Welcome! You will be asked to choose between two risky prospects. An example of a (risky) prospect: €8 ⅔ ⅓ €10 This prospect gives: €10 with probability ⅓; €8 with probability ⅔. Explanation of Experiment 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.

Procedure You will fill in three questionnaires with instructions (for us; explained later). participation each of you receives €5. 1 of every 10 of you, selected randomly, will receive prize, ranging from € 0 to > € How? Explained later. Average (expected) prize if you are selected for prize, and if you choose completely at random: € (But you will choose better than random!) 2

We have 100 envelopes, numbered 1 to 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. 3 Envelopes

Each envelope contains two risky prospects. If prize at the end: you receive one 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. 4 Contents of the Envelopes

Give all instructions according to your true feelings. 5 Recommendation 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.

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. 6 Contents of the Envelopes

Participant name... Instructions for Choice from Envelope First value Second value Third value Fourth value x 1 = €.... x 2 = €.... x 3 = €.... x 4 = €....

€10 Determining first number x 1 €8 ½ ½ ½ ½ Left prospect Right prospect Your envelope may contain two prospects of the above form. €1 €X€X (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. x 1 =... - 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 x 1, your preference switches. - Fill this switching value in below, and then on page €300€11 What would you choose if X = 11? What would you choose if X = 300?

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 reporting x j ’ 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. €X€X Determining second number x 2 €1 €8 ½ ½ ½ ½... First substitute your value x 1 here. - You have substituted your value x 1. - To specify your instructions, determine your switching value of X again. - We call it x 2 (obviously, x 2 > x 1 ). - Fill it in below and on page x 2 =...

€X€X Determining third number x 3 €1 €8 ½ ½ ½ ½... First substitute your value x 2 here. - You have substituted your value x 2. - specify your instructions by determining your switching value of X again. - We call it x 3 (obviously, x 3 > x 2 ). - Fill it in below and on page x 3 =...

€X€X Determining fourth number x 4 €1 €8 ½ ½ ½ ½... First substitute your value x 3 here. - You have substituted your value x 3. - specify your instructions by determining your switching value of X again. - We call it x 4 (obviously, x 4 > x 3 ). - Fill it in below and on page x 4 =...

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

Summary By reporting X=50 as the switching value, subject 9 receives: - The right prospect for any X<50 - The left prospect for any X>50 If there is 10 (or less) in the upper branch of the right prospect. General example of Implementation of Your Instructions 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. €10 €8 ½ ½ ½ ½ Left prospect Right prospect €1 €X€X If there is 10 (or more) in the upper branch of the right prospect.

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 reporting x j ’ 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. €X€X Determining second number x 2 TO €1 €8 ½ ½ ½ ½... First substitute your value x 1 here. x 2 =... P. TO.2 with the extra text that disappears+ for my memory.