Perfectly fair != fun
Strongly biased against you != fun.
Any system you implement is guaranteed to piss off some element of the player base. Make it based on:
- Prestige, or time in realm: you'll be accused of setting up a good-old-boy network designed to lock out the newer players, and solidify existing power blocs.
- A one-day run-off: You'll piss off people who weren't able to log in on that day. Or people who don't like having to log in on a specific schedule. Or can't make it early in the turn change, so can't get their campaign speech out fast enough to sway votes their way. (And you'll probably be accused of violating the IRs against activity, too.)
- Honor (and prestige, too, but not as much): You'll piss off the people who enjoy playing priests, courtiers, traders, and other non-combat roles.
And just to let you know: we've seen all these complaints before, over the course of several years. We're not just pulling crap out of our asses.
Random selection may not be the preferred choice of everyone. But it has one major, undeniable advantage: It's a simple, transparent mechanism that everyone can understand, and
most people can see the logic behind.