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The Bedrock of Fairness

For every possible division of pie into three pieces (including pieces of 0 size), take each person and ask how fair they would think the division if they received each of the three slices. Average those together to get each person's overall fairness rating for a given pie distribution.

Average those per-person results into an "overall fairness" rating for each pie distribution.

This includes:
- You can have people involved who don't like pie and don't want any. It seems pointless to say that division into thirds is the only fair division, if one of the three people is equally happy with any division.
- There can be more than one fair division
- The inputs are not as simple as "I want half the pie", but are a function of fairness in proportion to size of slice, and distinguish between whether your happiness is in direct proportion to the size of pie slice, or whether it peaks at "half the pie" and stays the same for any value above that, or declines for any value above that.

Zaire says he wants half the pie and the other two want to divide it into thirds, but they may at the same time all have a linear link between happiness and amount of pie, leading to thirds being the fairest division.

- Situations such as the murderer and murderee in the alley, the murderer is happy to kill but unhappy to be killed, the murderee is unhappy to be in either situation, leaning towards both of them walking away as the 'fairest' outcome.

The process may lead to a less than happiest outcome for a given situation, but when applied to many situations over your lifetime such that you may be in a different position in the situation each time, gives the most long-term happiness.

I've wandered into describing "happiness" rather than "fairness" in several places, and seem to be heading towards "fairness as position-independant happiness".

This seems to be similar to Don Geddis's answer, except where he says it is meaningless to talk about "what position you could have been in", I suggest that it's a process you can agree to apply to situations you will be in in the future to get a 'fairest' outcome, even though you don't yet know which position you will be in the next time pie-slicing turns up in your life. So, fair is the process that gets you the best outcome for all situations for the rest of your life, given that you don't yet know what the situations are or what position you will play in them.