Love by the numbers

One of the guys in my lab had his heart broken last summer and, in spite of our best efforts to cheer him up, has been fairly depressed ever since.  Last week, in an effort to socialize him more with people outside of the department, I took him to a few local bars, were he continued to mope.  He eventually asked me if I thought that there was one person for everyone.  Out of hand I dismissed that sort of thinking as naive and childish, but didn't really give it any more thought than 'there is no physical basis for there to be one ideal person for everyone.'   What I failed to consider was the rational basis for why there wouldn't be and why that sort of thinking is down right counterproductive.  

First of all, there is the simple sex ratio.  Although it is close, there are not the same number of men as women.  For the purpose of this discussion, I'll just look at the 20-44 years age range since I consider older or younger than this unlikely to be when people meet the love of their life.  There has been a steady decrease in the proportion of men in the general population, but this is accounted for by much lower proportions of men in the 45-64 and 65 and above age ranges.  In the 2000 and 2005 censuses, there were more men than women in this age range, which has been part of a trend of an increasing number of men relative to women since 1940.  As of the 2005 census, for every thousand women, there were 1029 men.  1.51 percent of Americans describe themselves as bisexual or homosexual.  Of the general population, 0.7% are gay men, 0.32 are lesbians and 0.49% are bisexual.  I'll just assume that the bisexuals are evenly distributed between males and females.  This only changes the ratio of heterosexuals by 0.21% in favor of a more equal distribution.  Therefore, for every 1000 women, there are 27 lonely guys that will never have any of them as their one love.

If one were looking just for sex, the numbers are a bit less publisized.  Six percent of the 638 men and 1.2% of the 843 women indicated that at least one of their sex partners in the past 12 months was a "casual date or pick-up."  This means that there is a relatively small proportion of women, having allot of casual sex.  I expect that the distribution of the number of sexual partners one has follows a Zipf or Pareto distribution, whereby 80 percent of changing sexual partners is done by 20 percent of the people.  It just means that it is a random process that reinforces itself.  What does this mean in terms of finding the one love?  It means, don't start dating a slut expecting her to suddenly start being loyal to you.

Suppose for a second that there was one person for everyone.  What would your odds of finding that person be?  The answer depends on how many people you know, but in any case, the odds are against.  For example, suppose that you are really, unbelievably popular and know 2000 people of the opposite sex and that the one person for you just happens to live in your home state.  I'll use Tennessee as an example since that is where I am.  Assuming that of the 6,038,803, people in Tennessee, 1,752,751 are women between 18 and 64 years of age, your probability of meeting your one true love is 0.114% or 998.859 to 1 against.  Not exactly betting odds.  

The moral here is that there can't possibly be one person for everyone, otherwise we'd never find them.  If you can't have the one love, love the one you're with.