The small business class is famously the most conservative in society. They are the backbone of anti-democratic movements, and the supporters of dictators. Even in very democratic societies, they like leaders who act, and regard political negotiation as weakness.
One of the solid findings of happiness research is that we hate loss more than we like an equivalent gain. We continue to be anxious about possible losses, but quickly get used to sizable gains.
I believe the petite bourgeoisie favors the strongman because their own economic position feels perpetually precarious. They have a little and hate to lose it. They fear the poor - whom they tend to regard as lazy, dependent, and undeserving - as coming for their stuff. Democratic politics, which tends to give something to every group of potential voters, is dangerous because it enables and encourages the poor. Strongmen are better because they don't have to give any group anything.
Once again, fear appears to be the great solvent of a happy, trusting society.