Please give an example of the interpersonal influence tactic of "use rational persuasion."

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When you try to persuade, you usually appeal to one or more of the traditional rhetorical techniques for argument and persuasion: logos (appealing to logic); ethos (appealing to an ethical or belief system); and pathos (appealing to emotions). In any context in which rational persuasion is used, it can only work if it is fact-based. In business, the appeal to logos is often deemed rational persuasion—that is, persuasion that avoids emotion and even belief systems and relies on logic, facts, and well-thought-out, reasoned approaches to any given problem or task. In most cases in business, rational persuasion is the technique used by teams to decide how to or even whether to achieve a particular goal.

If you have a team, for example, whose job is to either accept or reject a new business endeavor for a company, the leader often begins the rational persuasion by asking the team to use what is called a SWOT diagram or analysis as a starting point. The SWOT analysis—which stands for Strengths, Weaknesses, Opportunities, and Threats—encourages rational responses because, by its nature, a successful SWOT analysis can use only valid, verifiable, known information. An emotion-based response, like "I don't like this kind of business," will stick out like the proverbial sore thumb. Under the Strengths category, for example, let's say that a team member says, "We'll make a boatload of money." That, of course, is an emotional response, and the leader would probably ask someone to find out what a reasonable market share might be for the company and what the total market is for that business.

Although rational persuasion is useful in any context in which persuasion is the goal, in business is it particularly important because, if used correctly, it avoids the subjectivity created when people act or make judgments on the basis of belief systems or emotions.

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Since you have asked this in the business section, I will give an example from the field of business.  The basic idea here is that this tactic involves trying to use logic and rationality to persuade someone rather than doing something like trying to use emotional persuasion.

So, for example, imagine you were doing a presentation to your bosses, trying to persuade them to make a change in your firm's processes.  You would provide statistics about the problems that you think the firm has and you would then give a logical explanation of how your solution would solve those problems.  This would be an example of persuading through rationality rather than emotion.

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