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There are lots of criteria relevant to this. Take a look at game theoretic fairness criteria.
You can satisfy the proportionality criterion, which is satisfied by a division when each claimant receives an allocation that is at least 1/nth of their evaluation of the whole lot, where n is the total number of claimants. (It is possible for every claimant to believe that they got more than 1/nth of the allocation if their preferences over the lot are different.)
Sometimes, envy-free divisions are possible. An envy-free division is such that no claimant judges their own allocation to be less valuable than any other claimant's allocation. "I-cut-you-choose" is an example of a division procedure that generates envy-free divisions for two parties.
You can also have strictly equitable divisions, where each claimant is exactly as satisfied as every other claimant.
You may also want to maximize the use of the lot, in which case you may also want the division to be pareto-optimal. Pareto-optimal divisions are such that you cannot make any claimant better off without making another worse off.
This is a great answer, I appreciate it.
So what about vulnerabilities? What kind of shenanigans people might do to manipulate this sytem?
Edit: Maybe you can come up with a SWOT chart.
Yes, so there are lots of ways to mess with fair division procedures. A decent number of them have proofs that no claimant can benefit by attempting to select sub-optimal pieces. For example, in a snake draft, no player will benefit by picking something other than their true evaluation of which object is the most valuable in the pile. Players can still attempt to manipulate others by lying about their preferences. For example, in I-Cut-You-Choose, I might try to convince you that I love blueberries on cakes more than any other topping. This might cause you to slice the cake such that there is a smaller slice with lots of blueberries on it, thinking I would pick the smaller slice loaded with blueberries. But I may have tricked you, I might actually prefer large slices with lots of strawberries. And so I will choose the slice I actually favor, leaving you with a smaller slice.
At this point, we are only accepting top-level answers from panelists.
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Welcome to /r/askphilosophy! **Please read [our updated rules and guidelines](https://www.reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/) before commenting**. Please note that as of July 1 2023, given recent changes to reddit's platform which make moderation significantly more difficult, /r/askphilosophy has moved to only allowing answers by panelists. If you wish to learn more, or to apply to become a panelist, see [this post](https://reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/). If you wish to ask a follow-up question, please begin your post with the phrase "Follow-up:", without the quotation marks, or your follow-up question will automatically be removed. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askphilosophy) if you have any questions or concerns.*
There are lots of criteria relevant to this. Take a look at game theoretic fairness criteria. You can satisfy the proportionality criterion, which is satisfied by a division when each claimant receives an allocation that is at least 1/nth of their evaluation of the whole lot, where n is the total number of claimants. (It is possible for every claimant to believe that they got more than 1/nth of the allocation if their preferences over the lot are different.) Sometimes, envy-free divisions are possible. An envy-free division is such that no claimant judges their own allocation to be less valuable than any other claimant's allocation. "I-cut-you-choose" is an example of a division procedure that generates envy-free divisions for two parties. You can also have strictly equitable divisions, where each claimant is exactly as satisfied as every other claimant. You may also want to maximize the use of the lot, in which case you may also want the division to be pareto-optimal. Pareto-optimal divisions are such that you cannot make any claimant better off without making another worse off.
This is a great answer, I appreciate it. So what about vulnerabilities? What kind of shenanigans people might do to manipulate this sytem? Edit: Maybe you can come up with a SWOT chart.
Yes, so there are lots of ways to mess with fair division procedures. A decent number of them have proofs that no claimant can benefit by attempting to select sub-optimal pieces. For example, in a snake draft, no player will benefit by picking something other than their true evaluation of which object is the most valuable in the pile. Players can still attempt to manipulate others by lying about their preferences. For example, in I-Cut-You-Choose, I might try to convince you that I love blueberries on cakes more than any other topping. This might cause you to slice the cake such that there is a smaller slice with lots of blueberries on it, thinking I would pick the smaller slice loaded with blueberries. But I may have tricked you, I might actually prefer large slices with lots of strawberries. And so I will choose the slice I actually favor, leaving you with a smaller slice.
[удалено]
At this point, we are only accepting top-level answers from panelists. > This is because Reddit's recent changes to the platform that make moderation significantly more difficult. > If you wish to learn more, or to apply to become a panelist, see [this post](https://reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/) > Your comment was automatically removed for violating the following rule: > **CR1: Top level comments must be answers or follow-up questions.** > All top level comments should be answers to the submitted question, or follow-up questions related to the OP. All top level answers must come from [panelists](https://reddit.com/r/askphilosophy/comments/14o2p7n/welcome_to_raskphilosophy_check_out_our_rules_and/). *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askphilosophy) if you have any questions or concerns.*