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Some people are very emotionally prone. They experience strong emotions and then tend to think with how things make them feel. These are the kind of people that share lots of returning-soldier-reunited-with-dog videos on your Facebook wall. For these kinds of people, when you talk to them use language and arguments that play to their emotions in order to convince them. In the study of argumentation, this is called appealing to "pathos." For example, make them feel sorry for you. If you're trying to convince your mom to let you go to summer camp, say something like, "I just don't want to stay home all summer while my friends are away. I get so sad when there's no one around." People whose emotions are easily swayed tend to be vulnerable. Think carefully about the effect you'll have if you succeed. Are you comfortable causing regret or panic to get what you want, or will that spoil your victory? There are other people (and sometimes these two groups overlap), that like arguments that hold up to logic. They want evidence and good reasons to line up before they'll be convinced. These are usually the people that post news stories refuting the latest Supreme Court decision with evidence of its negative effects. When talking to people like this, use logic in order to appeal to them. In the study of argumentation, this is called appealing to the "logos." For example, convince a boss to give you a sabbatical by listing the job-related skills you'll learn, and showing studies that breaks make employees more productive. With just about anyone, use language that makes them feel capable, confident, smart, knowledgeable, important, and kind. Using subtle, flattering language will make them like you more but it will also distract them. If they're too busy thinking about how good they feel to get a compliment that they really like and weren't expecting, then they won't think about how your argument doesn't make 100% sense to them. For example, say something like "You know, I'd like to be the speaker for our presentation but I feel like I would just say everything wrong. Probably freeze up too. You're just so much better at talking to people and making a convincing argument than I am. You'd probably have the whole group eating out of your hand." Women have been saying for centuries that the best way to get a man to do something is to make him think it was his idea. However, this is basically true of anyone. If they think that not only is the idea probably good but that it was also their idea, then they'll be much less resistant to doing that thing. For example, say something like "My poor friend Dale is such a good guy. It's a shame he never seems to catch a break. He's got so much going for him too: he works so hard and he's really smart. He's even charming, really charming, once you get to know him." if you want to try and get them to realize that they should hire/date/whatever Dale. They'll hear this fantastic description and think, "You know, he doesn't sound half bad. Maybe I should..." This shouldn't be your first stop, but planting concern in someone's mind can be a very effective technique. Use language that plays to their worries, or that suggests the decision is time-sensitive. For example, say something like, "You know, I heard they're not going to be making these any more. If you want one, it's probably better to buy it now, before you have to spend three times as much on eBay in order to get one." This kind of language and persuasion should be your last resort, because you usually only get to do this once. People quickly figure out that you're just fear-mongering in order to get what you want, and then they won't trust anything you say. This kind of reputation can spread as well, so be careful.
Appeal to emotions. Appeal to logic. Flatter them. Make them think it was their idea. Cause someone to worry.