Imagine you can choose between a million projects, each of which you rank by two criteria: practicality and inspiration. You want a project that is *both* practical and inspirational. How much of one must you sacrifice for the other?

Turns out this question is easy to answer if we make one key simplifying assumption: that these two ranking are independent of one another. In that case you can take the thousand best options by one criteria, and among those pick the best option by the other criteria, and in both cases get one in a thousand quality options. More generally, when picking among *N* options to gain *M* independently ranked features, you can on average pick the best out of *n_m* options on each factor *m* if *N = Product_m n_m*. So the more options you can generate to consider, the more selective you can be on more different criteria.

Thus the real key to getting everything you want is to be able to generate more options. With many options you can afford to be highly selective on many criteria. Which is why wealth and innovation are so important; they are what in effect give you more options.

What if the criteria are not independent? Well in general most good things are positively correlated with one another. In which case selection on one criteria already gives you better than average options on other criteria. So you can be even *more* selective than suggested by the above analysis.

Why does it often seem otherwise, that we face hard choices between good things? Because you are often looking a sets of options that have already undergone many rounds and processes of selection. The more you select, the fewer remaining choices you’ll have, and the more you will face stronger tradeoffs between them. Choose well, but note how grateful you should be to have such options to consider.

Your model implicitly assumes that it's costless to evaluate options.

Suppose I want to find a proof of some mathematical claim. Do I just look at options offered by professional mathematicians who have claimed to prove it or should I also consider a dumb automated reasoning system's submissions that simply iterates through all possible proofs?

In some cases evaluating options is cheap compared to the expected benefits. In other cases the cost of evaluating potential solutions is the dominate cost (in mathematics which is essentially just a search for proofs its really the only cost). You can't really derive what's more important in some context without more information about costs, benefits etc etc.

FELICES QUANTITY ENABLES QUATItY