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Revealed preference theory (RPT) is the idea that we can’t trust people’s self-proclaimed preferences as much as we can trust their actions. So if someone claims to care about the environment but still eats meat, doesn’t recycle, and doesn’t donate any money or spend any time working on the problem, we might say that their actions reveal that they don’t actually care as much about the environment as they claim to.
One alternative to RPT is misaligned incentive theory (MIT). This is the idea that when someone’s actions seem to contradict their self-proclaimed preferences, it might be because their long-term and short-term incentives are not aligned. For example, if someone says they are trying to quit smoking, but in the moment they can’t resist lighting up a cigarette, we wouldn’t say that they must not really want to quit, because it could just be that their long-term goal of quitting smoking is not aligned with their short-term desire for a nicotine fix.
RPT and MIT are both useful frameworks for looking at behavior which is seemingly contradictory. Just because someone acts in a way that obviously goes against their goals doesn’t always mean those goals are false, sometimes it’s just hard to do the long-term thing when the short-term thing is so much easier. Likewise, sometimes people are wrong or lying about about their preferences, and the only way to find out is by actually observing their behavior.
In general the RPT view is harder to verify, so a practical solution is to assume the MIT view by default. This means trying to help by pitching ways someone could better align their incentives. For example, you could recommend that a smoker try a nicotine patch, which allows them to satisfy their nicotine cravings without filling their lungs with tobacco smoke. Or you could suggest to your friend that instead of just writing rants against Republicans on Facebook about climate change, they could use that time and write a guide for young people on how to set up domestic recycling. If these recommendations are repeatedly denied, you now have evidence against the MIT view and can gradually switch to the RPT view.