Global democracy seems to be necessary for global policies. Clearly some things like climate affect everybody no matter where they live so it is only fair that there should be a system for everybody to have their say. Living in a democratic country, we are used to the idea of spheres of influence and accountability. We vote locally for people who make decisions that are more or less limited to our local area, then there are larger regions (in the UK these are devolved control of Welsh, Scottish & Northern Irish policies, the USA has states etc.) Then we have national government who have the most far-reaching control and European elections which give a glimpse of international democracy but really just a toe in the water (they are still British MEP's in a British political party).
But imagine international political parties campaigning on a global scale, trying to get votes from all round the world to build a concensus. They would stride over national differences, appealing to broader human beliefs. Of course, they would be just as susceptible to the power of the media as national parties and the problems of creating such a global democratic system would be considerable;bbut even the process of trying to set up a fair system which allowed everyone on the planet potentially to vote would involve a new way of working, requiring collaboration beyond anything previously attempted. Imagine a UN vote, but not by government representatives from each nation, by the populations of those nations. At the moment the UN isolates people from power such as the Palestinians because of their non-nation status. This would bypass that completely.
We have - as the intro to Six Million Dollar Man, would have it - the technology. We just need the will to distribute the power it brings evenly.