Love your use of “expected damage” in your analysis.
Here are some observations and a thought experiment and I hope you won’t be bored by it.
1) The transfer of power in a dictatorship can be “messy”
2) It will take some luck for a good dictator to transfer power to another good dictator.
3) A bad dictator can transfer power to his/her offspring or sibling (e.g. North Korea, Cuba) or simply be overthrown by another bad dictator
4) we may get lucky and have a few good dictators but once we get one bad dictator, the risk is that we will stuck with quite a few bad dictators in a row because of #3.
(note: I am sure there are some fancy stats/probability expression/formula that can be used to say what I said in so many words. (smile))
A thought experiment
Taking your transaction cost ranking as a given for a moment,
Good dictator (GD) < Good elected leader (GEL) < Bad elected leader (BEL) < Bad dictator (BD)
and combined with the idea of “expected damage” and the observation of good dictator can turn into one after another bad dictators (for a long time)
For me, a revised transaction cost after taking consideration of “expected damage” (over time) and the chance of Good Dictators turn bad and stay bad (over time),
E (GEL) <= E (BEL) < E (GD) < E (BD)
note: I assumed there is no cross-over between democracy and dictatorship. (which sometimes happen unfortunately)
P.S. Hmmm, I don’t know if the above makes any sense at all. Love to see my fellow lunchers’ comments.