Wealth, influence, and firepower are the three elements of the trinity of power. Wealth ultimately translates into resources, influence translates into the capacity to brainwash people, and firepower translates into the capacity to do damage. Wealth is at the top, because without wealth, influence and firepower are worthless.
You need wealth to survive. Also, you need wealth in the first place to acquire the other two, even if it's not that much, especially in the case of firepower. An M16 only costs about $800, and if a good 5% of the population were armed with M16s, the power dynamics would strongly be in favor of the common person. Democracy doesn't matter that much, since you can buy votes with influence you acquire through wealth, but power dynamics do. A non-democratic government would still be kept in check if the power dynamics favored the common person through, at the very least, firepower.