How about
Geniocracy
Rule by the intelligent; a system of governance where creativity, innovation, intelligence and wisdom are required for those who wish to govern. Comparable to noocracy.
Timocracy
Rule by the honourable; a system of governance ruled by honorable citizens and property owners. Socrates defines a timocracy as a government ruled by people who love honour and are selected according to the degree of honour they hold in society. This form of timocracy is very similar to meritocracy, in the sense that individuals of outstanding character or faculty are placed in the seat of power. European feudalism and post-Revolutionary America are historical examples of this type; the city-state of Sparta provided another real-world model for this form of government.
Plutocracy
Rule by the “haves”; a system wherein governance is indebted to, dependent upon or heavily influenced by the desires of the rich/ensconced. Plutocratic influence can alter any form government. For instance, in a republic, if a significant number of elected representative positions are dependent upon financial support from wealthy sources, then it is a plutocratic-republic.