The Math

We observe data in the form of past girlfriends, {gf_i}:

• Age_i The age at which gf_i was dated
• Duration_i The duration of the affair with gf_i
• Rating_i The hindsight rating of gf_i

We make the following assumptions: There are an inexhaustible number of women in the world, and, according to our individual tastes at any given time, they are normally distributed under our ”rating” of them:

Girls ~ Normal(μ,σ²)

This holds roughly if we believe a women’s rating is the summation of a number of different independent factors–looks, smarts, etc.

Every so many hours, days, or weeks we have a meaningful encounter with a new girl. These times we wait in between are exponentially distributed

Time between encounters ~ Exponential(w)

This follows if we believe having waited a certain number of days without meeting any women implies we are NOT any more likely or less likely to meet a woman the next day than we were when we first started waiting (memorylessness), long term trends aside. These two assumptions together imply waiting times between meeting level α girls (level α girls are the set of girls such that the probability of meeting another girl rated as high or higher is α) are also exponentially distributed

Waiting Times ~ Exponential(w * α^-1)

Once a relationship has begun, we assume it lasts for a duration that is (again) exponentially distributed:

Dating Times ~ Exponential(d)

Furthermore, as one goes through life, we anticipate that one makes choices such that one is surrounded by increasingly attractive prospectives. So we time-parameterize the mean rating of girls:

Girls ~ Normal(tβ,σ²), t is time in months

Then we estimate our model parameters from the data We want to estimate these parameters for an individual from their past relationships. Simple mean regularization is used. For each parameter, we research a reasonable guess at the population average (from surveys of American relationship behaviors) and estimate the parameter as:

For instance, in the case of relationship durations, broad surveys have shown the typical non-terminal relationship lasts 7 months. This is something we assume to vary substantially individual to individual. So we estimate our average duration d as:

This is equivalent to seeing two extra observations at 7 months duration. Specifically:

d	=	(1)
w * α-1	=	(2)

(This corresponds, roughly, to modeling the exponential distributions with a gamma(a,b) prior, with a = τ + 1,b = τ * μ₀)

We estimate β with L²-regularized regression (we think an extreme trend in mean rating is unlikely).

And then we simulate!