How could the concept of thresholds and limits be applied in an inductive way in explaining the development of "best friend" relationships, selection of an academic major, or career choice? What specific variables would you identify as crucial, and how you determine when the threshold and the limits are reached?
In sociology, the idea of thresholds is closely connected to Georg Simmel. Simmel argued that people perceive thresholds in a variety of aspects of life. When thresholds are passed, a qualitative change occurs. It is not simply that a variable has changed by one unit, for example. Instead, a tipping point has been reached and we move from one state to another, much as a light switch is either on or off, with nothing in between. We can certainly apply this concept to the issues that you mention in this question.
In all of these examples, we clearly have thresholds. A person is our best friend or they are not. We choose a career or we do not. There is no such thing as having a line of work that is almost my career.
So, what variables do we think of in these cases? With a friend, we surely think about interests we have in common. We think about whether we feel that we somehow “mesh” with the person. We think about whether they treat us in ways that we like and that we feel are good for us. At some point, however, a limit is reached and some intangible thing makes a person a best friend or leaves them short of that point. It is not really possible to say what that limit is or what variable will push a person past the threshold.
The same is true of picking a major or a line of work. In these cases, we consider whether we would enjoy the classes or the job. We think about how well the job would pay or whether the major would lead to a good job. We think about whether the work will be too difficult. Again, though, the ultimate choice rests on some sort of intangible factor. At some point, the entirety of our feelings about the job or major comes to push us over the edge and we decide to enter that line of work or study.
Thus, we can see that thresholds do exist in the situations that you ask about. We can easily identify the variables that matter, but we cannot know exactly what moves us beyond a given threshold.