Suppose you plan to get married sometime. When should you take the leap? What if you marry too early, and miss out on your ideal life partner (whom you hadn’t yet met when you married someone else)? What if you marry too late, after all the best potential partners have come and gone, and you end up with someone less than ideal?
Mathematicians don’t just wonder idly about such things; they work out the math. Professor Bruce Brown, of the University of New South Wales (where I studied), has done the sums.
Suppose you’re a male, hoping to find the ideal woman to marry. First you need to decide the age at which you will start seriously looking for a wife. Then you decide the age by which you want to be married. For this example, let’s say Fred will start looking for a wife at age 23, and certainly wants to be married by 38.
Take the difference between these ages (38 minus 23, which is 15). Multiply the difference by 0.368, which gives about five and a half years. Here’s what that answer means for Fred.
Fred will start looking for the ideal wife when he turns 23. For the first five and a half years, he shouldn’t propose to anyone. Fred is “just looking”. After those 5½ years, when Fred is 28½, he must change is strategy. From now on, he has a benchmark: the most suitable mate he has met in those 5½ years. Now, as soon as he finds someone who is better than his benchmark, he must pop the question. This maximizes his chance of finding his ideal mate.
Fred still has 9½ years to go before he reaches his upper limit, so it’s highly likely that he will find someone better than his threshold. Because Fred has taken the optimum time to establish his benchmark, he has maximized his chance of finding the best wife. In fact it gives him a better than one-in-three chance of proposing to the best possible candidate, and only a small chance of reaching the age of 38 and having to settle for the last candidate because he hasn’t found anyone better than those he found in the first 5½ years.
That makes it sound very calculating and mathematical, and of course the dating process is fraught with complications. Fred’s ideal wife might reject his proposal. Also, Fred’s criteria may not be consistent from age 23 to 38. For these and many other reasons, I wouldn’t actually recommend sticking blindly to this method.
This is an example of an “optimal stopping” problem. Faced with a choice of possibilities which present themselves in an unknown order, how can you choose the best one (or as close to the best as you can)?
Professor Anthony Dooley is head of UNSW’s School of Mathematics and Statistics, and he is at the cutting edge of research into “optimal stopping”. Most of his research is unrelated to “trivial” matters such as choosing a spouse. Instead, his work is applied to financial issues, where it is valuable to investors and governments alike.
Prof. Dooley presented a paper in 1993 where he applied the optimal stopping problem to the East Asian financial situation, and realised that Asian governments were digging themselves into a hole by effectively guaranteeing an ever-increasing amount of investment, way beyond the optimal stopping point. Sure enough, the Asian financial crisis developed later that decade: not directly due to budget deficits, nor to the defence of exchange rates, nor to expansionary spending. Instead, it was due to the panic and collapse that occurred when one temporarily-stable situation passed the point where it was inevitably going to become unstable at some point.
You can read about optimal stopping and the East Asian financial crisis of the 1990s here:
Oh, it was the marriage thing you were interested in? Here’s the press release about the fiancée formula:
You can use optimal stopping to your advantage when shopping. Do you need to buy shoes, and have 15 shoe shops to choose from? Simply visit the first five (and a half) while “just looking”, then buy the first pair that’s better than any you saw in the first 5½ shops. This stragegy avoids the need to visit all 15 shops, then return to the one that had the best shoes only to find that they’ve just been sold to someone else.
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