Imagine you're asked to decide the pay of partners that start a business.
They each give you a vote of how much they should make. If they agree with each other the answer is obvious - give them what they ask for. But they didn't agree. This is what they asked for:
Alice votes she should get 70% of the profits and Bob should get 30%
Bob votes he should get 40% of the profits and Alice should get 60%
They both agree Alice should get more, but they differ in how much.
What is the fairest way to decide how much each person should get, using only this data?
For instance, is it fair to take the average Alice 65% and Bob 35% ?
Or is it more fair to draw the line with more weight towards Alice since they both agree she should get more than 50%?
((alices average - 50%) * the difference) + alice's average ((65 % - 50 %) * 10) + 65 % (15 % * 10) + 65 1.5 + 65 = 66.5
In this case, Alice gets 66.5% and Bob 33.5%, is that more fair or less?
It seems to me that one of these is the fairest option, but I don't know how to decide. perhaps something else is fairer.
What do you think?