alternatehistory.com

Let’s say Constantine’s (or an alternate emperor in a similar position and context) sons all die due to ordinary reasons while their father is still going strong, except for one, whom Constantine (or our alternate emperor) comes to see as an idiot.
At this point, introduce a random philosopher that says something to the effect of:

“What will happen to Rome when you die? Will your son take over, even though you yourself described him as unfit to rule? And how will this new emperor come to power? Let me tell you, he’ll do it just like most of the old ones, by promising money to the legions and powerful backers and then defeating rivals who have done the same. But the legions are like a spoiled child, who may be satisfied by one sweet today but will require two the next day to keep from crying. So would-be emperors will constantly give out more and more money to the legions upon accession, until we reach the point where they won’t be able to any more, causing the legions to support another, who either out of ignorance or malice will promise them what they want to hear, leading to wars upon wars.

And since an emperor’s power is based on bribing the army, the moment he won’t be able to pay them due to a calamity or another, the army will turn on him. And so we get more and more civil wars until there is nothing left. You may think that the way is to make everyone accept that it is natural for an emperor’s son to succeed his father, thus averting civil wars. However, if that son is an idiot, there will surely follow great disasters for the state, until you have the army revolt and support someone promising them more and more money, and so we return to the point from where we started.
But even if that son where not stupid, who is to say his son won’t be? And won’t he be a king in all but name, something our ancestors have constantly warned us against, as kingship naturally leads to tyranny?

Why not then introduce a system, whereby the power of an emperor resides not in the support of the army, but in that of the people? Why not have the people choose between different candidates the best among them, and create rules and conventions whereby everyone accepts the winner as legitimate, with the promise that they can vote him out of office in a few years’ time, should he prove unworthy of his position ? You thus avert civil wars and expensive bribes to the army, and also ensure a succession that isn’t dependent on the whims of fate providing an emperor with a capable heir. Wrapping the whole process within a religious context will also make it much more acceptable to people and less likely that they abuse it.”

Our emperor becomes convinced in the basic merits of the system. He is adored by the soldiers and is lucky as hell in dodging assassinations. How does he go about introducing democracy? Can he, under any circumstance, succeed? (my guess is no, as you need an early modern state for genuine democracy to work). What are the potential butterflies of this (failed) experiment with democracy, assuming the empire still falls ?
Top