@sabahat

the easy and clear order about the administration of the country by Allah in quran is that

"beshak Allah tumhay hukam data hy k hakumat ba-ahel (eligible) logon k hawaly kro"

if we follow only this rule in all the fields of our country then you can see the golden era of our history again just like the period of Hazrat Umer (R.A) .
this is the only rule of a successful political system. the reason of success of pious caliphs is only this and in present time we also get our goal through this single rule by applying it although in present political system.

and if you want any example about political system in islam then you have the
"first walfare state" established by Holy Prophet(PBUH) in madina. first written agreement in shape of "charter of madina" first diplomatic principles in shape of "hudaibia agreement" first delegation assingment in shape of "letters to the heads of other nation".

all the points which are essential for a best political system are not only introduced but also implimented by our beloved Prophet(PBUH) just like justice ' equality' rights and walfare of the people . and along with it "democracy" is also another element introduced by Holy Prophet(PBUH). as He says

"dunya k mamlat ma tum mjhe mashwara da dia kro "

and Allah also says

"aur kamo ma apis ma mashwara kr lia kro"

so we can see that we have all the rules and examples of a successful political system the need is just to follow it witout any prejudice.

regards