This year’s project aims to assess risk attitudes and risk decisions when people are confronted with tasks involving risk taking (see for example Rolison and Pachur, 2016). In particular, an intriguing issue around the above topic is the following. In experimental tasks aimed to assess risk taking, the amount of fictional money at stake is relatively small. Often people are confronted with a series of gambles like those below that they are asked to either accept or reject.
win loss probability Win probability Loss
1 £1 £3 25% 75%
2 £2 £3 25% 75%
3 £3 £3 25% 75%
4 £1 £2 25% 75%
5 £2 £2 25% 75%
6 £1 £3 50% 50%
7 £3 £2 25% 75%
8 £1 £1 25% 75%
9 £1 £2 50% 50%
10 £2 £3 50% 50%
11 £2 £1 25% 75%
12 £3 £1 25% 75%
13 £1 £1 50% 50%
14 £2 £2 50% 50%
15 £3 £3 50% 50%
16 £1 £3 75% 25%
17 £1 £2 75% 25%
18 £2 £1 50% 50%
19 £3 £2 50% 50%
20 £1 £1 75% 25%
21 £2 £3 75% 25%
22 £3 £1 50% 50%
23 £2 £2 75% 25%
24 £2 £1 75% 25%
25 £3 £3 75% 25%
26 £3 £2 75% 25%
27 £3 £1 75% 25%
For each gamble there is a given amount of money that could be won with a given probability (in trial 16 £1 could be won with a probability of 0.75) and another amount of money that could be lost with a given probability (in trial 16 £3 could be lost with a probability of 0.25). The expected return (i.e. the monetary long term average of gains/losses on the gamble if this would be accepted an infinite number of times) on this gamble would then be £1 x .75 + (-£3 x .25) a loss of £0. The expected return should, in principle, be the key indicator for the participant to decide to either accept or reject each gamble.
To assess the relationships between risk attitude and risk taking, people are often asked to rate the likelihood of acceptance of each gamble using a 7 points scale (1 = ‘extremely unlikely I would accept the gamble’; to 7 = ‘extremely likely I would accept the gamble’; with a score of 4 being not sure whether to accept or refuse to accept the gamble) as well as, when confronted with the same gambles, to indicate whether they would accept the gamble or not.
Using a signal detection approach (something we will not use in the current lab class) Rolison and Pachur (2016) showed that when people were given the above type of unambiguous gambles compared to a condition where gambles were ambiguous (i.e. when the size of one of the monetary gain/loss was not clear – it could have been any of 3 different amounts of money), “participants’ likelihood ratings discriminated between acceptance and rejection cases less accurately in the ambiguous rather than in the unambiguous condition”.
In a nutshell, when likelihood rating was high more gambles where accepted than rejected in the unambiguous gambles condition compared to the ambiguous condition. Thus it appears that the relationships between rating the likelihood of accepting/rejecting gambles and the actual acceptance/rejection of the very same gambles is affected by the nature of the gambles (in Rolison & Pachur case the ambiguous/unambiguous nature of the gambles).
Going back to the early statement where an intriguing issue was referred to, indeed nothing was written on the nature of the issue, but time was spent to introduce one type of procedure often used to assess risk taking. The intriguing issue is the following: it appears that in the literature almost invariably the amount of money at stake in each gamble is minimal and it does not really reflect what could be at stake in relevant financial decisions in everyday life. Consider for example, financial investments: it is more likely that an investment would be in the order of thousands of pounds rather than pounds. If so, how would you react to a gamble (investments are decisions that carry a risk – a bit like a gamble – to lose as well a prospect to gain) of this type?
(A) £1,000 could be won with a probability of 0.75 and £3,000 could be lost with a probability of 0.25. Would you accept it or not?
Moreover compare this gamble with the previous one
(B) £1 could be won with a probability of 0.75 and £3 could be lost with a probability of 0.25.
In both cases the expected return is £0; so, if the expected return guides your decisions you should select both gambles with the same probability. However, which of the two gambles you will be more likely to accept? From the perspective of losses, in the small gamble, you could lose £3 at worse (or win £1 at best), in the large gamble the loss would be £3000 (or at best you would win £1000)! Would a potential win (albeit larger) of £1000 be sufficient to counteract the risk (albeit smaller) to lose £3,000, then select gamble A (more or less often than gamble B)?
Despite gambles like these being rather artificial, the type described in example A seems closer to what could happen in real life than the type of gamble described in the example B. Oddly enough, in the decision making literature it is rare to see tasks using large amount of money being at stake (for an exception see the Iowa gambling task – REFERENCE), therefore it is difficult to infer how people behave when dealing with decisions involving relatively large amounts of money, as often happens in real life (consider the Deal or no Deal TV show to see how people react to gambles involving large sums of money).
Therefore, the aim of this project is to compare the selection of gambles that people make when confronted with the A types of gambles v’s the B gamble types (see above), moreover we will also consider how people rate the likelihood to either select or reject gambles.
Overall the lab aims are to assess the following:
A. Do people select more gambles when a small amount of money is at stake rather than large amounts (i.e. do people become more risk averse if large stakes are put on the tables), or vice-versa? (please notice that across the two types of gambles the probability to win and lose the specified amounts would be the same, with gambles only differing in terms of the magnitudes of the amount of money at stake (by multiplying the amount by a factor of 1,000). What is your prediction?
Note: To answer question A, the independent variable is Type of gamble and the dependent variable is the proportion of gambles accepted per person.
B. Are people, in principle, more or less likely to intend to select large, rather than small gambles? (Notice that with respect to question A, where people either select or not select each gamble, in question B, people only indicate using a 7 point scale the likelihood they would accept, in principle, the gamble – so a measure of intention to act is obtained here, rather than a direct behavioral measure of risk taking as we ask people in order to address the issue relative to question A). What is your prediction?
