A Thought Experiment, pt. 2

Imagine a group of 100 people. Any 100 people will work just fine. For the purposes of this thought experiment the "sample" doesn't have to be random, and we need no control group.

Imagine these folks have five choices-- what Mr. Big Food will grill when they all come out to the Farm next weekend. They can choose only one. 

[If you don't think Mr. Big Food can grill for 100+ people, I refer you to the first post here at Big Food, etc.: 260 Pieces of Chicken.]

The choices are:

1. Salmon

2. Vegetables

3. Chicken

4. Hamburgers (made from freshly ground sirloin tip)

5. Ribeyes

Each individual writes the numeral corresponding to his or her choice on a slip of paper and drops it in a box.

Mr. Big Food is very busy so he asks a colleague whose specialty is Experimental Philosophy to determine what will please most of the crowd when they show up at the Farm. This is an important task because we have to purchase what will be grilled. 

Mr. X-Phi happily agrees to help. Shhh... although I am very busy, I do a quick tabulation of my own:

Lest there be any mistake, I do know how to properly label a graph. What I don't know is how to get Numbers to properly label a graph. X-axis: Numeral corresponding to choice; Y-axis: # of people choosing each choice.

Soon, Mr. X-Phi reports to Mr. Big Food that 3-- chicken-- is the average response.

STOP RIGHT THERE. IF THIS MAKES SENSE TO YOU, GO BACK TO BED.

Let us look at the calculation Mr. X-Phi did.

Mr. X-Phi multiplied the choice (1-5) by the number of people choosing each. He summed these, and divided by 100. 

So chicken. Right? So wrong.

Let us look at column B*C (i.e., B multiplied by C). Why do the 30 people who chose steak get five times as much weight in the calculation than the 30 who chose salmon? For that matter, why do the 15 who chose vegetables have the same weight as the twice as many who chose salmon? 

Why is it that both the (loosely) vegetarians and the meat lovers are having their potentially fine grilling experience spoiled by an Experimental Philosopher? (Not that there's anything wrong with grilled chicken. But I'm making a point.)

And why are we going to have to eat what the fewest number of people want?

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We really did this once for nearly 100 people. Mr. Big Food took orders, steak or salmon grilled to order? It was very funny. One fuss budgety guy came back three times because his steak wasn't right. In the end of course it was perfect. Daughter K had come home from work in the middle of all this and jumped in to help-- in her little chef's's outfit.* People thought we'd hired her. Ha!
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Thought Experiment pt 1.

* At the time, K was doing serious cooking at a restaurant owned by a very successful chef. I think she learned a lot working in restaurant kitchens.