Preference towards control in risk taking: Control, no control, or randomize?

Abstract

This paper experimentally investigates preference towards different methods of control in risk taking. Participants are asked to choose between different ways for choosing which numbers to bet on for a gamble. They can choose the numbers themselves (control), let the experimenter choose (no control), or randomize. Classical economic theories predict indifference among the three methods. I found that participants exhibit strict preference for control, preference for no control, and preference for randomization. These preferences are robust as participants are willing to pay a small amount of money to implement their preferred method. Most participants believe that the winning probability under different methods is the same. This result contributes to the literature by clarifying that for most participants who exhibit preference for control, their preference is not due to illusion of control, but by source preference. Participants invest less in the risky gamble when they are not offered their preferred method.

Appendices

Appendix 1: Instructions

The experiment was conducted in German language, and the original instructions were also in German (available upon request).The treatment titles were not shown in the original instructions.

1.1 Instructions (experiment 1a)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can choose to invest any point between 0 and 10,000 on one of the following two possibilities (but not both).

1.1.1 Possibility I. You choose the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. You will be asked to choose 3 numbers from 1 to 10. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of the numbers you chose, otherwise you lose the points invested.

1.1.2 Possibility II. Experimenter chooses the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. The experimenter will choose 3 numbers for you and distribute the numbers to you after you choose your investment level. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of 3 numbers you have, otherwise you lose the points invested.

You will be paid in cash for the points you have at the end of the experiment.

If you win, your payoff will be equal to

$$ 10,000 + 2.5 x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ 10,000 - x $$

You will be paid in cash for each point you have at the end of the experiment.

1.1.3 We now ask you to indicate your decision

I wish to choose possibility I/II.

Please proceed to A in below if you choose possibility I.

Please proceed to B in below if you choose possibility II.

1.1.4 A. Possibility I. You choose the numbers

I wish to invest ____ points.

I would like to choose the following 3 numbers (please mark).

1	2	3	4	5
6	7	8	9	10

1.1.5 B. Possibility II. Experimenter chooses the numbers

I wish to invest____ points.

1.2 Instructions (experiment 1b)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can invest any point between 0 and 10,000 using investment method I or II. However, if you use choose to use method I, you need to pay 0.1 Euro (deducted from your show up fee).

1.2.1 Method I. You choose the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. You will be asked to choose 3 numbers from 1 to 10. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of the numbers you chose, otherwise you lose the points invested.

1.2.2 Method II. Experimenter chooses the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. The experimenter will choose 3 numbers for you and distribute the numbers to you after you choose your investment level. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of 3 numbers you have, otherwise you lose the points invested.

If you win, your payoff will be equal to

$$ {1}0,000 + {2}.{5} x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ {1}0,000 - x $$

You will be paid in cash for each point you have at the end of the experiment.

Your Decisions:

I choose Method I/Method II (please circle).

The decision sheets for method I and method II are put inside two separate envelopes, labeled I and II. Please open the envelopes and write down your decisions. After that, please put back the decision sheet to the corresponding envelope.

1.3 Instructions (experiment 1c)

Same as instructions in experiment 1b, but participants need to pay 0.1 Euro for using method II, and using method I is free.

1.4 Instructions (experiment 1d)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can invest any point between 0 and 10,000 on each of the following two possibilities, yet only one of them will be implemented. After we collect your decisions for each possibility, the experimenter will roll a die and possibility I will be implemented if the number is greater than or equal to 4. Possibility II will be implemented if the number is equal to or smaller than 3.

1.4.1 Possibility I. You choose the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. You will be asked to choose 3 numbers from 1 to 10. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of the numbers you chose, otherwise you lose the points invested.

1.4.2 Possibility II. Experimenter chooses the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. The experimenter will choose 3 numbers for you and distribute the numbers to you after you choose your investment level. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of 3 numbers you have, otherwise you lose the points invested.

If you win, your payoff will be equal to

$$ {1}0,000 + {2}.{5} x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ {1}0,000 - x $$

You will be paid in cash for each point you have at the end of the experiment.

1.4.3 We now ask you to indicate your decision for each possibility

The decision sheets for possibility I and possibility II are put inside two separate envelopes, labeled I and II. Please open the envelopes and write down your decisions. After that, please put back the decision sheet to the corresponding envelope.

1.4.4 Possibility I. You choose the numbers

I wish to invest ____ points if the numbers are chosen by myself.

I would like to choose the following 3 numbers (please mark).

1	2	3	4	5
6	7	8	9	10

1.4.5 Possibility II. Experimenter chooses the numbers

I wish to invest____ points if the numbers are chosen by the experimenter.

1.5 Instructions (experiment 2a)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can invest any point between 0 and 10,000, using either method A or method B. You need to choose which method to use. Both methods are explained below.

1.6 Method A

There are two possibilities, yet only one of them will be randomly implemented. After we collect your decisions for each possibility, the experimenter will roll a die and possibility I will be implemented if the number is greater than or equal to 4. Possibility II will be implemented if the number is equal to or smaller than 3.

