The classic:

“It is difficult to get a man to understand something, when his salary depends on his not understanding it.” - Upton Sinclair

Except possibly even more high stakes than that, since academics' very reputations are on the line.

REM: sunk-cost-falacy

https://en.m.wikipedia.org/wiki/Hat_puzzle

Gödel's incompleteness theorem (philosophical); 'Theorem states that no consistent system of axioms can be listed by an effective procedure, capable of proving all truth' (-;

https://en.m.wikipedia.org/wiki/Epistemic_logic

Hint: HN in 2016

regards...

The only way to do this is to admit fewer PhD students, which probably should happen. There's only so many professorships, and some will always be more coveted than others, leading to those stakes.

I could posit a few other ways. Could also make it so that we aren't financially dependent on wild success, for example.

It's probably not the absolute number of PhD students that's the problem. It's the crushing despair of uncertainty, the publish-and-eventually-still-perish incinerator, the cult of positive results, the completely ridiculous inefficiency of the actual work (because it's done mostly by inexperienced grad students, and by the time they know what's up they are already off to some godforsaken postdoc or worse, or leave academia for good if they are lucky).

Not to mention the whole tenure system is questionable. Yes, it's good that at least a few percent of academia has job security, but the selection process is full of perverse incentives and arguably society could get better results if tenure was for 10 years and based on a lottery.