## Monday, April 22, 2013

### The 12 Bonk Rule

I am on a mailing list from Business Insider and against my better judgement (which often comes out when the internet is involved) I followed a link to an article on The Sexiest Scientists Alive. There are 50 scientists listed, and scientist number 43 is Clio Cresswell, a mathematician at the University of Sydney, who is the author of Mathematics and Sex

The book gained some notoriety for propounding the 12-bonk rule. Bonking is a term in Australia for having sex (usually casual sex as I recall), and Dr. Cresswell has stated that the best strategy for finding a good (sexual) partner is to bonk with 12 twelve different partners, note the best one, then keep bonking until you find someone who is better, then settle on that partner. You benchmark on a sample of 12 partners, discard them, then take the next best that comes along. Cresswell reports that this strategy gives you a 75% chance of finding a good mate. So it's not foolproof, but with the confidence of mathematics, it proclaims to be better than any other trial-and-error approach that leaves behind a trail of discarded lovers. Of course there is more at play in finding a mate than "bonkability", as opined in the Ask Sam column of the Sydney Morning Herald for example.

The result caught my eye as I was recently reviewing some statistical problems and I surmised that the 12-bonk rule had a similar sounding result to the secretary problem, a classic problem in probability. The secretary problem (which by now should be at least upgraded to the executive assistant problem, or simply just the candidate problem) asks for the best strategy to select a secretary for a position where there is a collection of candidates and you get to have one interview, upon which you must either hire the candidate or move onto the next one. It is assumed that the market is competitive and that you will not be able to return to a rejected candidate as they have found employment elsewhere.

The optimal strategy here is to interview 37% of the possible candidates, make a note of the best one, and then keep interviewing until you a find an additional candidate that is better than you previous best, and then choose the new best candidate as the one to employ. So if you have 100 candidates, interview the first 37, note the best, and then keep interviewing until you find someone better and then hire them. The graph below plots the probability of finding the best candidate using this strategy, as the percentage k of candidates interviewed and refused increases.

Here 37 is the double winner in that the point marked by the dashed lines indicates that the optimal approach is to reject the first 37% and then you will find the best candidate as the next best choice 37% of the time. This magic 37% is derived from 1/e = 0.37, where e is the base of the natural logarithms.

I just downloaded the e-book version of Mathematics and Sex and took a quick look at the 12-bonk section, and it seems that Cresswell's discussion is based on the work of Peter Todd in his paper Searching for the Next Best Mate. Todd looks at simpler heuristics to find a mate than applying the 37% rule, which he notes has the following drawbacks in practice. If we assume a sample of 100 people where they can be rated uniquely on a scale from 1 to 100, then when applying the 37% rule
1. On average, 37 additional people need to be interviewed (or bonked) to find the next best beyond the best found in the initial 37 people, for an average total of 74 people being considered from the 100.
2. On average, the best person found has rank 82, where 100 is the best on the scale. The 37% rule finds the best person 37% of the time, but averaging the success out over the remaining 63% of choices, lowers the result by about 20%.
Todd decided to explore other decision rules that performed better than the 37% rule on some criteria, and more closely match with our observed behaviours for finding a mate. It is unlikely that anyone will have the time and (emotional) energy to engage with 37% of all their potential mates, which could easily run into the thousands. Todd's computer models found that if you engaged 12 people from a mating population of 1000, then took the next best, you are highly likely to end up with someone in the top 25% of the population. I cannot quite tell from Todd's graph referring to this result as to how many people must be engaged in total, but seemingly around 30 or so (50 at the outside).

So this was the genesis of the 12-bonk rule, and I will read Crisswell's book a bit closer to see if she has teased out any further details or conclusions. A very quick search of the internet on the topic of the number of sexual partners seemed to indicate that for Western men and women 12 sexual partners is on the high side for most of them - actually more like half of that, after discarding "outliers". A further potential glitch in the 12-bonk rule is that it assumes when you have found your post-12-bonk lover that he or she will accept your overtures, and of course you cannot be certain of that. I am sure that someone is working on the mathematics of unrequited love.

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