In this experiment, I want to determine how much you value completing a task or how much you value an item.
I will use a procedure called the switch-point procedure for this purpose.
The switch-point procedure is where I provide you with two options, and ask when you'd switch from choosing one option to the next.
The procedure is explained below.
Let's suppose that I want to determine how much Tim values a pencil.
Here are the steps I'd take.
The first thing I'd do is give a Tim a list of questions like the ones in the table below.
Each row in the table (apart from the header row) shows a question that I'd ask Tim.
In each question, Tim picks either option A (the pencil) or option B (the money).
All questions are equally likely to be selected, but there is only a 5% chance that one question will be selected (and a 95% chance that no question is selected).
If a question is selected, I will give Tim the option he chose on that question.
Tim has no reason to lie on any question, because if that question gets selected then Tim would end up with the option he likes less.
A reasonable assumption is that Tim prefers option A for the first few questions, but at some point will switch to choosing option B.
So, to save time, I'll just ask Tim for his switch-point: the monetary value at which he'd switch from choosing option A to option B.
Once Tim has told me his switch-point, I can ‘fill out’ Tim's answers to all 2001 questions based on his switch point (choosing Option A for all questions before his switch point, and Option B for all questions at or after his switch point).
Tim still has no reason to lie as he might end up with an option he likes less.
If I randomly select a question, I will give Tim the option he picked on that question (determined from his switch-point).
For instance, if I randomly selected question 1001 (which corresponds to $10.00), and Tim said he preferred the pencil on that question, I would give Tim the pencil.
I can also apply the switch-point procedure to determine how much you value an item in terms of a lottery.
Let's suppose I want to determine how much Luke values a pencil in terms of a lottery with two outcomes.
In this case, I would give Luke a list of questions like in the table below (there is still a 5% chance that a single question will be selected):
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Option A means Luke gets the pencil, then gets to leave the experiment (receiving full payment).
Option B means Luke gets a lottery with the following outcomes:
I would then ask Luke for his switch-point: the percentage chance of leaving at which Luke would switch from option A to option B.
Then, if I randomly select a question, I will give Luke the option he chose on that question.
If Luke chose the pencil on the question I picked, he would get the pencil for sure.
If Luke chose the lottery on the question I picked, I would run the lottery in that question.
Luke would get to leave the experiment (and receive the full monetary compensation) if that was the outcome from the lottery, or have to complete the reading activity otherwise.
Luke also has no reason to lie about his switch-point as he might end up with an option he likes less.
Suppose Luke's true switch point is 33.5%.
If I offered Luke a lottery with a less than 33.5% chance of leaving immediately, Luke would prefer the pencil.
Likewise, if I offered Luke a lottery with a greater than 33.5% chance of leaving immediately, he would prefer to take the lottery.
Now, let's suppose Luke lies and tells me that his switch point is 50%. Let's suppose that question 41 (which corresponds to 40%) was randomly selected. Since Luke has said his switch-point is 50%, I would give him the pencil instead of the lottery. However, Luke would prefer the lottery to the pencil. So, if Luke lies about his switch-point he may receive an outcome he prefers less!
The switch-point procedure is a way that I can determine your valuation for a task or an item.
Your switch point is the monetary value (or percentage chance of leaving) that causes you to switch from option A to option B.
You have no reason to lie about your switch-point, because lying might leave you with an outcome that you prefer less.