Persuading people isn't (only) about presenting relevant facts and showing how your conclusions follow from them: your chances of success depend far more on how you present your case than on its merits from a formally scientific and logical perspective. There are several reasons for this, but fundamentally it arises from the fact that people aren't, in fact, formal logical systems. Rhetoric is the art of presenting your case in such terms as actually persuade, as distinct from being right. I'm no expert on rhetoric, but here are some notes related to it.

Why logic isn't enough

One reason is simply that people necessarily make at least some decisions where the facts of the situation aren't adequate to establish a formally proven right answer. Some of the facts needed for a decision are unavailable; or the situation isn't well enough understood to even allow one to determine which facts are needed. People used to making decisions where the prerequisites of rational analysis are absent develop skills that produce reasonably good decisions despite that; when they're adept at applying those skills, it makes sense that they sometimes use them even when rational analysis is an option.

Another reason is that some of the available facts are statistical in character; the formally right answer is, at best, the choice which maximises the expected value of some desirability parameter. On the one hand, human intuition is remarkably poor at dealing with probability theory – a fact that every confidence trickster has milked. On the other hand, statistical truth always leaves some lee-way for getting (un)lucky – so there's a degree to which it may actually be rational to deviate from the formally right answer in a direction motivated either by hope or by caution. On the gripping hand, there are often many other parties whose decisions shall affect the outcome; these are typically in a similar position to oneself; and so a strategy which seems best on the basis of available statistics may fail because of complications arising from interaction with the strategies pursued by others, who are acting on the same information as oneself. Sometimes, a strategy which is superficially sub-optimal wins as long as enough others pursue it (using an insecure and poorly designed operating system may work out well if enough of those you interact with via computer are using the same system, for example); sometimes, an apparently good strategy's value is heavily undermined if many others also pursue it (if many guys court the most attractive young woman, all but one of them loses out relative to the guy who pursued a marginally less appealing lass that they were all leaving unattended).

It should also be borne in mind that many people mistrust logic. This is not so much because logic is flawed (or, even, that they think it is) as because they've noticed that they can't use it reliably: they have discovered that, with their limited skill in logic and the limited information at their disposal, they sometimes get tricked into sub-optimal actions – either by their own mistake or by some trickster fooling them. Consequently, it's entirely rational for them to not be persuaded by an argument which, 'though entirely sound and correct, they can't follow with enough confidence to be sure that they've not been lead astray. This, sadly, leaves them open to tricksters who know how to present an argument that seems simple – so that it doesn't trigger their doubts about their competence to evaluate its correctness – but which, in fact, subverts their limited skill in evaluating logical arguments.

Furthermore, there are situations in which mildy illogical behaviour can work out better than fully logical behaviour; or, at least, the extent of our ability to rationally analyze the costs and benefits of our actions does not reach far enough to agree with choices we intuitively trust. Ultimately, this is properly reducible to the factors above; but, in practice, we must accept that no amount of understanding of the scientific and logical details shall ever make our intuitions utterly redundant. The best examples of how such intuitions inform our actions fall under the heading of altruism: there are (typically long-term) effects which cause there to be advantages to oneself in being generous to others; yet those effects tend to be nebulous and hard to quantify, hence they tend to be left out of rational analyses of costs and benefits.

One may object that this is simply a failing of the analyst's competence in applying rational analysis: if we took proper account of all the complexities, our rational analysis would agree with our intuitions (when they are right) and might well do better than them in some cases (particularly in novel situations). The objection is, as far as it goes, fair: yet it also serves to illustrate that, however much one takes into account in one's analysis, there may be subtleties and complications one has missed – which is a rational ground on which folk may mistrust a rational argument. Furthermore, taking into account the vast range of long-term and subtle factors involved greatly increases the resources (of mind and time) needed to perform the cost/benefit analysis needed to reach a rational conclusion: those resources may be unavailable. Even when they are, they're a cost, so a rational cost/benefit analysis of the process of applying rational cost/benefit analysis may conclude that this cost outweighs the gains – relative to simply trusting one's (cultural and genetic) instincts and intuitions – of doing the cost/benefit analysis thoroughly enough to empower better decisions.

For at least these reasons, many folk need more than just a rational (let alone logical) argument to sway their opinions and decisions; and often folk shall trust some non-rational motivation in preference to a rational one. Consequently, those who wish to persuade others need to understand what else is involved, beyond rationality.

What else matters ?

There are various well-documented features of how human minds work that bear on what is – and what isn't – effective when it comes to persuading people.

It's fairly well established that people are selectively attentive to details. In particular, not and similar reversal terms tend to escape attention. If you tell people to not eat fatty foods, they remember to eat fatty foods (hey, I like bacon); you need to tell them to eat vegetables and fish, without ever mentioning fatty foods, to get them to improve their diets.

A clear and simple argument, even if technically flawed, is more apt to persuade (most folk) than the complex argument you'll end up with if you repair the technical flaws in the simple one. Unfortunately, the same holds true for a simple argument whose technical flaws are irreparable because, in fact, the argument is wrong: still, the simple argument shall tend to persuade more folk than the complex argument that shows how flawed it is. To counter a simple but wrong argument, you need a right argument that folk find more compelling: and a simple one is more likely to fit that bill than a complex one, even if the latter is more correct.

You may have dozens of arguments for your case: but if you present them all, you'll bore most audiences. Pick three that are compelling: if they won't persuade your audience, belabouring the point isn't going to help. There may be many arguments against your case, particularly purported rebuttals of your chosen reasons, that you can overcome: but if you present them all, you'll not only bore your audience but reinforce the contrary case (by reminding them of it; being bored, they're selectively attentive, so aren't paying enough attention to find your rebuttal convincing). If you think your audience needs some of those arguments rebutted, pick one, rebut it and move on; leave the rest for your audience to ask you and answer them then. End your arguments and rebuttals with your strongest argument, start with your second strongest. Put the rest in between, and keep them brief. Holding your audience's attention matters more than covering all the details. When chosing which evidence and arguments to present, think about the matter from your audience's perspective – which means deciding what audience you intend to address. The counter-argument you most need to rebut is the one your audience is most sympathetic to; the arguments you need to present are the ones that touch most directly on what matters to them.

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