1.6.1 Possibility I. You choose the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. You will be asked to choose 3 numbers from 1 to 10. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of the numbers you chose, otherwise you lose the points invested.

1.6.2 Possibility II. Experimenter chooses the numbers

There is an urn which contains 10 balls that are numbered from 1 to 10. The experimenter will choose 3 numbers for you and distribute the numbers to you after you choose your investment level. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of 3 numbers you have, otherwise you lose the points invested.

If you win, your payoff will be equal to

$$ {1}0,000 + {2}.{5} x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ {1}0,000 - x $$

You will be paid in cash for each point you have at the end of the experiment.

1.7 Method B

The rule is the same as method A except that now you can choose your favorite method (i.e., you choose the three numbers or let the experimenter choose).

1.8 Summary

In summary, in method A, we will randomly determine whether you or the experimenter will choose the numbers. In method B, you can choose your favorite way of investing.

Your Decisions:

I choose Method A/Method B (please circle).

The decision sheets for method A and method B are put in three different envelopes.

If you have chosen to use method A, please note that the decision sheets for Method A possibility I and possibility II are put inside two separate envelopes, labeled AI and AII. You need to fill-in for possibility I and possibility II.

If you have chosen to use method B, the decision sheet for Method B is put inside the envelope labeled B.

Please open the corresponding envelopes for your chosen method and write down your decisions. After that, please put back the decision sheet to the corresponding envelope.

1.9 Method A

1.9.1 Possibility I. You choose the numbers

I wish to invest ____ points if the numbers are chosen by myself.

I would like to choose the following 3 numbers (please mark).

1	2	3	4	5
6	7	8	9	10

1.10 Method A

1.10.1 Possibility II. Experimenter chooses the numbers

I wish to invest____ points if the numbers are chosen by the experimenter.

1.11 Method B

Please circle your choice:

• 1. I wish to choose the numbers by myself.

• 2. I wish to let the experimenter to choose the numbers.

If you have chosen to choose the numbers yourself, please choose the investment amount and choose the 3 numbers now (please mark).

I wish to invest ____ points.

I would like to choose the following 3 numbers (please mark).

1	2	3	4	5
6	7	8	9	10

If you have chosen to let the experimenter choose the numbers, please choose the investment amount.

I wish to invest____ points.

1.12 Instructions (experiment 2b)

Same as instructions in experiment 2a, but participants need to pay 0.1 Euro for using method B, and using method A is free.

1.13 Instructions (experiment 2c)

Same as instructions in experiment 2a, but participants need to pay 0.1 Euro for using method A, and using method B is free.

1.14 Instructions (experiment 3a)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can invest any point between 0 and 10,000 on the following investment option. There is an urn which contains 10 balls that are numbered from 1 to 10. You will be asked to choose 3 numbers from 1 to 10. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of the numbers you chose, otherwise you lose the points invested.

If you win, your payoff will be equal to

$$ {1}0,000 + {2}.{5} x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ {1}0,000 - x $$

You will be paid in cash for the points you have at the end of the experiment.

1.14.1 We now ask you to indicate your decision

I wish to invest ____ points.

I would like to choose the following 3 numbers (please mark).

1	2	3	4	5
6	7	8	9	10

1.15 Instructions (experiment 3b)

Welcome to our experimental study on decision-making. The experiment will take about 30 min. Each participant will receive a show up fee of 2.5 Euro at the end of the experiment. In addition, each participant will have the chance to earn more money according to the instructions below.

You are endowed with 10,000 points (1,000 points = 0.5 Euro). You can invest any point between 0 and 10,000 on the following investment option. There is an urn which contains 10 balls that are numbered from 1 to 10. The experimenter will choose 3 numbers for you and distribute the numbers to you after you choose your investment level. Then, the experimenter will randomly draw a ball from the urn in front of you. You will win 2.5 points for every point invested if the ball drawn belongs to one of 3 numbers you have, otherwise you lose the points invested.

If you win, your payoff will be equal to

$$ {1}0,000 + {2}.{5} x $$

where x is the number of points invested.

If you lose, your payoff will be equal to

$$ {1}0,000 - x $$

You will be paid in cash for the points you have at the end of the experiment.

1.15.1 We now ask you to indicate your decision

I wish to invest ____ points.

Appendix 2: Questionnaire

2.1 Questionnaire (experiment 1a, for players who have chosen possibility I)

Thanks for your participation. Now we have one more question for you. Please answer it carefully. Your answer will not influence your final payoff.

Now, suppose the experimenter will choose the numbers for you, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.2 Questionnaire (experiment 1a, for players who have chosen possibility II)

Thanks for your participation. Now we have one more question for you. Please answer it carefully. Your answer will not influence your final payoff.

