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:
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)?
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.
