# It's possible that your stupidity will affect your ability to understand this post

Imagine that, over the course of a conversation with a friend from work, she makes the following two statements:

1. It's possible that my brother will be coming into town tomorrow
2. It's possible that our boss knows about the affair you had with the intern

(You might also have to imagine a more adventurous romantic life for yourself). Which of these two statements do you think your friend believes is most likely to be true? Let's make this a poll:

If I did a good job setting up this scenario, I should be able to predict the results of the poll. I'll get to my prediction in a minute.

First, let's talk a little about why this question is important. The most obvious application of judgments about probability comes from the field of medicine. We've discussed a key problem doctors have in communicating with their patients -- many patients don't understand numerical probability. So if a doctor says, for example, "there's a 1 percent chance you'll go blind from this surgery," many patients will systematically misunderstand what that means.

One possible way to get around this limitation is to use qualitative statements instead of percentages: "it's extremely unlikely that you'll go blind from this surgery." But, as we'll see, there are problems with this approach as well. Jean-FranÃ§ois Bonnefon and GaÃ«lle Villejoubert asked over 800 people from a broad range of backgrounds to imagine two different medical scenarios:

1. Your family doctor tells you that you possibly will develop insomnia soon.
2. Your family doctor tells you that you possibly will develop deafness soon.

For each scenario, the respondents attempted to convert the doctor's qualitative statement into a numeric value, by rating the likelihood that the doctor believed that they had a given percentage chance of developing insomnia or deafness. Here are the results:

When the condition is seen as more severe, people are significantly more likely to think the doctor believes the condition is more likely to develop -- even though the doctor used the same words to describe the probability. Bonnefon and Villejoubert believe the "patients" are using a similar process to how you might respond to your friend telling you your boss "possibly" knows about your affair. Since this news is possibly embarrassing to you, you believe that your friend is simply using the word "possibly" to help you save face. When your friend says her brother is "possibly" coming to town, there's no potential embarrassment or harm to you, so you take it as a legitimate assessment of probability.

Bonnefon and Villejoubert argue that the doctor-patient relationship is similar: your doctor uses "possibly" in the case of deafness to "soften the blow," not as an honest assessment of probability. When the condition isn't as severe (insomnia), you're more likely to believe it to be an accurate assessment of your chances of developing the condition. Their data backs this argument as well: they asked patients why the doctors chose the word "possibly," and in the case of deafness, they were significantly more likely to say that it was a case of "face management," rather than a judgment of probability.

So if some patients don't understand numerical probability, and if qualitative statements of probability can be misinterpreted, what's the conscientious doctor to do? With younger, more educated patients, it seems that numerical statements are the clear winner. But with less-educated and older patients, it may be extremely difficult to strike the right balance between accuracy and understanding.

Bonnefon, J., & Villejoubert, G. (2006). Tactful or doubful? Expectations of politeness explain the severity bias in the interpretation of probability phrases. Psychological Science, 17(9), 747-751.

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I voted for the "possible affair" choice but for a different reason. The question was which statement the co-worker believed to be true, and I chose the more lascivious one, because despite ourselves I think we're more inclined to want potentially troubling gossip to be true than something mundane like a family visit. After all the drama would sure as hell be more interesting.

This could, of course, be projection on my part.

I voted the opposite of Warren, for Similar reasons. A casual statement is made and it seems likely she would know. The more lascivious statement would (to me) be more likely to be gossip and exist primarily to get a rise or cause interesting discussion

I also voted for #2 but for other reasons. It was easy for me to imagine to have a more adventurous romantic life for myself. But I don't have a brother, and it was harder for me to imagine that, not to mention that there was no fine print allowing me to imagine that I have a brother, like it did with me having a more adventurous side.

I chose the affair, but not for the specific reason you outlined in your post.

It seems to me that the very fact that my co-worker brought up the topic of the affair makes it more likely that she believes it to be true. Perhaps this also ties into the fact that it's potentially embarrassing, in that she would refrain from mentioning such rumors if she weren't more confident of their truth than that of a non-emotional topic.

