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    Tasks 3-5
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In the next three tasks, you will rank payment options from your most preferred to your
least preferred. For instance, suppose you are faced with ranking the following set of options:

<ul>
    <li>You are paid $10 with 0% chance.</li> 
    <li>You are paid $10 with 100% chance.</li>
    <li>You are paid $10 with 50% chance.</li>
</ul>

<p>If you prefer a higher probability of earning the $10, you would choose the following ranking: </p>

<ol>
    <li>You are paid $10 with 100% chance.</li>
    <li>You are paid $10 with 50% chance.</li>
    <li>You are paid $10 with 0% chance.</li>
</ol>

<p>Two of the options from the set will be chosen at random. <b>You will be paid based on
the option that you rank higher among these two randomly chosen options.</b></p>

<p>Suppose “You are paid $10 with 50% chance." and “You are paid $10 with 0% chance." were randomly chosen. Since you ranked “You are paid $10 with 50% chance." higher, youwould earn an additional $10 at the end of the experiment with a 50% chance.</p>


<p>Notice that this procedure gives you incentive to <b>correctly</b> rank each option according
to your preference. Suppose you accidentally ranked “You are paid $10 with 0% chance.”
higher than “You are paid $10 with 50% chance.” If these two options were chosen, you
would receive $10 with a 0% chance rather than the 50% chance you prefer.</p>

<p>While the example above includes only three options, you will be asked to rank many options.
To make your decisions easier, we order some of the options for you. Therefore, you
will receive a set of pre-ordered options and a set of unordered options for each task.</p>

<p>For example, you could be asked to rank the following payment options:</p>


<b>Unordered Options</b>

<ul>
<li>You are paid $10 if the population of the United States is less than 400 million.</li>
<li>You are paid $10 if it rains tomorrow in Paris, France.</li>
</ul>



<b>Pre-ordered Options</b>
<ol>
    <li>You are paid $10 with 100% chance.</li>
    <li>You are paid $10 with 50% chance.</li>
    <li>You are paid $10 with 0% chance.</li>
</ol>

You simply need to chose where to place the unordered options. For instance, you might
choose the following ranking:

<ol>
    <li>You are paid $10 with 100% chance.</li>
    <li><b>You are paid $10 if the population of the United States is less than 300 million.</b></li>
    <li>You are paid $10 with 50% chance.</li>
    <li><b>You are paid $10 if it rains tomorrow in Paris, France.</b></li>
    <li>You are paid $10 with 0% chance.</li>
</ol>


<p>As a reminder, you will be paid based on the option you rank higher between two randomly chosen options. <b>One option will be randomly chosen from the pre-ordered list and one option will be randomly chosen from the unordered list.</b></p>


Suppose the two items chosen at random are:
<ul>
    <li>You are paid $10 with 50% chance.</li>
    <li><b>You are paid $10 if the population of the United States is less than 300 million.</b></li>
</ul>



<p>Since you rank “you are paid $10 with 50% chance” higher, you are paid according to this
option. To determine whether you earn the $10, the computer will randomly generate a
number between 1 and 100. If the number is 50 or less, you would earn $10 and otherwise
you would earn $0. The computer is equally likely to pick any number from 1 to 100, so
this provides exactly a 50% chance of being paid $10. The same procedure will be used for
any option that has less than a 100% chance of being paid the $10.</p>

<p>If instead you ranked “You are paid $10 if the population of the United States is less than
300 million” higher, you are paid according to this option. Since the statement is false (the
population is around 331 million) you would earn $0, but remember this payment is in
addition to the $5 you receive just for participating. If that statement had been true, you
would earn $10 in addition to the $5 participation fee.</p>


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