Mate selection in human are non-random, for that matter in any living being. To put it in simple terms, it is 'by choice' we find our partners and not 'by chance'. I got very inquisitive on the issue very recently, thanks to my age or an evolving mind!! Google guru, my brother, and a paper in The Public Opinion Quarterly of 1953 have all provided sufficient gum for me to chew.
I started off with an approach of thinking globally and acting locally. At a larger picture, especially in the West, finding a partner is more individualistic, while here, its more societal or familial affair. As male or female attains certain age, the family decides that its time for marriage and search would soon start, in the relative circles. At this instance, let me presume that the male to female ratio in the society is 1:1 and also that for a female there exist a population of suitable males and vice versa. In other words, the probability of getting a mate is 'one'. As my knowledge and understanding on the other than Hindu religion is very limited, I restrict my self to this religion, which is one of the key variable in mate choice too. If mate choice so easy, I think, even myself would not have tried on writing this piece. As we start scaling down ourselves, the complexity increases, so also the variables.
I tried my level best to put major variables in to two broad categories, Family and Individual. At the familial level, the key variable is religion. Followed by caste, sub-caste, gotra and pravara. Other important variables are family background, parents, siblings, tradition and region, but over the years, with the advent of nuclear families, these variables are losing their intial charm (In a way good, increasing the probability!). Individually, Janma Kundli (Jataka), at religion level and age, height, education, occupation/salary, complexion, at personal level forms key variables. The important point here is that, with the addition of each variable, the probability value starts dwindling, more so each variable are not uniformly valued. The weight to each of the variable is decided again by the family, an example would be, a traditional and orthodox family might give higher weight to caste, sub-caste, gotra, jataka etc, while it may carry least weight in an unorthodox family.
Whatever may be the weight, ultimately, with almost 10 major and 6 minor variables, the probability value of 1 decreases drastically. In some castes in India, this has gone to zero (fortunately, probability does not give negative values, otherwise it could have been -1 too), in the sense, there is no way of having a 'choice' of partners as there are no partners at all. Similarly, each of the variable has a threshold value, below which probability is on a higher scale, where as after breaching the threshold, the probability diminishes exponentially. An example is age (again this is not equally weighted and cannot be between male and female), 23-28 for male is considered prime, and so is his probability. Once you touch 30, its the danger mark of overflowing dam and beyond 32, the dam breaks! and probability is near zero.
At the outset, what looked as non-random selection, finally when it boils down to marriage, looks exactly the opposite of what is said, its purely a chance! and nothing else. In India, after 'Monsoon', Marriage is said to be the second only 'chance' Indians bet on (pers. comm. chandrakantha). Amidst all these, some sensical and some nonsensical variables, key set of variables called 'heart/mind/feel' were never considered at all and were no where in the picture too. These variables, which determine the entire after life of marriage, of a male or a female, should have been the prime factor, putting all others in the dust bin, during mate selection. Otherwise, we have to accept that mate selection is random, marriages are made in heaven and keep our fingers crossed!