Thursday, December 27, 2012

Changing the Odds

So far, most of my entries have been about general analysis of probabilities and their consequences. I don't have access to anything like the database I would need to look at anything more than the "average" single. Do we represent a standard probability curve, or are we perhaps, bi-modal? Do two deviations (~90%) stay within a few percentage points or does it cross over into probabilities so extreme they're virtual guarantees? I simply have no way to determine this. I know in a very vague way what the odds are based on standard bell curve distribution and I see that the results are that some are married and some are not. Experience from other areas strongly suggests that some that are not married actually had a very high probability of getting married but due to unlikely situations: did not. And of course the reverse is true is well: those who got married who really didn't have a great chance to do so also exist.

However, experience also suggests that a differentiation does exist. Some aremore likely to pair up than others. Which means we can change the odds in our favor. So Let's take a look at some fundamentals.
I'm currently single but wish to be married. In order for that to happen, to basic events must occur. I must come to the point where I want to marry someone (someone specific) and she must come to the point that she wishes to marry me (not true for all societies, but true for mine and for most who are likely to read this so I'll stick with it). Let's stay with random variables for now. There exists some probability, Let's call it P_m (P sub me) that a particular girl who has crossed my path will interest me, cause me to take action, and ignoring her wishes on if she wishes to date me or not, after I date her I will wish to marry her. Then there's some probability, P_h (P sub her [Smile] ) that a random girl would have the same experience (again ignoring if I'm interested in her at all) would end up wanting to marry me. In this situation the chance of me marrying any random girl is as follows:


So if I would want to marry one out of every ten girls, and one out of every ten girls would want to marry me it would be:

0.1*0.1, 0.01, or 1% of all girls (Note that this is half as likely as I calculated the actual value is in other places, and that's if I actually wanted to marry 10% of all women!)

Since marriage only happens once, the chance of being married after encountering 'n' people is this:


Again, if the chances were 1/10 in both directions and I encountered, let's just say, 15 girls, the chance I would marry one is:

1-(1-0.1*0.1)^15 or about 14%

A few words about definitions; key words are "encountered", "girl" (or "guy") and "want". The definition of all these words is very important for calculating probabilities. For example, if "encountered" means "saw them" then the number of encounters goes sky high. If "girl" or "guy" just means "anyone of the opposite gender" then the probabilities, likewise, skyrocket. If "want" means only that we would have a successful marriage, once more the probability goes up. But of course it doesn't, because in any of those cases P_m and P_h go down to compensate. So I will pick situationally meaningful definitions. 

“Encountered” means, let’s say, spending 6 months in my ward. Thus the barrier for “encounter” is very high. “Girl” (or for those playing along at home “guy”) means someone who is the appropriate age and LDS (again, high entrance hurdle). “Want” means that there would be enough desire before dating to spark dating, enough sparks to begin a committed relationship, and enough love to ignite a proposal (or acceptance thereof). So another high entrance requirement. These high requirements allow P_m and P_h to be quite low. If, for instance, we didn’t require “girl” or “guy” to mean LDS, then P_m would drop almost to zero, as I’m only interested in LDS girls when it comes to marriage. So it makes more sense to require it, as we would merely have to do an extra step of computations and arrive back at the same, basic number.

Now that I’ve lost almost everyone’s interest, let’s hit a bit more qualitative point and ask: so what? I do not intend to try to estimate either P_m or P_h, meaning I will not be calculating the actual probability, so again: so what? Well I want to use this set-up to look at what we can do to alter the odds.

The key equation has 3 variables, but I actually hid a 4th variable in it that you didn’t see because … well I hid it. The three visible ones are: P_m, P_h, and n. The odds I like someone, the odds someone likes me, and the number of someones I meet. The hidden variable stems from the fact that I assumed P_m and P_h are independent variables; meaning I assumed that the fact that I like someone makes them no more likely to be interested in me. This is not true; being liked makes you more likely to like (follow that?) and if I like someone it’s probably based partially on shared interests. Meaning the reverse is true. So P_h is actually a function of P_m (P_h is a function of P_m) and by changing the dependence of these variables, we can again alter the final probability.

So conclusion one is this: to increase by chance of marriage I can change any one (or any combination) of these variables:

1) How likely I am to love a random female.2) How likely a random female is to love me3) How many females I meet4) How correlated my loving someone is to that someone loving me

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