The LFR's ideologies have to do with the "All Men Are Free" concept. The government postitions help ensure that when the leader is unexpectedly missing, as Lord Civius is now, there will always be a second-in-command.
The members of the LFR decide who is the most fit to run, and since there is a government srtucture it is not so anarchist. With every three turnchats comes a new President elected, plus his advisors. This maintains order without coming to extremes. The elections will be regulated, and the President will make sure that they are polled when they are needed. The President may be impeached by the vote of the people. The President appionts a Vice President, the VP appointes a Secretary of the States, and so on.