My last blog talked about the “Tyranny of Choice” and the concept that too many choices may actually may satisfaction with a section less likely, or even less possible. Well, how appropriate, I thought, that Ian Kerner on the Today Show this week decided to talk about Peter Todd’s research on mate selection that has suggested there is a “magic number” for first dates.

Todd has applied cognitive models to what is called the “37% rule” (otherwise known as the “secretary problem” in the world of analytic heuristics) and the task of human mate selection. The results? Todd’s research suggests that your optimum solution is likely to be found within just 10 first dates.

To understand how Todd arrived at this conclusion, we need to start by understanding the “secretary problem.” This can be stated as follows (borrowing from my favorite font of wisdom, Wikipedia.org):

• There is a single secretarial position to fill.
• There are n applicants for the position, and this number n is known.
• The applicants can be ranked from best to worst with no ties.
• The applicants are interviewed sequentially in a random order, with each order being equally likely.
• After each interview, the applicant is accepted or rejected.
• The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.
• Rejected applicants cannot be recalled.
• The object is to select the best applicant. The payoff is 1 for the best applicant and zero otherwise.

Now, the secretary problem has received a lot of attention over the years for one particular reason: The answer, if you follow a couple simple rules, for any group larger than about 100, is always 37%. In other words, if you follow two simple rules, you can always arrive at an optimal selection after reviewing 37% of the applicants. So, what are the rules?

1. You skip the first n/e applicants, where e is the base of the natural logarithm (Ookay, you’re just going to have to take that on faith, or I’m going to have to whip out an equation, and none of us want that.)
2. You only interview applicants who are better than someone you have already interviewed. So, your n/e + 1 interview has to be better than all previous n/e interviews (we’ll come back to the assumption that something like this is knowable in a later blog).

If you follow these rules, as n gets larger, the probability of selecting the best applicant from the pool goes to 1 / e, which is around 37%. Whether one is searching through 100 or 100,000,000 applicants, the optimal policy will select the single best one about 37% of the time.

So, if there are 100 potential “mates” for you that are available to date, you should be able to select the “best” mate by 1. Dating 37 people chosen at random; 2. Selecting your 38^th date based on the criteria that they are better than the preceding 37; 3. Marrying your 38^th date!

Now, this is where Todd’s research gets really valuable, because let’s face it…dating 37 people just for the ability to choose a 38^th, is not sounding fun or, for that matter, like a good way to improve your karma. What Dr. Todd found is that if you set your “aspiration level” for what you are looking for to a range, in this case the top 25% of possible matches, and date only those people that you consider to be in that top 25%, then you can reduce your “sample size” to only 10 dates. Even better, this is assuming that you are examining a pool of 1,000 possible matches.

On the down side, unless you can be sure that date number 11 is going to be better than the first 10 dates, Dr. Todd’s model suggests that your best bet will be to go back to whoever seemed the best from the first 10 and select them as your “winner.”

No word yet on how well that maneuver is playing in Peoria. “Hi, Judy? Remember me? We went on a date last February….”

Further Reading:

Todd, P.M. (1997). Searching for the next best mate. In R. Conte, R. Hegselmann, and P. Terna (Eds.), Simulating social phenomena (pp. 419-436). Berlin: Springer-Verlag.