Note: To answer question B the independent variable is Type of gamble and the dependent variable is the average likelihood of gambles’ acceptance per person.
C. Finally, we could consider, with respect to gambles of different sizes, the relationship between the likelihood to act and the actual enactment of behaviours. In particular, what is the strength of the linear correlation between the likelihood rating and gamble acceptance for small and large size gambles? For example, for small gambles, do increments, across people, in the intention to gamble correspond to increments (or decrements) in the proportion of accepted gambles? And, for large gambles, would this relationship be stronger or weaker? What would you predict?
(p.s. In Rolison and Pachur it appears for unambiguous gambles, the relationship between likelihood rating and selection of gambles was stronger than for ambiguous gambles.
Could we consider large gambles akin to unambiguous gambles and small gambles as ambiguous gambles – or vice-versa – or is the analogy misleading?).
In order to run this experiment each of you will use a links to Qualtrics (the program used to run the experiment – link below)
• This is to be used to invite participants (e.g. by sending an email to a friend explaining that they are taking part into a study on decision making).
• In the email there will be one link. By clicking on the link participants will be able to partake on the appropriate tasks via Qualtrics (NOTE: the participants need to be online to use Qualtrics).
• Each of you should try and get at least 12 participants to be tested (assuming that 75% of the participants will complete the game each should get about 9/10viable participants for a total of about 400 participants).
• Participants should be aged between 18 and 40. The data will be automatically collected and a summary of the participants’ data will be provided to you at the end of the data collection.
• Data collection terminated Sunday the 10th of March! (Note: This is a common method of participant involvement you may engage in as a graduate and provides vital real-life experience in actual testing scenarios).
• One link does the job for four links!
• Each person will be asked to decide to either take or reject each of the 27 gambles of either small sizes (i.e. the one above) or large sizes (i.e. the one above with the amount of money multiplied by 1000) (thus size of gambles is a between-subjects variable).
• Each participant will see these gambles in different random order (so gamble sizes is a between subject variable). Also each participant will be asked to rate the likelihood to accept each of the 27 gambles (using the previously described 7 point Likert scale).
• This task will be performed before the risk taking task by half of the subjects, while for the other half the order will be reversed (hence 1 link doing the job of 4 – the 4 conditions are randomly allocated by Qualtrics to participants).
Below are the instructions players will see on the screen.
Please notice that participants will be asked to consider for each gamble before deciding to accept it or not (and also before rating the likelihood to accept it) that the money in each gamble they are facing are their own money. This to make the task as realistic as possible (i.e. as if they are not playing with Monopoly money but with real money).
Instructions to participants FROM QUALTRICS
We are inviting you to participate in a study of your choices. You will be asked to evaluate a number of hypothetical gambles.
Aims of the study
To investigate people’s choice behaviour.
Your participation is voluntary and you have the right to withdraw at any time. If you choose to withdraw your participation your data will be destroyed immediately.
Confidentiality of your data contribution
Your data will be stored in electronic form on a secure computer. You can withdraw your data up to one month after you have completed the study by contacting the researcher.
Ethical approval has been granted for this project by the Department of Psychology Research Ethics Committee, on behalf of the University of Essex (UK).
Participant consent form
· To participate in this research
· To participate with my own free will
I am aware that:
· I have the opportunity to ask any questions I wish
· I may withdraw from the study at any time, without giving a reason and with no adverse consequences
· Been given full information about the study (information provided above)
· Been given contact information for the researchers
I am aware:
· Of the confidentiality of the information provided
Please click the box below to indicate whether you agree or do not agree to give your consent to participate in the research
We have designed a set of 27 gambles that we would like you to evaluate. Each gamble has two possible outcomes (a win or a loss). Each outcome is characterised by an amount (£1,000, £2,000, £3,000) that can be won or lost and a chance (i.e., probability) of winning or losing (25%, 50%, or 75%):
(a) win or loss amount (£1,000, £2,000, £3,000)
(b) chance of winning or losing (25%, 50%, 75%)
Here is an example of the kind of gamble you will be shown:
Gamble: You win £1,000 with a chance of 25%
You lose £2,000 with a chance of 75%
To help you understand these chances, you can think of a bag containing 100 tokens, of which 25 are blue and the remaining 75 are red. Imagine drawing one of the tokens from the bag without looking. If you draw one of the 25 blue tokens you win £1,000. If you draw one of the 75 red tokens you lose £2,000.
In one block, you will be asked whether you would accept each gamble, and in another block, you will be asked how likely you would be to accept each gamble.
Finally: The papers provided in the Moodle folder are there to help you start, it is then up to you to independently search, consider, critique and expand the reading list you chose for your lab report.
a) Importantly, start thinking how you would like to analyse the data (comparing means; regression, correlation), keeping in mind the predictions you may make with respect to possible expected outcomes of the experiment.
b) Also, (for the brave amongst you!), you could think of a dichotomous variable to add to the analysis (if meaningful). This provides the opportunity to use your factor (2 levels, e.g. Gender) in conjunction with the factor Size of gambles (2 levels) to perform factorial ANOVAs on the appropriate dependent variables.
What will these analyses tell you?
Bechara A., Damasio A. R. Damasio H., Anderson S. W. (1994). Insensitivity to future consequences following damage to human prefrontal cortex. Cognition, 50: 7-15.
Rolison, J. J., and Pachur, T. (2017) How Well Do We Know Our Inner Daredevil? Probing the Relationship Between Self-Report and Behavioral Measures of Risk Taking. J. Behav. Dec. Making, 30: 647–657. doi: 10.1002/bdm.1979.