Writing an argument paper requires using the persuasive style of writing, and writing an argument paper well requires using the persuasive style of writing effectively. While persuasive writing can be considered a style in and of itself, the types of arguments to present are as different as the ways to present them. For an argument paper to effectively change people's minds, it should use a little bit of the wisdom from each style.
The ancient Greeks referred to fact based arguments as "logos." When arguments are based on scientific studies or statistics, they fall into this category. When using this type of argument, the facts must take centre stage. However, you must be sure to lead the reader toward the appropriate conclusion. For example, after providing factual data about a political candidate's voting history, the reader should be tipped off to the fact that this past makes the candidate untrustworthy.
Arguments that are based on the reliability of an individual or a group are referred to "ethos" based arguments. Sometimes these come from statements of support, such as when a newspaper gives support to a particular candidate. Ethos based arguments can also be combined with factual arguments by using authoritative sources. Consider the difference between "My sister forwarded me an e-mail that Brandless Cola is adding nicotine to its products," and "The FDA has tested Brandless Cola's products and found nicotine in many."
The Greeks referred to emotional arguments as "pathos." While no one wants to admit that he makes a decision based on his emotional state, this kind of argument is always an effective addition. Anecdotes, or short personal stories, are the easiest way to integrate an emotional argument into a piece of writing. When discussing the importance of special education programs, for example, you could win hearts and minds by incorporating anecdotes of Albert Einstein's early troubles in school and his mother's efforts to help him.
The classical structure opens with an introduction that gets the audience's attention and builds its trust in the writer. The narration follows, sometimes in the same paragraph, and gives background information that is necessary to understanding the argument. The confirmation is what most writers consider the body of the piece; it outlines and supports each claim of the argument. Refutation and concession follow the confirmation and anticipate objections from the audience. The summation brings the entire argument together into a strong statement.
Rogerian argument is not a type of argument per se, but a structure applied to the argument. Rogerian argument has its roots in psychology and emphasises the common ground between the two sides of an argument. This kind of structure uses concession as a way to open the minds of people that might disagree with an argument before presenting the support for that perspective. The arguments that follow in Rogerian argument are generally more in the "ethos" and "pathos" styles.