Now, suppose you will choose the numbers yourself, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.3 Questionnaire (experiment 1d)

Thanks for your participation. Now we have some questions for you. Please answer them carefully. Your answers will not influence your final payoff.

• Q1. Do you prefer to choose the three numbers by yourself or let the experimenter choose? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

• Q2. Which of the following is the right description of your thinking on the probability of winning? (Circle one)

  • 1. I believe the probability of winning is higher if I can choose the numbers by myself.

  • 2. I believe the probability of winning is higher when the experimenter chooses the numbers for me.

  • 3. I think there are no differences in winning probability between choosing the numbers by myself or letting the experimenter choose the numbers for me.

• Q3. What is your gender?

  • 1. Male

  • 2. Female

• Q4. What is your age?

  I am ____years old.

• Q5. And what about your religious background? Thinking about the present, how often do you pray?

  • 1. More than once a day

  • 2. Once daily

  • 3. A couple of times a week

  • 4. Once a week

  • 5. Less than once a week

  • 6. Never

2.4 Questionnaire (experiment 1b, for players who have chosen method I)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose the experimenter will choose the numbers for you (and you need to pay 0.1 Euro for using this method), how many points will you invest?

I will invest ____ points out of 10,000 points.

2.5 Questionnaire (experiment 1b, for players who have chosen method II)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose you will choose the numbers for yourself (and there is no charge for using this method), how many points will you invest?

I will invest ____ points out of 10,000 points.

2.6 Questionnaire (experiment 1c, for players who have chosen method I)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose the experimenter will choose the numbers for you (and there is no charge for using this method), how many points will you invest?

I will invest ____ points out of 10,000 points.

2.7 Questionnaire (experiment 1c, for players who have chosen method II)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose you will choose the numbers for yourself (and you need to pay 0.1 Euro for using this method), how many points will you invest?

I will invest ____ points out of 10,000 points.

2.8 Questionnaire (experiment 2a, for players who have chosen method A)

Identical to experiment 1d, except that Q1 is modified as follows:

• Q1. Suppose you can only choose between choosing the three numbers by yourself or letting the experimenter choose (i.e., without method A). What is your preference? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

2.9 Questionnaire (experiment 2a, for players who have chosen method B and choose the numbers by themselves)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose the experimenter will choose the numbers for you, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.10 Questionnaire (experiment 2a, for players who have chosen method B and let the experimenter choose the numbers)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose you will choose the numbers yourself, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.11 Questionnaire (experiment 2b, for players who have chosen method A)

Identical to experiment 1d, except that Q1and Q2 are modified as follows. Q3 to Q6 are identical to Q2 to Q5 in experiment 1d.

• Q1. Suppose you can only choose between choosing the three numbers by yourself or letting the experimenter choose (i.e., without method A and there is no charge). What is your preference? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

• Q2. Suppose there is no charge for using method B, which method will you choose? (Circle one)

  • 1. I prefer to use method A.

  • 2. I prefer to use method B.

  • 3. I am indifferent.

2.12 Questionnaire (experiment 2b, for players who have chosen method B and choose the numbers by themselves)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose the experimenter will choose the numbers for you, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.13 Questionnaire (experiment 2b, for players who have chosen method B and let the experimenter choose the numbers)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose you will choose the numbers yourself, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.14 Questionnaire (experiment 2c, for players who have chosen method A)

Identical to experiment 1d, except that Q1 is modified as follows:

• Q1. Suppose you can only choose between choosing the three numbers by yourself or letting the experimenter choose (i.e., without method A and there is no charge). What is your preference? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

2.15 Questionnaire (experiment 2c, for players who have chosen method B and choose the numbers by themselves)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose the experimenter will choose the numbers for you, how many points will you invest?

I will invest ____ points out of 10,000 points.

2.16 Questionnaire (experiment 2c, for players who have chosen method B and let the experimenter choose the numbers)

Identical to experiment 1d, except that Q1 is modified as follows:

Q1. Now, suppose you will choose the numbers yourself, how many points will you invest?I will invest ____ points out of 10,000 points.

2.17 Questionnaire (experiment 3a)

Thanks for your participation. Now we have two more questions for you. Please answer them carefully. Your answers will not influence your final payoff.

• Q1. Do you prefer to choose the three numbers by yourself or by letting the experimenter choose? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

• Q2. Now, suppose the experimenter will choose the numbers for you, how many points will you invest?

  I will invest ____ points out of 10,000 points.

2.18 Questionnaire (experiment 3b)

Thanks for your participation. Now we have two more questions for you. Please answer them carefully. Your answers will not influence your final payoff.

• Q1. Do you prefer to choose the three numbers by yourself or by letting the experimenter choose? (Circle one)

  • 1. I prefer to choose the numbers by myself.

  • 2. I prefer to let the experimenter choose the numbers for me.

  • 3. I am indifferent.

• Q2. Now, suppose you will choose the numbers yourself, how many points will you invest?

  I will invest ____ points out of 10,000 points.