Knowledge Problem (Information Throughput Problem)

The human brain can process around 40 - 50 bits/s
If we have 100 humans, this would equal a processing throughput between 4000 - 5000 bits/s.

In Lehman's terms this would mean 100 humans interacting and trading freely between one another with no centralised authority over them operates at max 5000 bits/s.

If we add Central planners to the mix, i.e. some central authority who will make decisions on behalf of the rest of the population; presumably for the betterment of all the humans rather than the individuals themselves. Then we should expect for the very least that we match our max processing throughput that 100 humans who had complete autonomy had, i.e. 5000 bits/s.

Consider a realistic scenario that 10 elected officials will now "plan" the economy

10 x (40 - 50) = 400 - 500 bits/s

Consider an unrealistic scenario that 99 elected officials will now "plan" the economy

99 x (40 - 50) = 3960 - 4950 bits/s

Just for brevity what about 100/100 central planners?
Well 100 people planning for no one would be pretty insane but ultimately fruitless since there's no one to enact any of the decisions made so that in turns equal 0 bits/s.

All 3 cases mathematically shows that Central Planning can never out perform individuals freely trading and making their own decisions for themselves.

It is not theoretically impossible for Central planners to make truly informed decisions on behalf of the rest of the population, i.e. we may be able to read people's minds within <1ms with some technology into the future, but this is strictly science fiction. To play devil's advocate, let us grant that they cant read people's minds and figure out what they want. Central planners will still face the question of how to provide what their population wants which is a question that is impossible for them to solve since they face the economic calculation problem.

As it stands now they cannot make truly informed decisions on behalf of the rest of the population since the data they are considering is always lacking the full picture.