The best choice out of 'n' unknown opportunities
In real life you often have to take a decision in a situation were you have to pick out "the best" opportunity out of "n" possibilities in a situation were you (ex ante) do not know much about what you can expect in terms of quality or quantity.
Making the right investment
You want to make an investment today. From your stockbroker you get each day about 20 opportunities to invest. But you want to make only one investment this day and it should be the best one. How can you be sure to pick the right one?
You have only limited time (say about 10 minutes) for
each investment to decide; after that, youíll have to wait for the next offer.
Choosing the best candidate for the job
personnel-manager of a certain company. You make a deal with your external
HRM-advisor that he will deliver you this month 10 potential candidates for
the vacancy you have. After each candidate you have to decide wetter you
accept him or wetter you go one for a possible better candidate. You want the
best candidate. What can you do?
Applying for the best job
You solicited for a new
job. Six companies have given you an invitation for a visit. After each visit
you are obliged to say wetter you take the job or donít. You want the best
Job. What is wise to do?
Buying a new car
You want to buy a new car. Although the price of that car is fixed, every dealer gives a quick-decision discount.
You decide to visit 7 dealers. After each visit you have to decide wetter you "buy" or "let go" (the dealer wont accept that you come back later after you came to the conclusion that he was after all the cheapest).
You want the
highest discount; How can you manage?
In each of these cases you can ask yourself: what is the optimal strategy? Take the first opportunity or wait until the last? Skipping the first 2 opportunities and than take the next one that is better?
In literature (management science) these kind of problems are known as "Best Choice Problems" (BCP's). BCP's are packaged in descriptions like "The Sultan's Dowry Problem" or "The Secretary Problem".
BCP's are characterised by the following assumptions:
- You want "the best" choice out of "n" possibilities
- You handle each opportunity after another. After each
opportunity you have to decide wetter you take the offer or go further (you
canít go back and take an earlier opportunity after all).
- You donít have enough knowledge about the group of "n" possibilities self (in terms of quality or quantity)
The best strategy in these kind of cases is to wait (donít choose) until the first "m" possibilities of the total number of opportunities "n" have passed. After these "m" possibilities you accept the first offer that is "better" than the one youíve had until the moment of decision. The word "better" stands for "better candidate", "better financial offer", etc.
If youíre interested in the mathematical theory behind this kind of problems, click on one of the links below:
The Secretary Problem
Mathworld Sultans Dowry Problem
Although itís nice to have a "rule of thumb", donít forget to decide on your gutfeeling as well.
Mixing intuition, experience and rules of thumb, guarantees the ultimate best choice.
J.N. Berkemeijer / July 2002
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