Would Somebody Please Do This?

Here’s something that an eager academic could benefit from. I could do it, but it seems a shame for me to hog such an opportunity that would do me no benefit, when it could definitely advance the career of a graduate student or academic. Besides, I already have too many things to do before I do. I just gave up my 1961 VW truck because I sadly realized that I will never have the time to get the old engine up and running. Sniffle, sniffle.

So here’s the project. 

Step 1: set up web pages for collecting data
The subject starts with a page listing lots of games; the subject is asked to check off the games that s/he is familiar with, including ONLY games that the subject has actually played.

Next, the subject is presented with a list of the games s/he has checked and asked to check the two games that are most unlike each other. This defines “9” for the next step.

The subject now sees a page cross-tabulating the selected games against each other: each game has one column and one row of a table. At the intersections of the rows and columns, the subject is asked to enter a digit from 0 to 9 indicating how similar the two games (one in the row, the other in the column) are. For calibration purposes, “9” is declared to be equal to the distance between the two most distant games that the subject previously specified.

The subject need only fill in half the matrix, as the similarity value is symmetric. Also, the subject will, obviously, not fill in the cell with the intersection of a game’s row with its column. That’s pre-filled with a “0”.

Step 2: collect the data
Use whatever protocol you think appropriate for recruiting subjects. Get lots of them. Collect all their data. For each and every pair of games, calculate the mean and standard deviations of the similarity values.

You now have a 2D matrix containing mean and standard deviations for every pair of games in the study. 

Step 3: relaxation algorithm in two dimensions
Now randomly assign each game an (X,Y) position in a 2D space with bounds ranging from, oh, ±50 in each dimension. Then begin a relaxation loop:

set a net energy scalar to zero
while (net energy > previous net energy * 1.001)
For each game i {
   For each game j {
      set a “net force vector" to zero
      calculate Pythagorean distance in the (X,Y) space.
      calculate the difference between that distance and the similarity value.
      divide that difference by the standard deviation for that pair of games.
      That’s the length of a vector. Resolve that vector into X and Y values.
      Accumulate the vector into the net force vector
      add to the net energy scalar:
         the square of the difference value divided by the square of the std deviation
   move game i by a small fraction of the net force vector.

This will yield the best positions of the games in a 2D space, along with a minimum net energy. Graph the positions of the games on a plane. You will note that they form clusters, with similar games clustering together.

Step 4: extend to many dimensions
Repeat Step 3 using N dimensions, N ranging from 3 to, oh, maybe 10. Record the minimum net energy obtained for each dimension. Graph net energy against N. You’ll get something looking vaguely like this:


In general, the point values will fall with increasing N because more dimensions give the points on the map more room to spread out. What’s interesting here is the fifth data point from the left, representing N = 6. Notice that it is abnormally lower than the rest of the curve. Ta-da! You’ve discovered something: there are six basic traits that most strongly affect peoples’ perceptions of games. Look at the final positions of the games in the six-dimensional space. Sort all the games by its value in each of the six dimensions; this gives you six different lists of games. For each list, look at the top of the list and the bottom of the list and ask, what is most salient about this difference? You should be able to identify some factor that all the games high in the list possess and none of the games low in the list possess. That’s a “natural” dimension of game appreciation. 

Step 5: write it up and publish it
Sit back and wait for that Nobel to roll in.

If you need help with any of these concepts, contact me and I’ll explain it in more detail.