The proportional rule is normally used in law nowadays, and is the default assumption in the theory of bankruptcy.
The estate division problem has a large literature and was first given a theoretical basis in game theory by Robert J. Aumann and Michael Maschler in 1985.
This is a problem of dividing identical indivisible items (the seats) among agents with different entitlements.
The allocation of seats by size of population can leave small constituencies with no voice at all.
These power indexes assume the constituencies can join up in any random way and approximate to the square root of the weighting as given by the Penrose method.
This assumption does not correspond to actual practice and it is arguable that larger constituencies are unfairly treated by them.
Aziz, Chan and Li[11] adapted the notion of WMMS to chores (items with negative utilities).
They showed that, even for two agents, it is impossible to guarantee more than 4/3 of the WMMS (Note that with chores, the approximation ratios are larger than 1, and smaller is better).
This fairness notion is called Ordinal Maximin Share (OMMS) by Chakraborty, Segal-Halevi and Suksompong.
[14][15] Babaioff, Ezra and Feige[16] present another ordinal notion, stronger than OMMS, which they call the AnyPrice Share (APS).
Aziz, Moulin and Sandomirskiy[17] present a strongly polynomial time algorithm that always finds a Pareto-optimal and WPROP(0,1) allocation for agents with different entitlements and arbitrary (positive or negative) valuations.