In the final three tasks, you will be provided with two lists of payment options that you will combine to rank all of the payment options from your most preferred to your least preferred. List 2 will contain a set of options that are already ordered for you, from highest expected earnings to lowest expected earnings, to make your decision easier. List 1 will be another set of options that is unordered. Your task will be to choose how to rank the options in List 1 relative to the options in List 2.
If this task is selected for payment, one of the options from List 2 will be randomly selected by the computer and compared to the option you rank highest from List 1. Your payment will be determined based on which of these two payment options you rank higher.
If you rank the randomly selected option from List 2 above the option you ranked highest from List 1: your payment is determined by the randomly selected option from List 2.
If you rank the randomly selected option from List 2 below the option you ranked highest from List 1: your payment is determined by the option you ranked highest from List 1.
You are most likely to earn the $5 if you rank the options from the highest chance of paying $5 to the lowest chance of paying $5. For example, consider an urn filled with four balls. Three of those balls are red and one of those balls is green. You could be asked to rank the following payment options:
List 1: Un-ordered Options
List 2: Ordered Options
You need to chose where to rank the un-ordered options in List 1 relative to the ordered options in List 2. For example, you might choose the following ranking:
Remember that the randomly selected option from List 2 will always be compared to the option you rank highest in List 1, which is "You are paid $5 if a randomly selected ball is red" in the example ranking above. So, if the randomly selected option from List 2 is "You are paid $5 with 80% chance", you will be paid based on that option. If one of the other two options from List 2 is randomly selected, you will be paid based on your highest ranked option from List 1 ("You are paid $5 if a randomly selected ball is red") because you ranked it higher than the other options from List 2.
If one of the options from List 1 determines your payment, based on your rankings and the computer's random selection, the computer will execute the action described in a random and fair manner. You earn the $5 if the event occurs as described in the option. In the above example, if you were to be paid based on the option "You are paid $5 if a randomly selected ball is red", the computer would randomly select a ball from the urn filled with three red balls and one green ball (each ball is equally likely to be chosen). If the ball was red, you would earn the $5. Otherwise, you would not earn the $5.
If one of the options from List 2 determines your payment, based on your rankings and the computer's random selection, the computer will randomly select a whole number from 1 to 100 (each number is equally likely to be chosen). If that number is equal to or less than your chance of being paid the $5, you earn the $5. Otherwise, you do not earn the $5. Since the computer is equally likely to pick any number from 1 to 100, this procedure provides exactly the chance of being paid $5 described by the option.
Suppose you ranked "You are paid $5 if a randomly selected ball is green" above "You are paid $5 if a randomly selected ball is red", instead of how they are ranked in the example. In that case, you would have a lower chance of earning the $5 because there are fewer green balls (1) than red balls (3) in the urn.
Similarly, if you ranked "You are paid $5 if a randomly selected ball is red" below "You are paid $5 with 50% chance" then you would have a lower chance of earning the $5 if these two payment options were chosen. In this case, you would be paid based on a 50% chance because you ranked it higher, whereas there is a 75% chance of earning the $5 if you are paid based on a selected ball being red (3 balls out of 4).