There are many possible equality laws with regards to how the surplus of value is divided among people. There are also many equality laws that are beneficial to all people involved. Complying with the law generates some surplus of value. There are different ways how the split of the surplus of value between people can be decided. I will consider two splits: 1. Equal split of surplus. 2. [Shapley value](https://en.wikipedia.org/wiki/Shapley_value) The conclusion is that in case of both splits, if we assume that the lifespan of people is significantly higher than any other relevant variable (or even that there is non-trivial probability of that), then the split becomes close to equal. I will prove that now. # Equal split of surplus 1. Each person gets a deal of value equal to their BATNA (Best Alternative To a Negotiated Agreement) + surplus (the difference of how good the deal is collectively relative to no-deal collectively) divided evenly between each person. 2. I will assume that BATNA of each person is heading towards winner takes all scenario and each person has some probability that they are going to be the winner in that scenario (I think that this assumption might be wrong - the real BATNA is making a coalition with a smaller group of players rather than with all players. So, maybe Shapley value is more appropriate in this case). 3. $batna_i = win\_probability * log_{base} pie$ 1. Explanation: 1. If there is no coalition, then the world will end up with winner takes all scenario. If they lose, they will collect some resources until they have 0 resources (because the winner will accumulate all resources). If we assume that people will live very long, then that time before there is only 1 winner will be very short, so for simplicity in the above formula I only count the resources that they will have, if they win. 4. $surplus = n * log_{base} (\frac{pie}{n}) - log_{base} pie$ 5. $value_i = batna_i + \frac{surplus}{n}$ 6. $value_i = win\_probability * log_{base} pie + \frac{n * log_{base} (\frac{pie}{n}) - log_{base} pie}{n}$ 7. $value_i = win\_probability * log_{base} pie + log_{base} (\frac{pie}{n}) - \frac{log_{base} pie}{n}$ 8. Where: 1. $batna_i$ - the value of BATNA of the $i$-th person. 2. $win\_probability$ - probability that the player will be the winner in the winner takes all scenario. 3. $pie$ - the pie to split which is how many resources collectively all people will accumulate. 4. $surplus$ - the difference in collective utility between when the deal is made vs when it's not made. 5. $n$ - the number of the people participating in the deal. 6. $base$ - we assume that there is a logarithmic relationship between number of resources and utility. $base$ is the base of that logarithm. Also, $base$ > 1. 7. $value_i$ - the value of the share of the pie that the $i$-th person gets. 9. If we assume that the number of years the players will live is significantly higher variable than any other variables in the formula (because of achieving LEV - longevity escape velocity), then $pie$ will be a very high number. 10. If we assume that $pie$ is very high (significantly higher than any other relevant variable), then the part $log_{base} (\frac{pie}{n})$ will be significantly the highest part of the formula from point 7. It will be higher than $win\_probability * log_{base} pie$ and $\frac{log_{base} pie}{n}$. 11. The higher the number of years people will live, the higher the pie. The higher the pie, the higher $log_{base} (\frac{pie}{n})$ comparing to the other parts of the formula. That part is the same for each player. Therefore, the more we increase the number of years, the more equal deal we get. 12. Therefore, if we assume that people will live super long, then they have close to equal negotiating position when it comes to equality law. 13. If we assume that there is a certain probability that people will live super long, but it's not certain, then it doesn't change the conclusion, that conclusion will still hold. # Shapley value Here's a good article on Shapley value: https://medium.com/the-modern-scientist/what-is-the-shapley-value-8ca624274d5a With split being decided by Shapley value, the value of the share that each person gets is a weighted average of all marginal contributions of a given person in all possible combinations of coalitions that the person can make. If you look at the formula, the number of possible combinations doesn't depend on the lifespan of people. The weights in the weighted average also don't depend on the lifespan of people. But the marginal contribution depends on the lifespan of people - the longer people live, the higher is the marginal contribution of people who have low win probability relative to the marginal contribution of people who have high win probability. The share is based on the marginal contribution, therefore the more equal the contributions are, the more equal the shares are. Therefore, the longer the expected lifespan of people, the more equal split they will be able to negotiate.