What is the name of this fallacy?

Suppose the conditions are: a regular die is rolled and the outcome noted “6” or “not a 6” (which, of course, have the probabilities of 1/6 and 5/6 respectively).

If you guess the outcome, you win a dollar.

You guess “not a 6”, the die is rolled, it is a 6.

Someone says “Haha! Should have chosen 6!”

What is the technical name for their fallacy? I was tempted to call it “post hoc reasoning” but Googling I find that’s synonymous with “Post hoc ergo propter hoc” which isn’t the error in this case.

I don’t think post hoc reasoning is synonymous with post hoc ergo propter hoc. To me, post hoc reasoning means assuming you should have used information you didn’t even have at the time the decision was made–just like your “roll of the die” example.

I don’t know if it’s properly called a fallacy or not.

I’m not seeing any fallacy here.

If the person means “You would have been better off if you had chosen 6” (which is IMHO the most obvious interpretation) they’re simply stating an obvious truth.

If the person means “You should have known or guessed that it would come up 6” they’re saying something that’s false, but a falsehood is not the same thing as a fallacy.

Thanks both.

74, that’s what I wanted too, but all the links I could find to Post Hoc reasoning led me to Post hoc ergo propter hoc. Maybe my Google-foo is weak.

Thudlow, I really would want to say that a falsehood is a fallacy. But okay, rider question, what is the difference between a falsehood and a fallacy? Especially in this case where the falsehood amounts to A therefore B (where B ceratinly does not follow from A (as you acknowledge).

…what is the difference between a falsehood and a fallacy?

A fallacy is faulty logic. A falsehood is simply something that isn’t true.

It seems to me that you’re trying to say that because “not a six” is statistically the more likely outcome, that the person saying “you should have chosen six” is using faulty logic, but it’s not faulty logic to lack an understanding of statistics. If it’s a statistics thing you’re considering, their statement is just falsehood and not a fallacy.

It seems to me the underlying mistake being made by the Monday Morning Quarterback (MMQ for short) is confusing an assessment of the situation with a prediction of the outcome.

When I assess the situation, I see that the odds are 5 to 1 against rolling a six, therefore betting against the six is the best strategy. This is a correct assessment, regardless of what actually happens when the die is rolled. When a six comes up (which it will, eventually) and the MMQ laughs at me for being a poor prognosticator, they are indeed committing an error in thinking. If you don’t like labeling it as a “fallacy” then fine, call it a falsehood. Whatever.

I see this come up all the time when people criticize meteorologists. When the meteorologist says “10% chance of rain” and then it pours, MMQs laugh and say the meteorologist was wrong. But this is a mistake. The meteorologist would only be wrong if you kept track of how many times they said “10% chance of rain” and counted how many times it actually rained and found that the outcome was significantly different from 10%. If the meteorologist said “10% chance of rain” 200 times in 2 years, you’d expect it to rain 20 times and not rain 180 times, so no one should be surprised when it actually does rain 20 times. Yet MMQs will say the meteorologist was wrong 20 times. That’s unfair. Our fictional meteorologist correctly assessed the situation every single time.

Of course, it goes without saying that assessments can, in fact, be wrong. But it takes more than just one data point to prove that it’s wrong.

Right, sbunny, that’s exactly as I see it.

Bob, I do not believe that it is a lack of understanding of statistics, I think it is a proper fully-fledged logical fallacy: “*X occurred THEREFORE you should have chosen according to this hindsight knowledge *”, but that’s wrong – that hindsight knowledge was necessarily unavailable at the time of choosing. One should choose according to the criterion of maximum likelihood (IMHO).

Anyway, falsehood or fallacy, this thing should(!) have a name because it happens often enough to merit one, this cannot be the first time someone has thought to name it, can it?

Actually “the falsehood/fallacy of the great unwashed” is nearly catchy, doncha think?

Historian’s Fallacy.

This is an informal fallacy, also known as “retrospective determinism.” It is not the same thing as “Presentism,” which is judging the past by modern standards.

That’s a good example. And I think this example, and maybe the OP’s as well, could be described as a fallacy involving an Unrepresentative Sample: the single weather forecast, or single die roll, is an unrepresentative sample of all such forecasts or rolls.

That certainly looks like it fits what Unwashed was talking about in Post #7.

Thanks RivkahChaya: I’ve never heard that term before but that is it (the fallacy*, however, I meet on a daily basis).
*see, I told you it was a “fallacy”!

To use “fallacy” as you seem to want to use it, empties the word of any useful meaning (and would be graded as incorrect in any elementary logic class). A fallacy is, by definition, a flaw in an argument, that renders it invalid (though it need not necessarily render the conclusion false). No argument is presented in your OP, so there is no possibility of diagnosing a fallacy.