I voted for the brother statement. My reasoning was that the boss learning about my affair is a serious matter, and she might warn me even if there was a slight chance of it being true, just to be safe. On the other hand, I think she wouldn't mention her brother's visit unless it was fairly likely.

I voted for number #2 because it felt more likely that she knows her brother (and that situation) better than what information the boss has.

I voted (with the majority) for her brother coming to town. Because, while possibility does not convey any information on probability whatsoeer, I felt it more likely she would be attuned to what her brother is doing more than what your boss knows.

Evaluations of probability are not impacted only by severity or assessment. They are also impacted by (implicit) prior probabilities. The doctor has a greater prior probability of being able to predict deafness (obviously a medical condition) than insomnia (a psychological condition).

Did this stud show that the doctors were being tactful, and that this was in fact the reason for the results? Or is this just an unwarranted speculation on the part of the author. Sadly, since the research is locked behind a paywall, we have no way of knowing - and readers are led into believing what may well be an invalid inference from this coverage.

If you ask me, this is the sort of speculation in the name of "science" that gives social science a bad name. How can you meaningfully evaluate the question? It depends on the circumstances, and on the personality of the co-worker, and a myriad of other factors. In the medical context it depends on the relationship or lack thereof between doctor and patient, on the way the words are said, on the background and information available to the patient, and many other factors as well. To isolate this kind of statement and then speculate over how people interpret it, without any meaningful testing, is really to have a lot of trust in your own opinions and a high opinion of your own analytic abilities.

BTW, would this same speculation apply equally to poor people in a public hospital setting as to wealthy people in an exclusive private one? To people of different faiths and cultures? What set of doctors and patients are we discussing? Or are the factors you mention proposed to be universal?

By Albion Tourgee (not verified) on 05 Nov 2007 #permalink

I voted for number two, but it was simply a case of wishful thinking...

I voted for #2, but again for a different reason. Statement #1 regards the future, which is always indefinite to some degree; your friend can't know this for certain. Statement #2 is about the present; the boss either knows or does not know. It seems that if she brought it up, then there must be some evidence of the actual state that caused her to mention it.

I don't think the coworker is a good analogy for the doctor. The tendency to gossip adds another dimension to the coworker's motive for speculating on what the boss knows, and gossip has little to do with certainty.

I voted for "brother coming to town" and was quite surprised that so many people had voted the other way (though apparently I'm still in the majority). If the friend actually thought the boss knew about the affair, I'd expect her to say "I think our boss knows", not "It's possible our boss knows". To me, "it's possible" makes it sound like she's going out of her way to avoid saying it's either likely or unlikely.

So why don't I have the same intuition about the brother case? Not sure, but it may have to do with the fact that there are two interpretations of the first statement (either "I don't know for sure what my brother is planning" OR "I know for sure that my brother hasn't made up his mind yet") but there's only one interpretation of the second statement ("I don't know for sure what the boss knows").

There was no good data for either. I chose #2 because it was about things that were potentially work related an perhaps the boss was more likely to know.

I voted for the brother. This was my reasoning: If she said to me, "It's possible that X," she is implying that she knows some fact Y that supports X. That is, she must have some grounds Y for asserting that X is possible. So I asked myself, what kind of grounds would she have for asserting that her brother might come into town? Most likely, her brother told her that he might come into town. On the other hand, what kind of grounds would she have for asserting that our boss knows about the affair? Most likely, our boss said something that hinted at such knowledge. Now, which of the two kinds of evidence is most reliable? It seems to me that her brother's statement would be more reliable than something that was merely hinted at by our boss.

I think this kind of reasoning is not unusual. When people say something is possible, we naturally wonder what grounds they have for such an assertion.

