Creating a categorical probability distribution based on scores

Question

I am looking for a method to create a categorical distribution from a set of possible options with an associated known score.

Example:
In a game where there are 4 options each rewarding the following a scores
Option 1: 1000 points Option 2: 675 points Option 3: 2 points Option 4: 230 points

I want to create a categorical probability distribution where the likelihood of an option to be chosen is proportional to how good it is. That is, option 1 should have the highest probability and option 3 should have the lowest.

score 0 · Accepted Answer · answered Mar 14 '15 at 08:18

0

For the given example:

$P(1)=\frac{1000}{1000+675+2+230}$
$P(2)=\frac{ 675}{1000+675+2+230}$
$P(3)=\frac{ 2}{1000+675+2+230}$
$P(4)=\frac{ 230}{1000+675+2+230}$

Note that $\sum\limits_{n=1}^{4}P(n)=\frac{1000+675+2+230}{1000+675+2+230}=1$.

answered Mar 14 '15 at 08:18

barak manos

43,109

Looks kind of obvious now but that's exactly what I was looking for. Thanks! – user1417861 Mar 14 '15 at 08:55
@user1417861: You're welcome :) – barak manos Mar 14 '15 at 10:27

Creating a categorical probability distribution based on scores

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