• riccardo

Life hacking _ choose before exploring 50% of the options




 

Imagine we just moved to a new city and we are looking for an apartment to rent. We schedule 10 appointments and we know that at each apartment we have the opportunity to either take it immediately or pass on it losing the opportunity.

When faced with similar choices ( job-candidates to interview, used cars to purchase … ), we may tend to investigate at least 50% of the options, being ready then to make our choice anytime after that moment. Unfortunately, that strategy is often wrong.


Mathematicians have been studying this for quite some time and while there are different assumptions characterizing different cases, general takeaways from this kind of situations are the followings:


1. We can increase our chances of picking the best candidate by making our decision anytime after exploring about 37% of the choices at our disposal.

2. In that case, we have about 37% chances of success (the 2 numbers are the same for some math dynamics) and yes, even though that is the best case scenario we are still very likely not to pick the best one.

3. The good news is that, by choosing any good candidate after about 37% of the options, we are maximizing our chances of success regardless of the number of options (either 10 or 1MM).


You can read more on the math of specific cases on different resources; one you may find entertaining is Algorithms to Live By by Brian Christian and Tom Griffiths.


With this post, if possible, we want to generalize even more by showing a result of a simulation we ran on python. Below you can find the average payoff of a similar case we described at the beginning of the post: we have 100 candidates, each one with an attached value between 1 and 1000 and we need to pick one of them (without the possibility to go back to previous candidates). Each time we imagine to stop exploring anytime in-between the number of candidates and then pick the first one better than the best of the candidates explored before that limit. Here is the result:




In our simulation, the optimal picking point is after only 10 candidates. That is just the example we ran; we do not want to focus on the specific number because, as anticipated, it depends on the assumptions and in real life conditions are often not that hard ( e.g. maybe even after passing on a candidate, you can go back and convince the owner of the apartment or the job-candidate to go back over his / her decision … ).


Here, we want to give you an intuitive reason for choosing before we have explored about 50% of the candidates; a possible life-hacking tip:

By exploring longer, we are raising the bar because we are likely to be passing on good candidates; at the same time, we are reducing the possibilities of encountering better candidates because we are reducing the number of remaining possibilities. On the contrary, by choosing earlier, we initially build some knowledge useful then to pick good candidates among the many yet to be met. Anyway, even though we are optimizing our strategy, we have to remember that our choice is likely not to be the absolute best.


A final note; in general this discussion holds for limit in time too, example: we set 1 hour to find the best restaurant and we maximixe our chances of success by choosing during the first 1/2 hour.


 

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