Grade schools in the US ignore philosophy as a subject. A few high schools give it brief mention (and then it's only to cover historically important people). Even in many colleges it remains elective. The result is that many important subjects in philosophy are unknown to the general public, despite the fact that they are simple and can have a great influence on our everyday lives.
I've mentioned concepts like confirmation bias and the sunk cost fallacy before. These are common mistakes all people make in reasoning that can be avoided if we learn about them. These have aspects of psychology as well as philosophy. A more purely philosophical concept everyone should understand is the Prisoner's Dilemma. A typical example goes like this:
Two suspects are arrested for a robbery. Each is questioned separately by police and told this: Our evidence against the two of you for the robbery is thin, but we can give each of you a year in jail on a lesser weapons charge. If you confess and squeal on your buddy, he'll get five years and we'll let you walk. But if you both squeal, you each get three years.
|A keeps silent||A confesses|
|B keeps silent||A: 1 year|
B: 1 year
B: 5 years
|B confesses||A: 5 years|
|A: 3 years|
B: 3 years
Each suspect reasons like this: I can't talk to my buddy, and I have no control over what he does. If he clams up, I get a year if I do as well, but I go free if I confess. If he squeals, then I get five years if I stay silent and three if I confess. In both cases, I'm better off confessing. Both suspects reason this way, so both confess, and each gets three years in prison. But if they had both remained silent, they both would have gotten only a year. So the essence of the Prisoner's dilemma is this: reasoning separately, both parties doing what is clearly in their best interest end up with a result that is worse that what they would have gotten if they had cooperated.
Many situations in life mirror this. Take doping in sports, for example. Whether or not your opponent is doping is out of your control. If he is, you must dope to compete. If he isn't, doping won't lessen your chance of winning, so individually you are always better off doping. But if everyone in the sport is doping, the results will be roughly the same as if no one is doping, so as a group, it would be better if everyone didn't. Other situations like the tragedy of the commons can be modeled this way.
The way out of these dilemmas is to find some means to encourage or force cooperation. For example, a criminal gang might have a prior agreement—or strong social taboo—against snitching. Sports regulators might have strong rules against doping and do regular testing. It has even been suggested that one of the primary motivations for which people create governments is to have a third party to resolve such dilemmas between citizens.
Like any simplified mathematical model of complex human interaction, there is a danger of applying it to situations that don't quite match. In a recent episode of the Philosophy Bites podcast, Jeff McMahan suggests modeling aspects of the gun control debate as a prisoner's dilemma: for example, the interaction between a burglar and homeowner. Each reasons that if the opponent is armed, he is certainly safer being armed himself, and if his opponent is unarmed, being armed doesn't hurt, so it is better to be armed in each case. But collectively, they are safer if both are unarmed.
I don't think this particular argument holds water, even ignoring all the other aspects of a very complicated issue. First, the “payoffs” (that's mathematical jargon for the relative value of the results to each of the participants) are not symmetrical. In the “both unarmed” condition, the winner of the interaction is likely to be whoever is bigger, stronger, or the more experienced fighter—probably the criminal. The “both armed” condition raises the stakes and the danger for both, but is also equalizes them, so it is likely to benefit the homeowner relative to the burglar. Second, it assumes that both the criminal and the homeowner place equal value on their own safety. This is a psychological question. Perhaps the burglar is a sociopath who values violence for its own sake. It also makes the assumption that the “both unarmed” condition is something that's possible to achieve in real life.
Another way out of the prisoner's dilemma is available when situations are repeated more than once: reciprocity. When we have multiple interactions with people, we can gain a reputation for being cooperative, making others more likely to cooperate with us. Robert Axelrod's classic experiments along these lines are explored in his book The Evolution of Cooperation. Reciprocity can also explain how our moral sense (and things like our ability to recognize faces) can evolve from the essentially selfish process of natural selection.
This concept is simple, and recognizing it in real life situations can make such a difference in life that it should be taught to everyone in grade school.