As noted above, our global democracy requires a grant of authority from countries at the outset, by treaty, to handle matters that can only be addressed globally. These include climate change, taxation & redistribution of wealth, human rights including free movement of people, nuclear disarmament & demilitarization, extending education worldwide, and disease response.
This is a broad mandate. It may at times come into conflict with the desires of national or local powers; when it does, we all must understand that the global layer must prevail if it is to accomplish its mandate.
A helpful historical analogy with respect to conflicts between different layers of power is the racial desegregation of US schools beginning in the 1950s. To enforce a constitutional decision by the US Supreme Court, President Eisenhower deployed the US military to assert federal authority over the defiant governor of the state of Arkansas.
Nonetheless, our principle of subsidiarity dictates that every decision must be made at the most local level capable of addressing it. Under this principle, many decisions will be properly left in national, state/province, or local hands.
Our primary mechanism to prevent the abuse of power is the global constitutional court. Its role is to upholding global constitutional rights in the face of potential threats from majority voting, or from overreach by global enforcement authorities, or from actors within any country.
All our global elected officials, including constitutional judges, enforcement officers, and question framers (including translators) are subject to recall by popular supermajority vote.
Today, countries have the option of initiating war in response to grievances (or otherwise). We are phasing out war, for the betterment of all humanity.
One final form of power that may be abused is often called “star power”: the ability of famous individuals to command attention. Consider a scenario in which a celebrity exploits their fame to call for liquid democracy proxies, then uses those proxies to vote in ways that undermine the public interest.
We have plenty of recourse in this situation. First, proxies can be revoked and reassigned instantly, as voters see the celebrity voting against their interests. As noted above, depending on a design choice, voters may also be able to directly reverse votes cast by the celebrity proxy.
Most importantly, the entire citizenry is highly empowered, through liquid democracy, to participate directly in formulating and approving policy. Nobody is shut out. This will help counterbalance the power of celebrities.