I tried to run an experiment on it by having a different luck parameter for each mayor and then keeping stats, but once the adoptee aged beyond 16 it became almost apples to oranges comparing a 2 week mayoral tenure to one half as long, especially as the maturity of the game came into play. Early mayors spend more money on projects, for instance, and the first mayor makes much less on Mrs. M's quests. If I ever get a mature game that I'm just coasting along in, I'll try it again.

I assume that luck parameters (and rabbits' feet, and the fortune telling lady) make small changes in your luck with something but don't make you omnipotent.