Furthermore, the statement “Should have chosen 6,” is not even false, although, if it is said in a contemptuous way, the contempt is not justified, and it is possible (but by no means certain) that the speaker might have silently arrived at his contemptuous opinion of the gambler via the “historian’s fallacy”. However, all this can be no more than speculation. Not only is no argument (fallacious or otherwise) stated, but there is also no unjustified claim or conclusion, such as “Therefore, you are an idiot,” that is clearly and explicitly stated.

The Historian’s Fallacy is interesting, but I don’t think that’s what we’re talking about here. The problem with the dice isn’t so much that future information alters the decision. The problem is that the situation itself involves random elements. The disconnect is that optimal strategies don’t perform 100%, and yet this doesn’t prove they aren’t optimal. In almost any situation, there’s a plan which has the best chance for success… and yet, at least some of the time, that plan will lead you to failure. But it’s silly to claim that these failures prove the plan was flawed.

The examples given in RivkahChaya’s link to the Historian’s Fallacy seem to be more of the type where something totally unexpected happened, like you rolled the dice, predicting the number would be 1-5, and a dog ate the dice so there was no number at all. Then, with 20/20 hindsight, we can criticize your choice by saying you forgot to consider the dog.

As I tried to say in my first reply, and was tempted to elaborate on more fully, the exchange described in the OP could be interpreted in more than one way, from a simple taunt (“Ha ha, you lost!”) to a conclusion arrived at through some unstated reasoning. “Should” statements are tricky to assign a truth value to; I think you have to unpack or reword them before you can analyze them logically.

sbunny, I don’t see what you aren’t seeing, RivkahChaya’s link gives an example (not exactly analogous to my die, but pretty close) “You should have never taken the back roads to the concert. If you had taken the main roads, you would not have been stuck in all that traffic due to the accident.

Worse, if you’re right and this isn’t the Historian’s Fallacy we still don’t have a name. This thing should have a name.

<sound of can of worms being opened>

njtt, the link says “The Historian’s Fallacy is an informal fallacy”, so perhaps calling it a fallacy is too much. But given that other errors of argument, ad hominem, *ad populum *etc, are frequently listed as logical fallacies (when they too are merely informal fallacies) I don’t see what the problem is, unless it is that “no argument is presented”. I disagree, I think the argument is implicit and patent:

You chose “not a 6”
The die rolled a 6
You should have picked 6

And here, if you want to devoid the conclusion of meaning by interpreting it as “had you chosen 6 you would have won” then for the moment I agree there is no fallacy (but I see other problems*). However, it’s my OP so let me clarify what I meant the meaning to be, the meaning is, “You made a bad choice!”** That is wrong, the choice was the best choice and always will have been the best choice.

A wrong conclusion following from such a construction? Doesn’t seem unreasonable to call this a fallacy.

Still, you see it differently, so it’s not a fallacy, it’s just an error. What is the name of the error? We could use MMQ as per sbunny, but I find it hard to believe that this hasn’t been codified and named before (in fact I believe it has been codified and named, it is the Historian’s Fallacy).
Now, my footnotes, in quixotic reverse order:
** it might look like dirty pool to start (re)defining my terms after you’ve already committed some effort to your response, but that’s not my intention: I had assumed that the “Haha! Should have done X” was universally recognised to mean what I say it means. Mea culpa, sorry for the inconvenience.

  • “had you chosen 6 you would have won”. There is no reason to suppose that had I chosen 6 that 6 would have shown. The mere act of choice is an initial condiction, and if it is made in the proximity of the dice thrower certainly has the potential to affect the outcome.

But further still, the imaginary worlds where I would choose 6 are worlds significantly different from this one, there is no reason to suppose that were I able to slide from this world to one of these other bizarro worlds that the outcome there would also be a 6 (it is in THIS world that a 6 was thrown, not all possible worlds).

The scenario described in the OP can be turned into an explicit argument with fallacious reasoning with a small tweak. I encounter this form of this situation regularly, and it is indeed pretty damn infuriating. Consider:

Bob: Dude, you should totally bet “6”, I’ve got a great feeling about it.

Tim: No, for that is stupid.

[Tim bets “not 6”. Die comes up 6.]

Bob: See, you should have listened to my advice!

At that point, the argument Bob is making is that because his stupidity happened to produce a correct result in a single instance of random chance, the reasoning he used to reach his original conclusion — a statistically disadvantageous ass-pull — was sound, and should be relied upon in future decision-making.

TGU, is that what you had in mind?

That’s another flavour of it. It’s the idea that the outcome determines what should have been chosen, but it doesn’t.

Neglect of probability?

It’s not a fallacy, it’s hindsight bias, the " inclination, after an event has occurred, to see the event as having been predictable."

People often want to describe biases as fallacies, but those are two different words. Fallacies are specifically for errors in logic linking propositions and conclusions. That doesn’t happen in the OP.