In the next two tasks, you will be asked to rank one payment option relative to other payment options in order from your most preferred payment option to your least preferred payment option. The other payment options will be pre-ordered from highest likelihood of winning $5 to lowest likelihood of winning $5. We'll call this list of pre-ordered payment options the "Pre-ordered List." The one payment option you must choose how to rank is called the "Unordered Option."
If this task is selected for payment, one of the options from the Pre-ordered List will be randomly selected by the computer. Whichever you rank higher, the randomly selected option from the Pre-ordered List or the Unordered option, will determine your payment.
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 Unordered Option:
Unordered Option
...in the following Pre-ordered List:
Pre-ordered List
You need to chose where to rank the Unordered Option relative to the payment options in the Pre-ordered List. For example, you might choose the following ranking:
If one of the options from the Pre-ordered List 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.
If the Unordered Option 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.
Suppose you ranked "You are paid $5 if a randomly selected ball is red" below "You are paid $5 with 50% chance," instead of how these two payment options are ranked in the example. Then you would have a lower chance of earning the $5 if "You are paid $5 with 50% chance." is the randomly selected option from the Pre-Ordered List. 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). So, you are most likely to earn the $5 if you rank the payment options from highest likelihood to lowest likelihood of occurring.