In this post I will try to model the chances of finding a psychologically ideal partner.
The difficulty of this exercise is distinguishing between "wants" and "needs" in the realm of psychological compability. Someone, for instance, may "want" a partner that makes a lot of money and has achieved professional success, but in reality they may be just as psychologically content with someone without these qualities. Someone may think they need someone who is an accomplished athlete like they are, only to find, much to their own surprise, that they feel perfectly at home with someone who is distant from the world of sports.
For the sake of this exercise we are going to assume that the purpose of the sought-for relationship is friendly, intimate romantic companionship, not establishing a safe haven for children, etc. Therefore, we will consider only factors that definitely impact the possibility of a psychologically intimate and comfortable relationship between two people.
The first division we will make is for gender. Only 1/2 of people are of the right gender for such a relationship (well, for the vast majority of people).
Next, only 1 in 16 has a psychological type that allows in principle for maximum intimacy. It is my belief and experience that the types are distributed rougly evenly, meaning that no type is more than twice as prevalent as any other (and probably quite a bit less than that).
For people who are not convinced of the importance of socionic intertype relations, but have considerable relationship experience, it shouldn't seem too far from the truth to suggest that, with all the kinds of personalities to be found among people, maybe only about 1/16 of people have the right psychological makeup to make ideal living partners and friends.
Next, a generous 1 in 4 of these people are of an age range that would allow for real intimacy. Social stereotypes of acceptable age differences don't necessarily correlate to what is actually possible. For some people the age range will be wider, and for others narrower.
Now, of these people, we will eliminate half for various psychological, physical, or cultural characteristics that make it impossible to become attracted to or deeply intimate with them. This generous estimate includes things like specific temperamental and physiological characteristics that may have a significant effect on real-life compatibility. Many people think they are far choosier than this, but circumstantial factors and long-term exposure to a person often spark friendship and intimacy where neither person would have expected it.
This leaves us with 1 in 256 people being a potential ideal partner. That may sound like too few, but we are talking about the population at large, not eligible candidates looking for a mate of your gender. 1 in 256 applies if you are looking for a partner by calling random numbers in the phone book.
But we're not done yet. Another factor that has an indisputable affect on people's ability to connect with others is the difference in IQ between them. I have read estimates of between 15 to 30 IQ points being the point at which communication difficulties arise. I will be a conservative and choose 30 points as being the maximum acceptable IQ difference for a high degree of emotional intimacy and psychological compatibility between people. Because of the bell-shaped distribution of IQ, this means that for most people in most circumstances, the influence of this factor will be negligible. For people at the upper and lower extremes, however, potential IQ differences can become as serious a communication issue as any of the others, even among duals of the right gender and age.
Here we will list the percentage of people who are in the acceptable range for people of a given IQ, and below that the chances of finding an ideal intimate partner among the population at large.
94% of people within range
1 in 272
80 or 120:
73% of people within range
1 in 351
60 or 140:
27% within range
1 in 948
40 or 160:
3% within range
1 in 8,533
20 or 180:
0.09% within range
1 in 284,444
Increasing your chances
Going to college increases your chances by 4, since all people are in an acceptable age range. Since you don't pay attention to all the people of the wrong gender, you can multiply your chances by 2. If your IQ is above or below average, you can increase your chances of finding an ideal partner by being a part of communities whose average IQ is as close as possible to your own. For example, if your IQ is 140 and you go to a university where the average is 120, your chances of finding an ideal partner from among your college peers are now the same as someone whose IQ is 120 (or 80) from among the population at large. If your job brings you together with people of your IQ range (and interests), this increases your chances, too.
Connecting with communities of people who share one or more of your interests is important in that it provides a convenient context to establish a connection with people who might be compatible with you. People with unusual interests often have difficulty at ordinary dating sites, where their interests are an oddity rather than the norm.
To summarize, the person in the best position to find an ideal partner is someone who is part of a community or communities of people of the same age range, IQ range, and general interests.