The important thing isn't that you promote the best worker; the key is that it isn't possible for the ambitious-but-incompetent to game their way up.
Edit: Wait, that was promoting.
(Also, if people are interested in randomness in antique decision making, me & my wife made a simulator of an ancient lot oracle unearthed in modern Turkey: https://sortesalearum.com)
The sad thing is, I feel that this method may actually produce better results than whatever popularity voting schemes we're currently using.
(It's somewhat enshrined in modern-day RNGs used in simulation and forecasting models.)
Michael Schulson's 2014 Aeon essay, "How to Choose" remains at the top of my best reads of the past decade:
... It makes sense that it should have taken Dove some 15 years to realise that randomness could be an asset. As moderns, we take it for granted that the best decisions stem from a process of empirical analysis and informed choice, with a clear goal in mind. That kind of decision-making, at least in theory, undergirds the ways that we choose political leaders, play the stock market, and select candidates for schools and jobs. It also shapes the way in which we critique the rituals and superstitions of others. But, as the Kantu’ illustrate, there are plenty of situations when random chance really is your best option. And those situations might be far more prevalent in our modern lives than we generally admit. ...
<https://aeon.co/essays/if-you-can-t-choose-wisely-choose-ran...>
Examples include swidden farmers in New Guinea, China's I Ching, the Athenian Greek elections (more a lottery than today's FPTP precise-count balloting), Renaissance Italy's Doges, and contemporary college admissions, with references for further reading.
https://imperiumromanum.pl/en/curiosities/alectriomancy-fort...
A few years ago I'd thought that the US Supreme Court might benefit by both expansion and selecting by lot the judicial panel for any given case. This would throw far more uncertainty into the outcome of any given Supreme Court case, as well as the capacity to throw the court in the benefit of one party or the other for years at a time. That's been proposed by others.
Another possibility might be to apply a similar approach to legislation, with an expanded Congress closer to the 30,000:1 constituent to representative ratio initially in the US Constitution rather than the 616,000:1 ratio presently in place. That would result in a House of 11,000 members, however.
(I'm willing to accept that this might prove infeasible, though I'd still like to see approaches enabling greater direct representation.)
What if, as with the Supreme Court reform proposal, legislative votes were based on a subset of representatives, again allocated by lot from amongst members? Again, though outcomes would over time average to partisan representation, any given vote might, or might not, favour the majority party.
One possible consequence: given the impossibility of guaranteeing a known outcome in votes, legislation might be written to more broadly consider overall views. This could avoid exremes, though it's worth noting that extremes gave rise to both highly discriminatory and civil-rights-reform practices. Some extremes seem less bad than others.
There's also the probable outcome that the locus of control would shift elsewhere. I'd still like to see some discussion of such concepts.