Optimal Stopping and the Secretary Problem
What matters.
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Hi!
A good friend I was having a chat with said I should write something about the Secretary Problem. I first read about this in the book Algorithms to Live By, which described the problem far better than I can. Its a fun read if you enjoy thinking about trade offs and finding balance.
How to hire a Secretary
The Secretary Problem is an optimal stopping problem. Imagine you were a hiring manager trying to hire the best candidate for a secretary position. According to some complex mathematics, the optimal approach is to reject the first ~37% of candidates, using them purely as a data gathering exercise. Then, hiring the first candidate that is better than all the others seen so far.
Like any intellectual exercise, this is of course subject to many assumptions and qualifications - the numbers change if you factor in whether the potential secretary might reject an offer, or if you could go back to an earlier option after spending some time gathering data.
Still, it provides a useful heuristic for decision making: spend the first 1/3 of the time you've set aside for the search only looking, commit to a decision quickly after that. Technically it could be applied to finding a job, buying a house, or even choosing a romantic partner. I use this when searching for parking lots, where the assumptions of the problem seem to be most consistent with real life.
Against perfectionism
This theory resonated in me for its reminder that at some point, the best thing we can do is to act. We can’t keep holding out for something better, or trying to do more to achieve the best possible result.
With infinite information and tools for comparison, its even easier now to spiral into wanting to make every decision perfect. Housing in Singapore is an example, its common to hear people really obsess about their home. I recall reading a blog about someone who spent 2 whole days in a tile shop so that she could pick the perfect floor tiles.
There's a common aphorism to avoid “Perfect being the enemy of good”, recognizing this same danger. Tiago Forte also had an interesting thought that perfectionism is not high standards, it's a fear of judgement from others.
Its good to have high standards, to want to push the boundaries and do better. However, its easy to let high standards become an exercise in being overly critical of what is not there, ignoring what has been done. The problem compounds when our bias against subtraction makes it hard to ask others to moderate those standards, especially those in positions of power.
The Secretary Problem appears to provide an alternative heuristic to this, reminding us to stop and not waste energy trying to get the best result. But it's still framed in the terms of optimization. Applying it is still trying to give comfort that we have gotten the best we can.
What matters
The focus on what is optimal distracts from a more important question - what actually matters? What is “best” is a comparison against other options, it requires us to think about what we are missing out. Asking what matters is an examination against what we truly need.
True comparison is impossible. Things are often too different to know which is really better. It likely devolves into comparing quantifiable attributes, public opinions, or trying to force distinct attributes into a side by side view. We end up with a shallow comparison that is not useful.
But, trying to ask ourselves what matters is difficult. It requires us to think hard, search inward, and also take a stand on what is not important. We hate cutting things out, we hate missing out. This takes energy and convinction to work out in our heads.
Its worth that energy though. Once we know what’s important, we can decide as soon as we find a decision that meets that threshold. We save time from searching and maximising, or from dealing with our fear of missing out. That time can be used elsewhere. More importantly, we save our emotions from the pain of comparison, and can use it that presence to enjoy life better.
Laws of Singapore
Code on Accessibility in the Built Environment - increasing requirements for nursing rooms.
The Code on Accessibility in the Built Environment is a policy document created by BCA which sets out guidelines for including accessibility features in our buildings - things like drop off points, disabled toilets, or even the optimal width of corridors. While the Code is not a statute, it's effect is almost as strong as law, as the BCA requires compliance with the Code before it grants planning permission to new buildings. For existing
Becoming a parent makes one very aware of Accessibility features. I know where to expect ramps to push a pram, or a diaper changing station in a mall. In Singapore, it's easy to take for granted that these features will be present.
But if we rewind the clock about 20 years, such features were far less common. For example, if my memory serves me right, those little dots in MRT stations only started to be implemented when NEL was launched.
What may not be obvious to us is that this expansion of these accessibility features is the work of the BCA, who reviews the Code every 5 years. Things like dedicated family rooms in shopping malls were all recent additions.
I had the opportunity to work on submitting a policy paper to the BCA recently for them to consider in their current review of the Code. One of the gaps in the code is in the requirements for nursing rooms in workplaces. They are currently only mandated for offices and business parks above 10000sqm in gross floor area, which only covers a few buildings in Singapore.
The point was reiterated in parliament last month in Louis Ng's adjournment motion, and I was happy to hear that the BCA is going to consider the proposal to lower the minimum floor area threshold in its next review of the Code.
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Take care and have a good week!
James
Hey there, another insightful article as usual. I have to admit I have not come across the Secretary Problem before, so it’s a learning point for me.
Finishing up a book now which somewhat resonates with your topic: The Art of Clear Thinking: A fighter pilot’s guide to making tough decisions. It looks at another perspective of decision-making, when we have to make them under pressure. Perhaps you might find it to be a good read. Cheers!