I voted for the affair because she used the phrase "the affair you had," which I took to mean that an affair had come up previously and was now being discussed again-- as when you say "the cop stopped my car," rather than "a cop ..." you mean this particular cop had been mentioned before, who we both are aware of. So I thought even if she hadn't discussed this intern matter with me, she had discussed it with someone else, and she believed it. "An affair" woud have also expressed more uncertainty.

Actually, continuing my previous post above, this may kind of reasoning may also explain the deafness versus insomnia example. Deafness is likely to be caused by some biological problem, whereas insomnia seems more likely to be caused by some psychological problem. Doctors seem to be more reliable with biological problems than psychological problems. So it is natural to reason that, if a doctor has grounds for believing I might go deaf, that is probably more reliable than the grounds for believing I might have insomnia. Thus both results (insomnia + deafness and brother + boss) can be explained by the hypothesis that we reason from our models of what the speaker can reliably know.

I think the affair statement is more likely to be perceived as true by the co-worker. Otherwise, why would she even say it?

Hell, I didn't even think she knew about the intern.

Yeah, those two statements have two different meanings. The first is uncertainty about an event in the future (brother in town), and the second is uncertainty about an event in the past (boss found out about the affair). Uncertainty about the past is of greater degree than uncertainty about the future.

Wouldn't the doctor be considerably more reckless, not to mention inconsiderate, to say, just casually, that it's possible I will develop deafness, than if he simply says it's possible I will develop insomnia. It seems a matter of relevance -- why would he mention a serious condition unless he thought I really should prepare myself for the event of a serious condition (which preparation is not so crucial for a less severe condition)? That wouldn't be face management, but implicature. But I would assume that Bonnefon and Villejoubert consider this possibility.

Also, how did the patients give their answers to the question about what was meant by 'possibly'? It seems unlikely that they simply all thought up 'face management' by themselves, so I'm also assuming that this is a category Bonnefon and Villejoubert are using to interpret the answers they actually received.

#2 is more domain-specific; you are co-workers and not family members. But my instinct was to believe both to be false.. but I sure don't the boss to know of my indiscretion. (Even if P. Tane is in the same boat? LOL) It's attention-directing info to a much greater degree than #1... (Unless you have MY brother... LOL)

But I agree with the comment above that there is a gut reaction "what if X is true?" where the loss function is much more meaningful for #2.

Rewrite this as your sibling tells you those 2 questions -then #1 should seem more true.

Or rewrite it with #2 as a positive event. That would be interesting...

By Norris Krueger (not verified) on 05 Nov 2007 #permalink

It seems that you didn't set up your poll right, because I voted the same way a lot of other people seem to have - Peter Turney I think outlined the same pattern of reasoning re: reliability of evidence that I followed.

Nonetheless, this is indeed interesting. As part of my work and my casual interest it's been made very clear to me how bad people are at assessing risk and probability, even when presented with numbers. One of the skills in communicating any kind of technical data to a lay audience is in adding a translation layer that converts rational information into information digestible for a non-rational actor, which is what we all fundamentally are despite economists' hopeful assertions to the contrary. It is, as you have pointed out, an incredibly difficult minefield to tread, so any research that may point to specific trends in irrationalities is welcome.

Hmm,

I'd be curious to hear what Tversky and Kahneman (1982) would have to say about these study results, given that their work proposed two implicit mental heuristics used when one makes probability judgements about decisions involving a high level of uncertainty.

The availability heuristic concerns judgements of probability based on how easily information can be retrieved from memory--easy retrieval implies higher probability; harder retrieval implies lower probability. Thus as an example (and I'm making a large assumption), most will probably choose the situation concerning the brother because it seems like it would be a more easily retrievable memory since it seems like a more realistic situation for most. The other one seems like it would be a higher probability, if, there's much time spent watching drama tv.

I suspect the situation concerning the insomnia vs. deafness diagnosis could be explained by a combination of both the availability and representative heuristic. People are likely not going to believe that there's a greater than 50/50 chance that they will develop insomnia, presumably because they can easily retrieve memories in which they did not have insomnia. Furthermore, those memories are likely to be representative of the probability of their likelihood of developing insomnia in the future. So basically, it's unimaginable what would cause them to develop insomnia at a greater than 50% chance.

