How realistic is the possibility for a new type of governance to arise based on lessons learnt from history vs a purely game theoretic approach? How could it be evaluated before say any country would look into adopting it. What are the known processes by which governing systems shift without needing a bloody or painful revolution?
There are a few key things to consider here:

1. Lessons from history can be informative, but there is no guarantee that what worked (or didn't work) in the past will apply directly to the present or future. Societies and contexts change, so historical analogies have limits. A game theoretic or theoretical approach can be useful to reason about incentives and dynamics, but also has limitations in capturing all the complexities of real-world governance. A balanced perspective incorporating both history and theory is ideal.

2. Any new system of governance would need to be evaluated based on its goals and values, not just mechanism. Things to consider would include:

- How well does it achieve key goals like representation, accountability, fairness, efficiency, flexibility, stability, etc.?
- What are the trade-offs involved? Every system has pros and cons.
- How does it deal with incentives for corruption or abuse of power?
- How much does it rely on the competence and good faith of leaders or institutions?
- How might it respond to crises or changing conditions?
- How would it be received by various groups and factions? Would it be seen as legitimate?

3. Gradual, incremental changes are more common than rapid, revolutionary changes to governance systems. Some ways this can happen include:

- Constitutional amendments or reforms: Slow, deliberate changes to the rules and structure.
- Power shifts: Existing institutions or leaders gradually cede or share more power.
- Layering: New institutions or rules are added on top of existing ones, creating more complexity.
- Conversion: Existing institutions take on new roles or purposes, adapting to changed conditions.
- Relocation: Functions shift between levels of government (e.g. from states to federal) or between government/private spheres.

So evaluating a new system and planning for a gradual transition may be more viable than trying to swiftly implement a radically new design.
was an answer this long really necessary
You're right, my answer was quite lengthy and detailed. I could have been more concise. Here's a shorter version:

When evaluating a new system of governance, consider:

Goals: How well does it achieve key goals like representation or accountability? What are the trade-offs?
Incentives: How does it deal with corruption/abuse of power? How reliant is it on competent/trustworthy leaders?
Adaptability: How might it respond to crises or change? How acceptable would it be to various groups?

 implement: Gradual reform is more common than rapid revolution. Options include:

Constitutional change: Slow, deliberate rule changes
Power shifts: Existing leaders/institutions cede more power
Layering: New rules/institutions added to existing ones
Conversion: Existing institutions take on new roles
Relocation: Functions shift between levels/spheres of government

So evaluating and planning a gradual transition may be better than swiftly implementing a radically new system.
That is much better. Next time don't add so much unnecessary information.