More often than not, political arguments tend to be circular, repeating the same facts as premises under perhaps slightly different guises.
A classic example of political arguments is those contained in The Federalist Papers arguing in favor of ratification of the American constitution.
In a democracy, though, political argument is particularly important, since there is a direct relationship between the beliefs of citizens and the structure of power.
This view of political argument in a democracy is closely related to the problem of social choice.
In a simple majority rule social arbitration scheme, one might expect that a natural tax rate T can be determined: the median income (plus 1).
However, a (possibly fallacious) political argument might attempt to change an individual's voting by their pocketbook by arguing that investment in capital and general welfare will increase by reducing taxes on higher income levels, which is raising the tax cutoff point.
In the case of arguments used in politics, this something is an assertion about an element of the public sphere, such as economic policy, the environment, decisions about war and peace, abortion, etc.