If I were to solve it, I would just give people democratic rights (pretty much everyone the same vote) to decide how economic resources are allocated. But lots (if not most) of people are against that idea.
- People optimize locally, working for what they think is their best interest, even if on aggregate they lose. This is basic coordination problem; the very reason we form societies is because global optimization, often requiring to fogoe individual short-term gain, leads to better outcomes.
- The way people vote strongly depends on education they get; especially in our technological civilization, a lot of important issues (like energy) are beyond the understanding of majority of electorate. Democracy depends on educated populace.
- People are not independent actors wrt. to voting; in the age of free media, your votes will not reflect the "will of the many", but the will of most charismatic people on TV. Note that "the most charismatic" usually does not mean "the smartest".
The last objection I don't understand. The best way to know person preferences is just to ask them. If someone charismatic changes their preferences, so what? People change their preference based on other people all the time. As long as it is clearly their preference, we have to assume that it's in their interest.
The point of democracy is that people express their interest. There may be smarter people doing smarter decisions, but why should they make the decisions in the interest of someone else?
In any case, I think it's a good idea, often neglected, to structure society so that impact of any wrong decision at any level is minimized. Things like democratic decision-making, subsidiarity principle, reversibility of laws, non-discrimination, limited liability, social security, no capital punishment, time limited government contracts and free access to information all help.
As for the last objection - the typical voter's preference will be reflecting the political battles described above.
> People change their preference based on other people all the time. As long as it is clearly their preference, we have to assume that it's in their interest.
The problem is, it's not people changing their mind because they've heard someone reasonable saying something that makes sense. Politicians lie. Lie blatantly and lie on purpose. They hire the entire advertising machine, built out of professional liers and bullshiters, to convince people that their side of the debate is right by whatever means necessary. The average voter has to oppose people who are trained specialists in lying. I don't see how you could argue it's actually their preference.
But back to the primary reason. I could accept that start of affairs as fair, as long as we're dealing with things that don't matter much. But at this moment in time, we have several important problems - like supergerms, climate change and depletion of fossil fuels - that are going to destroy humanity in few decades, or at least pull us back into the medieval age. This shit matters. We need to make some hard choices and do some decisive actions soon if we want to have any kind of civilization surviving to the end of this century. And the democratic process is by design incapable of making those hard choices.
TL;DR: I don't want to "give power to the smarter" or a king or anything. I just want someone to actually do something about global warming and power issues before this stupid textbook-level coordination problem kills us all.
And the `elite' optimizes locally as well, directly at the expense of the weakest.
To be clear - I'm not that big on authoritarianism. I just don't see the value proposition of democracy being actually realized. Given the points I mentioned previously, we are still ruled by elite, except that it is constrained to choose their options only based on popularity, and unable to make hard decisions in areas that matter[0]. About the only thing democracy delivers as promised is bloodless government transition. Even the actual work in democractic country's administration is done by unelected officials.
At this point I've given up hoping that democratic governments will help solve climate change or energy problems. Private companies may be able to, but that's only because they're capable of behaving in inherently undemocratic ways, like releasing a new technology upon the world (nobody asked us to vote whether we want to have Facebook or not) or projecting the will of single individuals onto the society ("you will drive electric cars, whether you want it or not", said Musk, and proceed to burn as much money as it took to make electric cars compete with ICE ones[1]).
[0] - even if such decision wouldn't immediately piss of half of the electorate by itself, your political opponents will make sure it will render you practically unelectable
[1] - yes, there were electric cars before, but it took Tesla to basically force the market into accepting them as an option, and they did that on purpose