I’ve been interested in this topic in the past, especially from the economics / game theoretic perspective. There’s one journal I know of that explores this topic that might be worth looking into:
The Journal of Mechanism and Institution Design
http://www.mechanism-design.org/
Mechanism design in this context being the kind of inverse of game theory that starts with a desired outcome and designs a system that produces that outcome, as opposed to the traditional approach of game theory where you start with a system and figuring out the outcome. More info: https://en.wikipedia.org/wiki/Mechanism_design
I also think this topic of ideal governance & mechanism design has a lot of overlap with the field of cryptoeconomics, or the economic analysis of how cryptocurrencies work / enforce behaviors via incentives: https://policyreview.info/glossary/cryptoeconomics
If you’re curious about cryptoeconomics more in depth, Tim Roughgarden out of Columbia has an excellent lecture series on the topic: https://www.youtube.com/channel/UCcH4Ga14Y4ELFKrEYM1vXCg/playlists
Some more general literature that might be of interest to you:
The Dictator’s Handbook: Why Bad Behavior is Almost Always Good Politics
https://en.wikipedia.org/wiki/The_Dictator%27s_Handbook
The Logic of Political Survival
https://en.wikipedia.org/wiki/The_Logic_of_Political_Survival
Both these books are by the same author(s) and provide a solid intro to the Selectorate Theory of politics (https://en.wikipedia.org/wiki/Selectorate_theory) which also provides a framework for answering some of the questions you posed regarding things like the ideal number of representatives.
Hope this helps!
I’d pay a lot of money for an app like this. I wonder if recent development’s like Google’s MedicalLLM could come into play here, where all your symptoms are logged and then expert knowledge / a thorough review of medical literature is done automatically to recommend potential solutions