# 4 people, 4 unrelated Tasks. Each person gets one task, based on preferences

Looking for the fairest way to distribute tasks based on preferences. Was thinking of preferential voting, but not sure how to generalize that for multiple people.

Here is an example of how a person might vote.

Person 1 ranks their preferences of tasks (A, B, C, D) in the following order:

1. B
2. D
3. A
4. C

All four people do this, and we distribute tasks according to these preferences.

Is there a fair process for doing this (allowing for a coin-toss in case of perfect ties)?

• Directly assign tasks that only one person prefers to do. For tasks that more people want to do just have them battle it out with rock, paper, scissors :-) May 14, 2022 at 12:59
• Unless you're trying to reinvent the field of game theory, with a team that small just ask them to agree. If someone gets the short straw one time, the team can let them pick first next time (or whatever). Don't over-complicate this. May 14, 2022 at 18:09
• Auction: they pay you to get the one they want :) May 15, 2022 at 6:44

You could see this as an optimization problem, and there are several possible fitness (goal) functions. For a truly satisfactory solution, you might consider a "satisfaction" value for each task/person pair, and optimize such that either total satisfaction is maximized (on average, everybody performs the task they're most happy with), or individual dissatisfaction is minimized (nobody is significantly unhappier than the other ones), or some other complex function.

For small numbers of tasks and performers, enumerating all permutations is quite feasible, as is evaluating the fitness function for each and selecting the best solution.

However, as Todd Jacobs rightfully pointed out, just letting the people come to a solution on their own might be best if they can be expected to consider fairness towards each other. Algorithmic solutions aren't always the best solutions.

Check out the assignment model.

Here is a link to a solution to another question posted on here that I solved using the assignment model: https://stackoverflow.com/a/50183650/4961700

You might fined this one interesting as well: https://stackoverflow.com/a/63080995/4961700

Get solutions for skills matching or quickest time etc

The solver in Excel is a very good tool for this type of problem.

For a reference see Practical management Science by Albright & Winston.

• This sounds like a recommendation to look elsewhere for an answer, rather than directly answering the question. May 16, 2022 at 16:54