There’s something magic about the number three, isn’t there?
Three-leaved clovers… no, hang on, that’s something different.
Anyway, the magical number three makes a stealth appearance in an amazing number of real-life problems:
For example, if a restaurant owner wants to maximize her profits, she needs to optimize the prices (one), the number of seats (two) and the time customers spend in her restaurant (… and three).
Since you’re a smart cookie, you probably noticed right away that this is a classical optimization problem: We’ve got three variables, and we want to find “the” optimum.
There are tons of other examples of such “magical threesome” problems, in all areas of life:
For instance, in any given project, your boss will hope to optimize three things: speed, quality and budget.
But anybody who has ever been involved with a project of any kind knows that if you hit two of these targets, you ain’t done bad. 😉
Or take elections:
With the advance of technology, governments increasingly consider electronic voting.
(My guess is that this is mainly because it’s cheaper, but hey… maybe they’re all hidden nerds. You never know.)
But at the same time, an election in any democracy should also be secret. And it should be comprehensible – you don’t want a lot of votes to go to waste just because people didn’t get the voting system.
So you’ve got the magical threesome again: secret, comprehensible, electronic.
Again, hitting all three requirements is fairly impossible:
If you want your election to be electronic and really secret, it cannot be comprehensible – at least not for all groups of people.
And making an electronic election truly safe and secret is hard enough. But if you want it comprehensible and electronic, it’s pretty much impossible to be secret and safe.
Which also means that if you want your election to be secret and comprehensible, it cannot be electronic.
But the magical threesomes continue right after the election:
Ideally, you want your government to handle any crisis that is thrown at your country.
But you also want it to keep the taxes low (who doesn’t?). And of course, they shouldn’t borrow more than your country can afford, because nobody likes to pay the interest in ten years time either.
So you want strong, accessible and well-financed health and educational systems plus investments, support for local businesses, shops, jobless people etc – but without a high tax rate (which would be a strain on businesses and/or people). And of course, there’s only so and so much which can be financed through debt.
Well, I’m sure you can imagine how these three things will never be possible all at the same time…
(Btw, it’s quite interesting to see how different governments in different countries deal with this optimization problem, and which of the three requirements they put more focus on…)
I’m stopping here with the examples, but I’m sure you can come up with more from your own life, or from your fields of expertise. (If so, leave them in the comments for us so that we can all gain from your insights!)
Now, I keep calling these problems “magical threesomes”, and you might have been wondering why…
Apart from the fact that it sounds cool and intriguing (hey, I’m just human, too!), there is something magical about these problems – the magic of choice.
Because, yes, this kind of problem is an optimization problem.
But to view them just as optimization problems means we’re missing out on something really important. Because, in their essence, these magical threesome problems are not about optimization…
… they’re about choices, and about decisions.
In these real-life situations, there never is just one optimal solution – there is always a range of options:
You could maximize one of the three requirements at the expense of the other two.
You could try to find a carefully crafted balance which takes all three equally into account.
(Which, in itself, leaves a ton of options because how do you decide if they are “equally” weighed?
Right, you need criteria for that. And somebody else might pick different criteria.)
You could go with two of them, and largely ignore the third one.
You could place more emphasis on one or two of the requirements, but still kinda satisfy the other one or two a bit. Somehow.
Or any combination thereof, of course.
What this means in practice is:
There is not one perfect solution for magical threesome problems. At least not in real life.
Instead, they are about choices. About preferences. About what’s important to you, or to your group of people.
And ultimately, they are about making decisions:
Do you want your restaurant to be upscale and posh?
You can demand higher prices, but your customers will (rightfully) expect a nicer atmosphere in return: more room between tables, and more time to eat in leisure.
Do you need your project to finish on a tight deadline?
Expect to make concessions either in the quality or amount of the output, or in the budget, or both.
Do you expect your government to handle the corona crisis like champs, to make sure everybody gets decent health care and all businesses are supported?
Then it’ll need to spend a boatload more money, and that means raising taxes and/or borrowing money.
Of course, in all these examples, it’s really easy to see how your choices could be completely different.
(Well, apart from the fact that everybody should have fair and equal access to decent health care. I mean, come on!)
So yes, each of these magical threesome problems is an optimization problem: You want to find the optimal solution.
But what “the” optimal solution looks like, that depends largely on your choices, your goals, your preferences.
Or, in other words:
Whenever you come across a magical threesome problem in your life, you need to first figure out what’s important to you – and only then you can find “the” optimal solution.Real-life optimization problems aren't really about finding THE optimal solution - they're about making choices! Click To Tweet
And once you’ve wrapped your mind around this kind of thinking, you’ll quickly realize that two outa three really ain’t bad! 😉
Image: Thomas Q on Unsplash