In this experiment, we wish to determine how much you value an item.
We will use a procedure called the switch-point procedure for this purpose.
In the switch-point procedure we 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 we want to determine how much Tim values a pencil.
Here are the steps we wouldd take.
We provide Tim with 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 we can 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 20% chance that one question will be selected (and a 80% chance that no question is selected).
If a question is selected, we 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, we can 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 stated his switch-point, we can ‘fill out’ Tim's answers to all 3001 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 we randomly select a question, we will give Tim the option he picked on that question (determined from his switch-point).
For instance, if question 1001 is randomly selected (which corresponds to $10.00), and Tim said he preferred the pencil on that question, I would give Tim the pencil.
Suppose Luke's true switch point is $2.
If offered less than $2, Luke would prefer the pencil.
Likewise, if offered Luke more than $2, he would prefer to take the money over the pencil.
Now, let's suppose Luke lies and states that his switch point is $3. Let's suppose that question 251 (which corresponds to $2.50) was randomly selected. Since Luke has said his switch-point is $3, we would give him the pencil instead of the money. However, Luke would prefer the money 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 we can determine your valuation for a task or an item.
Your switch point is the monetary value 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.