How to equitably divide the economic benefits of a licensed patent among academic inventors? I am PI of a research group and in different projects regarding sample analyses, it looks like we will be able to license 4 patents to 4 different companies. I can tell you this success was not neither expected nor planned. And now the problems come; the money we receive from each patent, how to distribute it among the different participants. In order to avoid problems, I decided to distribute it equally between the number of people involved on each patent, which varies from 5 to 7, including me. 

But some people are disappointed because they consider that other people did much less and should receive less percentage. In addition, I do not like this completely since I got all the funding for the projects, infrastructures and negotiate it hard with the companies, so I think I should deserve it a bit more, but I know that with this I will have problems in the group. Of course, I should have written everything down, the regulations, before starting the projects, but now it is too late. In order to solve this I thought about preparing a document, in which everybody writes down what they think they did, and how that part contributed to the invention. Then I think we could start a reasonable discussion, so people that did less, could not say the opposite, and finally we would reach an agreement. Another solution I thought would be to leave my University to decide on this. 

My questions here is, how would you solve this problem, and if you think (and why) that a PI should get more part of the contribution.
(Expanding a bit on Buffy's answer)
Short answer: Use some math to make everyone happy.
This is actually a well-explained problem in economics for which there is a solution.
It is possible to mutually assess everyone's contribution, without anyone unfairly boosting their own contribution, so that the proceeds are distributed in a way that everyone is likely to be satisfied with. This is, as Buffy said, a type of cake-cutting algorithm.
A Tool
If you'd like to skip the theory and go straight to a solution, check out spliddit.org/apps/credit. They provide a web app for everyone to subjectively assess everyone else's contribution and computes the fair proportions. The theory behind it is pretty clever, and you will likely find that everyone finds the splitting to be satisfactory.
A Theory
If you're looking for a more principled answer (other than &quot;try this tool&quot;), here's the paper that describes the theory and method used by Spliddit in rigorous depth: Impartial Division of a Dollar - Clippel, Moulin, Tideman
The method satisfies two formalized criteria:
Impartiality - no one assesses or covertly influences the assessment of their own contribution
Consensus - the ultimate division is compatible with every individual's assessment of others' contributions
Good luck!