If I would start a new governing system, it would be having the next step for democracy.
We have the internet, we trust it enough to use it for nearly all of our banking needs, people are willing to trust it with all of their money. So its about time we also work out a system so that we can trust it with our votes. Internet voting can be made more reliable than paper voting. Sure there are some challenges that need to be looked at, for example find a way for people to actually verify their vote is counted (which we surprisingly don't have right now) while also having ensuring privacy from the state and as much privacy as possible from other people.
Next up, you need to make it that people can easily vote themselves or defer their votes for certain items to politicians of their choice and change their choice whenever they wish.
I want to enable people to vote personally on issues they themselves find very important, but also they could chose a politician per issue (say, business, environment, education, whatever) for any issue they do not personally want to vote for. You think Trump would be great on all but one issue? Have your votes linked to his for all those issues, and vote yourself or give your vote to another politician on the last issue.
Yes, there are still many things to keep in mind that need to be adressed, most of them related to either security of the system (but anybody that thinks that paper voting is not horribly corrupt already is just stupid) or to privacy (in a voting booth, at least you have some privacy of family members that may wish you to vote otherwise, but then again, anybody with power over you could force you to fotograph your voting balot when you selected his candidate of choice, making it so at the most, you can void your vote, not chose who you wish). You would mainly need harsh penalties and a high rate of finding all such abuse to stop it.
I just don't understand why we do not yet have a system in our democracy to allow people to vote themselves on issues they find important. Why do we still accept that we transfer our vote to another person, often for a 4 year+ period. Do you really trust any person to vote exactly as you would or at least in your best interest for 4 years?