My ideal would be a global government staffed by representatives who would themselves governed by their constituent regional councils, that themselves would have representatives that would be governed by direct democratic constituencies. In short, any representative would be directly ordered by the people they represent.
Not that it's compatible with the current system, but it's a nice thought to have.
Anyway, given that globalism is our current reality now, we need the development of democratic power that surpasses the national level. I think so particularly because our system of relationships currently doesn't have any sufficient constraints upon oligarchy on a global level. After all, the reason that the welfare states of old were replaced was because the capitalism that they were organized to contain outgrew them. So even as the world was unified, it was not integrated on a representational level, which meant that capitalism could run free without the democratic restraints which bound it on a national level. This in turn increased income inequality, reduced trust in the democratic order of many countries, and increased supremacist extremism as a result.
I imagine, therefore, that the powers of democratic representation, and the constitutional bindings which keep them democratic, should expand for the sake of a peaceful, integrated world. How so. I've got no clue, but given that it is my belief that capitalism is an anti-democratic force by the nature of its organizational structure and paradigmatic logic, I conclude that we ought to create supranational public organizations that further unify the world, not in the sense of private capital interests but through policies conducted by democratic representation (and ideally, direct democracy, though that seems far fetched for many).
Others may disagree that capitalism is incompatible with democracy, which is a perfectly fine position, but consider this: corporations are organized dictatorially, with bosses holding direct power over their private organizations. When their private interests are applied to government, the logical result is the perpetuation of oligarchy, not democracy, as their position in the social hierarchy automatically grants them special leverage over the represented officials. Case in point, oligarchy is what usually happens under unrestrained capitalism, because by dint of private interests being placed over communal mandates the government assumes an oligarchical structure.
We need effective public democracy on a globalized level, the constitutional base to give it weight, and the institutional power to make informed democracy effective, especially if we are to effectively combat the anti-democratic, ethno-nationalist, and white supremacist ideologies which assail us. With such effective representation, people's needs can be given voice against oligarchs and supremacists alike, who thrive on ignoring the rules of democracy for their own ends. Democracy should be resilient as the organized manifestation of the people, and to be resilient, asides from constitutional boundaries on acceptable actions (like, no nazis, no persecution of minorities, no hate speech as a political tool, no ending the democracy you're running for, etc.), it needs legitimacy from the people and popular participation to make it legitimate.
Whether you believe that capitalism can coexist with democracy when contained by the mandate of the people, or if it needs to go to ensure effective democratic control, it is easy to see that democratic representation and legitimacy on a globalized level is what can combat the disparities and injustices of our world and the tyrannies and hateful ideologies which arise from them. We need this, too, or something like it, to face the existential problem of climate change.
Edit: in other words, global public entities with democratically controlled power that constrain or replace capitalism. I would personally imagine it as a form of globalized socialism.