C.G. Jung once wrote that it was totally clear that the amount of conscience of a group of people is inversely proportional to the size of the group. So, if countries are like people they mostly are like psychopaths.
I think the difference in sizes between the organizational groups of different countries goes a long way towards explaining the vast differences in political flavor. How many people are in the smallest political constituency you identify with? Dozens? Hundreds? Millions? This is the range of scales we're dealing with.
What would it look like if we layered government so that at no level was any group larger than tribal size (~150)? In the US you'd only need 4 levels to cover the entire population, roughly corresponding to: neighborhood (150 people), town (~20,000 people), city/state (3-4 million people), country (327 million people). At that scale, each representative can be on friendly personal terms with a) everyone in the constituency they represent and b) every other representative at their level. So the access to government ought to be much better with this system. In the US, local and federal governments are divided - there's not a lot of continuity between the town government and your friendly local congressperson.
Related the disturbing root of the problem has been historically been not just the leadership that is objectively terrible and accepts bad outcomes for the sake of hurting the other but that frankly the people and the values they hold dear. Storm Thurgood even admitted that he tried running on things which would actually help them and got no real interest but running on racism propelled him forward.
For the US Senate, N=100 and IQ = 50.
Do you have any rules for nested groups?
A nested model may be difficult because at N=10 or less, the IQ depends a lot on the selection of the individuals and their fit with the tasks to be undertaken.
A nested governmental organization would be a good idea, and that is my impression of how the US worked early in its history. The voters would elect town officials who would elect county officials who would elect state legislators and at least in the case of the Senate, the state legislators would elect US Senators. Ideally the electors at each level would be able to assess the abilities and character of candidates and the cream would rise to the top. This is sort of how the two political parties still work, although the modern methods of getting elected and penchant for direct democracy enable candidates to run for offices without working their way up the party, e.g. Bloomberg.
That kind of math led to the greatest financial collapse in world history.