First, I have deliberately pointed towards election methods adopted in beginning of Islam. It is a sacred period for all Muslims so i have avoided going into detail. I do not want to spark any kind of controversy here. The point is that no structure of any kind regarding Political system was given.
Second, as far as qualities of " Justice, Fairness, Equity, Social security etc etc " are concerned, these are present in every religion, in every society, in every country. Which school of thought support bad things? Take constitution of USA, England, France,,,any country, or law of any country, They all support justice, fairness , equity. No one is in favour of Injustice, crime or bad society?
So the conclusion is that there is no such thing as Islamic Political system.