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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?

closed as off-topic by Eliran, Philip Klöcking Oct 8 '18 at 13:38

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  • How should we decide it? It all depends on the amount and difficulty of work done and we don't need numbers to say it depends. – rus9384 Sep 17 '18 at 18:36
  • Why does it matter what they ask for? Even if both agreed that A gets 70 and B 30, that doesn't mean it's fair. – Eliran Sep 17 '18 at 18:56
  • Well, @EliranH in order to really know what's fair, you'd need to be omnipotent. But you're not. So given this data, the question is, what's fair? What's our best guess at what's fair? You're right even if they agreed completely it would very likely still not be fair, but its your best logical guess at what's fair since you don't have any other information. – Legit Stack Sep 17 '18 at 19:19
  • It is not right to judge without any information. – rus9384 Sep 17 '18 at 19:20
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    @LegitStack This problem is about dividing winnings, looks like a question in game theory rather than philosophy. – Mark Andrews Sep 18 '18 at 4:58
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A fair distribution requires criteria of fairness : to each according to their need, to each according to their work, to each according to their merit, to each according to their investment and so on and on.

The only data you offer is the opinion of each voter about how much they should have. There is no indication of the criteria by which they support or could support their respective opinions.

In the absence of criteria it is fair to divide equally since no grounds of need, work, &c., have been provided on which differential shares could be justified.

I don't think you should average the figures if you want fairness since you are working from opinions - initial claimed percentages - for which such no justification of fairness has been given. Suppose Alice had asked for 60% or 90%. How does she justify any percentage she might claim ?

There might be a contractarian way out. If you allow Alice and Bob to argue between themselves, produce whatever considerations they regard as relevant,and come to a voluntary agreement on percentages, the result would be fair. But this would require a procedural process on their part, not a calculation by you.

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