Let's begin with the single person, and the quality of partner they can expect to attract. A classic study in 1973 (Becker) found, unsurprisingly, people generally pick up other people of similar quality. This is
why, unless a lot of money is involved, nice pretty people tend to pair up with other nice pretty people, and not slobs.
A more recent study (Fishman et al, 2004) found people tend to pair up with others of similar aggregate qualities of traits--pretty people with few brains could attract far smarter, though uglier people. In that study, also, men tended to be attracted to women who they perceived as of slightly lesser quality than themselves, which probably says as much about men's perceptions of themselves as their perceptions of women.
Building on these ideas, we can say that `singles have a budget constraint of qualities--looks, intelligence, humour, riches, etc.--with which to shop for a mate'. This is illustrated in Figure 1 below by the curve concave to the origin (joining the axes).
You will notice the budget constraints for any given trait (we use here Looks and Brains) exceed one's own endowments of them. That is, one could possibly date someone far more beautiful than they, or far smarter. However, according to Becker, it is unlikely they pick up someone who is better at everything, which is why the constraint passes through their own combination of looks and brains.
We also need to think about what people are attracted to. If we separate one's attraction to potential partners into bundles of qualities, there must be levels of indifference between qualities for each person. That is, one may be equally attracted to a cuter, boring potential mate and an uglier, interesting one. I for one like funny girls, but compromise willingly if they have an excellent knowledge of geopolitics, or are very beautiful. These levels of indifference are illustrated in Fig. 1 below, by the curves convex to the origin, labelled "Attractiveness level 1", "2", and "2.3".
On each of those curves, one is equally attracted to a potential partner on it. So, for every combination on "Attractiveness level 1", I am equally attracted to them. If they are on "Attractiveness level 2", I am more so.
The curve which bisects the axes is the 'budget constraint'--the area within is the quality of people one could 'afford' to mate. The curves convex to the origin join bundles of characteristics of equal attractiveness--one may be indifferent between one hot dumb person and a smart ugly one...
Now, to optimising.
Under the conventional, monogamous approach, we consider it `optimal' here to snag the best quality mate within one's budget constraint. To hook up with someone, when one could do better, leads to inevitable cheating and separation (unless emotions become involved, but we don't like to deal with emotions here--they're harder to graph).
This optimal `purchase' of a mate is represented here on figure 1, by the tangent point of the budget constraint and the highest attractiveness level, here "2.3". They lived happily ever after...
But wait, there's more!
Under the above model, we limit ourselves to just one partner. Asking how "I can give all this love to just one man" is a valid question here. How do we adapt our model to deal with the nymphs, sluts, philanderers, and womanisers?
I suggest we look at what drives the polyamorist.
Let's say for a moment that one `consumes' mates not as bundles of qualities, but as individual qualities. So, one may decide to have a smart girlfriend, a pretty girlfriend, a funny girlfriend, a bushwalking girlfriend, a rich girlfriend etc. (I am a modern gentleman--women under this model are happily able to have multiple lovers, too).
How do we represent this on our model?
In figure 2, instead of dating the "optimal partner" from above, we date two people--one smart, one pretty--but both less attractive than the optimal partner by themselves. In aggregate, however (all summed up), one is dating someone far beyond their budget constraint! In loving many, they have `purchased' a (non-existent) partner so far out of their budget constraint, they would otherwise need much surgery, much education, and many riches to woo.
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