Wednesday, April 27, 2022

Making the best choice

I wrote my dissertation about a possible application of mathematical decision theory.  The idea is an abstraction but it can be helpful in making actual decisions and thinking about them. It is handy to think in terms of a table or a software spreadsheet such as Microsoft Excel or Google Sheets.  These tools are basically tables with smart and capable cells that can relate to each other.  Let's say you are being paid to decide on which of four novels is the "best".  I put best in quotes because there are many ways of deciding on the best, from asking your sister which is best, to comparing their prices, to more complex ways.  I searched "What makes a novel good?" and found a list of "strong opening, compelling characters, an absorbing story, sharp dialogue, unique style."  Let's use the first suggested variable, a strong opening, as a basis for the decision example.  


Novel

Strong open

Good middle

Fine finish

A

5

8

2

B

4

9

7

C

6

6

5

D

3

7

1


Summing the points

A 15

B 20

C 17

D 11


We could use a "weighted" formula to increase the importance of the Finish if we feel that the finish is more important.  We could double the score for the Finish or multiply it by 1.5.  A table like this may disguise or cover all sorts of choices and issues.  That article suggested "compelling characters", an "absorbing story" and two other variables, none of which were used.  


In more detailed approaches, each cell in the table can be calculated using two figures, one for the value of the outcome and one for the probability of getting that value, the utility and the probability.


Given this approach, novel B wins but personally, I never liked that book.

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