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Here's the problem:

I have some options. Each is represented with three attributes or say criteria (with normalized values between 0 and 1). I want to randomly choose one of these options based on these three criteria.

The first issue would be how to combine the three attributes. The weighted sum can be a way.

The second would be how to choose one based on the outcome of this combination. For example, if the weighted sum for one of the options gives 1.26 and the other gives 1.5, how do we choose between them?

Note that I want the one with the higher score to have a higher likelihood of getting selected.

When I search, I only come across multi-criteria decision-making methods that rank the options based on several attributes (like this one). From then on, the option ranked first is just selected. However, I am looking for a way where these attributes determine the likelihood of choosing an option, and the final outcome is based on something like a weighted random process, and not just chosen deterministically.

Edit:

F.C. Akhi has asked me to clarify my specific problem. Here is my attempt at this:

I have an agent who should choose between a number of goals (say two). Each goal has three attributes which have values between 0 and 1. The higher the value the more likely it should be for the goal to get selected. Reaching a higher combined score should increase the goal's chances of getting selected, however, as the process is random we might end up with the goal with the lower score. I am looking for a method to implement this process.

I hope this added explanation helps to clarify the problem.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – F.C. Akhi
    Commented Aug 10, 2022 at 14:29

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There are any number of ways to achieve what you want. A fairly simple way is to select an option with probability proportional to it's share of the total score. For example, suppose there are 3 options that have weighted scores $S_A$, $S_B$, $S_C$. Then we randomly select option $A$ with probability $\frac{S_A}{S_A+S_B+S_C}$, option $B$ with probability $\frac{S_B}{S_A+S_B+S_C}$, and option $C$ with probability $\frac{S_C}{S_A+S_B+S_C}$.

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