This is so wrong since it implies that a decision is binary, thus taking the opposite decision of a "wrong decision" is well defined and automatically right.
Well, in the author's defense, they specifically stated that "Each assignment required a yes-no decision". I agree, though, that there really is no great lesson to be learned here since the real world doesn't work like that.
The technical bit about channel capacity was honestly more interesting. It's a neat result (that should be fairly obvious to anyone who's worked with probabilities) with a not-so-great example to illustrate it.
Agreed, "Yes/No" is in no way correlated with "50/50 chance".
Will I win the lottery? Yes/No. 50/50?
My favorite conflation is the "are we in a simulation?" argument. That's a yes/no also, and the ignorant conclusion is that its very likely we are. Without any statistics on the probability either way.
Also, Pascal's wager. The presented sides of the bet aren't equal, because on the one hand you have existence of a particular God, and on the other hand its non-existence, whereas in the real world, there's a whole space of possible Gods that people believe in that are not included in the wager.
But the conditions omit the all-important consequence. "What are your priors?" Suppose 99% of choices have hardly any consequence, and Bob is wrong on 95%. But Bob is right on the most expensive places to fail. Then, choosing the opposite could be disastrous, even though you get 95% of the choices right.
TL;DR: when facing binary choices (yes/no), stupidity is being ~50% correct, not ~0% correct. When someone is correct e.g. only 5% of times, it means they're strongly anticorrelated with reality, and you just have to do the opposite of what they say to be 95% correct.
Binary choice describes a range not a distribution. Suppose Bob is optimistic and always decides "yes". The opposite of Bob's decision is always "no".
The right course of action requires looking at the data, not theory. In a context where the probability that "yes" is right is 0.05 -- 19/20 proposals being bad ideas is not an implausible reality -- there's no excuse for keeping Bob, just answer 'no'. There's no reason to assume that correct yes's and no;s are equally distributed.
There's also no reason to assume that an incorrect yes has the same cost as an incorrect no or that a correct yes has the same benefit as a correct no. Silicon Valley venture financing comes to mind.
To me, it's probably a good idea to base business decisions on business facts rather than the beauty of a theory. It's not that theories shouldn't inform decisions, but data is probably a better place to start.
I think the problem with this example is assuming that both decision outputs can equally impact profits (that both are perfectly symmetrical on their effects).
For example, if this person is deciding whether or not to extend a credit line to a client, the NO decisions are not going to have an effect on the profits bottom line.
Saying NO a lot, in this case, means having the same cost to operate but fewer opportunities to profit from new and existing clients. On the other hand, saying YES a lot means that the company can profit from extending those credit lines but there's a risk that they would lose money from unrecovered credits and a more heavy collections operation.
So, actually, Bob is only useful if he is the conservative one that says NO a lot. If Bob says YES a lot, his impact is only as good as the 5% of his correct decisions.
In any big enough group there is always an Oracle of Wrong. They are very precious. It's very hard to be right all the time, but less hard to be wrong all the time.
Over decades I have puzzled over the existence of Oracles of Wrong. One clue is that they always come from privileged backgrounds. Taking the easy, wrong choice has never caused them any personal discomfort, but has often saved them some minor inconvenience that the hard, right choice would have cost.
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[ 3.8 ms ] story [ 42.8 ms ] threadWhich is hilariously different to reality.
Each assignment required a yes-no decision.
Will I win the lottery? Yes/No. 50/50?
My favorite conflation is the "are we in a simulation?" argument. That's a yes/no also, and the ignorant conclusion is that its very likely we are. Without any statistics on the probability either way.
But the conditions omit the all-important consequence. "What are your priors?" Suppose 99% of choices have hardly any consequence, and Bob is wrong on 95%. But Bob is right on the most expensive places to fail. Then, choosing the opposite could be disastrous, even though you get 95% of the choices right.
https://www.youtube.com/watch?v=cKUvKE3bQlY
The right course of action requires looking at the data, not theory. In a context where the probability that "yes" is right is 0.05 -- 19/20 proposals being bad ideas is not an implausible reality -- there's no excuse for keeping Bob, just answer 'no'. There's no reason to assume that correct yes's and no;s are equally distributed.
There's also no reason to assume that an incorrect yes has the same cost as an incorrect no or that a correct yes has the same benefit as a correct no. Silicon Valley venture financing comes to mind.
To me, it's probably a good idea to base business decisions on business facts rather than the beauty of a theory. It's not that theories shouldn't inform decisions, but data is probably a better place to start.
For example, if this person is deciding whether or not to extend a credit line to a client, the NO decisions are not going to have an effect on the profits bottom line.
Saying NO a lot, in this case, means having the same cost to operate but fewer opportunities to profit from new and existing clients. On the other hand, saying YES a lot means that the company can profit from extending those credit lines but there's a risk that they would lose money from unrecovered credits and a more heavy collections operation.
So, actually, Bob is only useful if he is the conservative one that says NO a lot. If Bob says YES a lot, his impact is only as good as the 5% of his correct decisions.
In any big enough group there is always an Oracle of Wrong. They are very precious. It's very hard to be right all the time, but less hard to be wrong all the time.
Over decades I have puzzled over the existence of Oracles of Wrong. One clue is that they always come from privileged backgrounds. Taking the easy, wrong choice has never caused them any personal discomfort, but has often saved them some minor inconvenience that the hard, right choice would have cost.