How to Arrive at The Perfect Decision When You are Overwhelmed by Too Many Choices
Choices. Choices. Choices. The average person making a complex decision is often faced with sampling an overwhelming array of alternatives before committing. However, sampling is expensive in both time and effort. But while too much sampling can lead to diminishing returns in information as you continue, too little sampling may lead to a small choice set that leaves out the best options. What, then, is the proper sampling size? While statistical science will give you formulas to determine how many samples to collect, decision-makers face another problem: to explore or exploit.
Have you ever been house hunting? The choices can be vast, and sometimes you come across a home you think is so good that you need to jump on it now. But what if this is only the third house you have seen? Could you find a better option in the following ten homes you could view? This is an example of the explore or exploit conundrum. Do you continue to explore more options, or do you now exploit the choice in front of you?
Mathematicians have an answer for you in the 37% rule. In the book, Algorithms to Live By: The Computer Science of Human Decisions, author Brian Christian says that if you commit a month to your home search, the first 37% of that time should be spent “calibrating” yourself to the market. Christian advises that you should not purchase any home during this time but keep the best choice from this initial choice set top of mind. The key to exploiting this calibration period is that any home you view in the remainder of the month that beats your previous best choice, you should buy immediately. The 37% rule allows you to maximize the explore vs. exploit conundrum’s potential while minimizing your cost.
Insight & Application
Decision-makers facing the task of wading through a large sample face two potential regrets if they choose to stop a search or continue; the fear of losing something found and the fear of losing a better option in the future. Researchers call this the optimal stopping problem, or when a search should be stopped to maximize the relative benefit to cost. That event turns out to be the best option past a 37% sample size.
Developed by various mathematicians, the problem was posed as a game in a 1960 issue of Scientific American magazine by Martin Gardner. Gardner proposed the following scenario. A company wants to hire a secretary from a pool of applicants. The question is how many applicants management should interview to maximize the probability of selecting the best candidate while minimizing the cost of the interview process. In its simplest form, the rules for the secretary problem were:
· There is a single position to fill.
· There are n applicants for the position, and the value of n is known.
· The applicants, if seen all together, can be ranked from best to worst unambiguously.
· The applicants are interviewed sequentially in random order, with each order being equally likely.
· Immediately after an interview, the interviewed applicant is either accepted or rejected, and the decision is irrevocable.
· The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.
· The objective of the general solution is to have the highest probability of selecting the best applicant of the whole group. This is the same as maximizing the expected payoff, with payoff defined to be one for the best applicant and zero otherwise.
While there are many approaches to calculating the optimal number of candidates to interview, mathematicians have determined that the best candidate available after interviewing the first 37% of the pool is when you should stop.
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