Hobbes is another common framework ran in LD. Typically, the standard under a Hobbesian framework is "consistency with the will of the sovereign." Essentially, the standard mandates that citizens must listen to the sovereign (in almost all cases) and says diminishing the power of the sovereign is wrong. Hobbes is very much a political framework, so it concerns itself with the ethics of governmental actions.
To understand Hobbes, one must understand the idea of a social contract. The social contract says that governments and its citizens have an implicit contract with each other that is mutually beneficial. The citizens agree to follow the government and listen to their rules and laws, and in return, the government provides protection and services such as the police, military, public works, etc. Without a government, Hobbes argues that society would devolve into the state of nature, where there would be infinite violence in society. Citizens, therefore, have a responsibility to listen to the sovereign so a government exists that can protect citizens own rights.
Importantly, both the government and citizens must uphold their own end of the contract. If the citizens break the laws of the sovereign, they would not be upholding their end of the contract, and if the sovereign failed to protect the lives of citizens, they would not be upholding their end either. This answers the most common objection to the Hobbesian framework which is that it is morally repugnant. However, the framework is arguably not morally repugnant because if the sovereign is not upholding their end of the contract by violating the citizens' safety and right to life, they would not be upholding their end of the contract, and as a result, a new sovereign could form.
There's a second way that some people justify the Hobbes framework, which argues that the sovereign is necessary for meaning creation. That is, to establish a unified conception of truth, there needs to be one unified body which establishes the standard by which we measure truth. For instance, take a unit of measure like a foot. The foot, in principle, is an arbitrary measurement that has been established as the standard for measurement. However, without the sovereign in place to establish meaning, forming any basis for actions and ethics would be impossible because it presupposes that agents have a common understanding of each other. This argument, while different than the previous one, is similar in that it shows why the sovereign is a necessary facet to promote a just life.
However, the most notable argument against Hobbesian frameworks is that Hobbes technically justifies dictatorships and monarchies over anarchy. For example, Hobbes may have claimed even Hitler was preferable to the alternative of anarchy. Luckily, there are a few key ways to respond to such arguments. First, it is important to clarify that these instances are actually examples of bad social contracts as they aren't really preserving basic human rights (liberties that don't infringe on others). Next, if one wants to run a Hobbesian framework, one must really stick true to the idea that anarchy is the absolute worst type of governmental system and lay out numerous reasons as to why. While Hobbes may argue any government is better than no government, it is possible to interpret this in such a way where one says a good government (one that preserves a stable social contract) is better than any government is better than no government.