The self-sampling assumption (SSA) is a philosophical tool which follows from basic principles. It suggests that we should reason as if we are typical observers in a suitable reference class. The SSA is part of a larger class of phenomena known as observer selection effects.
For example, say you're participating in a psychology experiment where there is a reward for guessing the correct answer to a given problem posed to you by an experimenter. The scenario is this - you join 99 other people in front of a large building. All 100 persons, including yourself, are blindfolded and equipped with noise-cancelling headphones. You are all led inside the building. The 100 persons are split into two different groups. 95 persons are led into room A, 5 persons are led into room B (everyone is informed this). Without removing the blindfold or headphones, it is your task to guess whether you have been led into room A or B. If you guess correctly, you are rewarded $100, otherwise nothing. Given no other information, which room should you assume you were led into? A, of course, at odds of 19:1.
The self-sampling assumption suggests that we should assume we are typical observers out of the class of all observers. (Or, more accurately, that the observer-moment we are experiencing is a typical example selected from the class of all observer-moments.) It is possible that our specific situation is an exotic or rare one, but relatively unlikely. It's possible that there is a planet somewhere with a quadrillion intelligent observers living on it, but if so, we have to ask ourselves: why were we born on this planet, rather than that one? The probability of any given observer being born on the planet with a quadrillion observers is much higher than being born on the planet with so much fewer persons.
Many thinkers' first reflex is to challenge the idea of the self-sampling assumption, because it can lead to counterintuitive conclusions. Many may feel uncomfortable with the idea that we can get so much theoretical firepower from a method largely independent from empirical testing. But it seems like observer selection effects are just something we just have to deal with - justifying their existence requires far fewer assumptions than those required by many other beliefs people frequently argue for.
Perhaps the most unsettling conclusions followed by this line of reasoning are those represented by the Doomsday Argument. If we are typical persons, then it's likely we were born at a time where most persons are born. In other words, the height of our civilization is likely to be occurring right now. If there are many generations in the future, then why weren't we born then...?