The purpose of an argument is usually to sway belief. A political argument can occur in the context of political theory; for instance Machiavelli's The Prince can be regarded as advice to rulers based on various kinds of arguments. Political argument though is not generally a purely intellectual activity, since it may also serve the strategic goal of promoting a political agenda. One usually thinks of political argument as exclusive to democracies, but in fact, some kinds of political argument may occur in undemocratic regimes as well, for example, to encourage greater sacrifice from the population, although it is more likely in such cases that propaganda will take the place of argument. 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. Moreover, the institutions of democracy in part define the relationships between beliefs and power. In this case, political argument is an important element of political strategy. It is also possible that in a democracy, propaganda may also replace argument; indeed, much political advertisement has no discernible logical structure, and in our definition falls under propaganda.
This view of political argument in a democracy is closely related to the problem of social choice. Consider a social decision model of the kind used in the theory of social choice (such as used in stating Arrow's theorem). In this model society has a set of individuals X and it faces a set of (political) alternatives A which need to be ranked in some way. A ranking is a relation R between the elements of A which is transitive and reflexive. Two alternatives a, b can satisfy a R b and b R a. If this is the case, we say R is indifferent to a, b. Each individual x in X will have an idiosyncratic ranking Rx of the alternatives in A. A profile is any function P that associates with each individual x a ranking of alternatives Px; a profile is thus a function from X to rankings of A. An arbitration scheme (or constitution or voting scheme) is a way of producing a ranking Rsoc for the whole society from any profile P. Thus an arbitration scheme is itself a function P → Rsoc.
Though any argument about politics is in a sense a political argument, an effective political argument is one that can actually change the social preference ranking. Effective political argument is a concept distinct from valid political argument.
Consider an idealized system of tax policy; tax is based on a tax cutoff point T, that is individuals with income in excess of T pay taxes, and everyone else pays no taxes. 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.
A political argument may be ineffective but may still have a purpose, for instance as a justification for an unpopular political action, or as part of a historical narrative.
