportingxj’s that are too high or too low. Summary: Misinstructing has no advantage for you; it can only harm yourself. Now back to the experiment. • You have substituted your value x1. • To indicate your instructions, determine your switching value of X again. • We call it x2 (obviously, x2 > x1). • Fill it in below and on page TO 0.0. x2 = ...

10. TO 0.3 Determining third number x3 First substitute your value x2 here. ... ½ ½ €1 €8 ½ ½ €X • You have substituted your value x2. • Indicate your instructions by determining your switching value of X again. • We call it x3 (obviously, x3 > x2). • Fill it in below and on page TO 0.0. x3 = ...

11. TO 0.4 Determining fourth number x4 First substitute your value x3 here. ... ½ ½ €1 €8 ½ ½ €X • You have substituted your value x3. • Indicate your instructions by determining your switching value of X again. • We call it x4 (obviously, x4 > x3). • Fill it in below and on page TO 0.0. x4 = ...

12. TO 0.5 Right prospect Left prospect ½ ½ €10 €8 €1 ½ ½ Example of Implementation of Your Instructions Subject 9 (in pilot experiment) had instructed switching value €50 in Right prospect Right prospect Left prospect Left prospect ½ ½ ½ ½ €50 €24 €10 €X €32 €32 €8 €8 €1 €1 ½ ½ ½ ½ Imagine his envelope contained the 2 prospects below. Which one would he get? His envelope actually contained the 2 prospects below. Which one did he get? Subject 9 was extra happy to receive the right prospect with the improved €24 (and then was lucky to subsequently win €24).

13. TO 0.6 General example of Implementation of Your Instructions Left prospect ½ ½ ½ ½ Right prospect €10 €X €1 €8 • Summary • By reporting X=50 as the switching value, subject 9 receives: • The right prospect for any X<50 • The leftprospect for any X>50 If there is 10 (or more) in the upper branch of the right prospect. If there is 10 (or less) in the upper branch of the right prospect. Thus your instructions concern many possible envelopes! You are now asked to fill in 3 questionnaires. For each questionnaire your instructions can determine your real outcome.