On the other hand (if the patient can hear), they likely are unable to retrieve any memories associated with factors likely to cause deafness. This further leads to having no representative memories/prototype experiences for factors that could possibly lead to deafness. Given that, it is most likely that a patient will believe the doctor at a rate greater than 50/50, since the likely thinking here would be that the doctor might know something/have experiences concerning deafness the patient knows nothing about.

By Tony Jeremiah (not verified) on 05 Nov 2007 #permalink

Not that it probably affected anyone's responses much (I didn't think of it until I decided not to vote), but your poll is asking about the coworker's belief in the relative probability of two statements being true, while what she asserted was technically about her belief in a specified probability of the statements being true.

For example, she could be extremely certain that there is a very small probability that her brother will come to town tomorrow, say that he will come if and only if he wins a drawing for tickets to the big game tomorrow night. Meanwhile she could be expressing the possibility that the boss knows about your affair in much more reserved terms, e.g. that she thinks your boss encountered some evidence which would be an excelent tip-off about the affair, but doesn't know for sure.

The situation could of course be reversed for any number of reasons. If your coworker is rather cautious, she could be expressing strong certainty that her brother is coming (but could be waylaid by car troubles or a storm or something), while alerting you to even a very small chance that your boss knows about your affair.

In practical terms, I would normally assume that the coworker was more certain of her estimation of the probability of her brother coming to visit, since trying to figure out what secrets other people do and don't know is inherently hard (otherwise they're not very good secrets), but that doesn't really bear on what her estimation is.

Besides the issue of trying to soften the blow of especially bad news, I wonder if similar effects caused by patients estimating the certainty of the doctor's probability estimate appears there also. The ratings for the doctor's belief that you might become an insomniac is not only centered at a lower probability, it peaks at a lower rating of belief and is flatter, which to me suggests some sort of intuitive application of a certainty estimate---i.e. that the doctor will only give an estimation of your probability of becoming deaf with great seriousness, no matter what the probability is, while a prediction of insomnia might be tossed out without bothering to acquire as much certainty.

By Matthew L. (not verified) on 05 Nov 2007 #permalink

Haven't had time to read the comments, but another interesting note is that people tend to assume "possible" means "plausible" or "likely"; thus, when someone says, for example, that "it's possible that women's brains simply aren't wired in a way that makes them as good at math as men" (which is a technically true statement, in the sense that the situation described is "possible" in the sense that a "square circle" or "married bachelor" is not), people infer (almost always correctly, it seems) that the person actually believes this to be the case. This seems like it might be related...

(Note to other commenters: please do not hijack the thread by jumping on my specific choice of examples, kthx?)

Great discussion!

One possible explanation for the discrepancy between our poll results and the study results is that the study used a different methodology -- respondents rated the chance that the doctor had each of a series of percentage chances, whereas in the case of our poll, there was only one judgment to make.

But it's also possible that the nature of the question I asked simply doesn't match the questions in the study. It would be interesting to know if the simpler methodology would have worked with the deafness/insomnia example.

I voted for #2 on the basis that revealing the boss's knowledge is a more serious statement - you wouldn't want to say such a thing unless you had some actual evidence that the boss knows something (like unusual behaviour or comments).

Whether the brother comes to town or not matters little so it is not important if the statement might be wrong (i.e. the probability of the brother coming to town is low).

If there's, say, a 10% chance that the boss knows, then it is vitally important to inform you of that possibility. However it is not vitally important to inform you of the brother coming to town.

My relatives are a bit flaky. They share this trait with a lot of the population. People who say "let's get together sometime soon" and do not. So if somebody says "I'm coming to town tomorrow" I don't believe it until they actually do it.

Well, the fact that I know I didn't do #2 made things a bit more tricky (I also wondered if my stupidity was affecting the results). But I chose #2 because in general, a person would be more concerned about something more serious like that. Oh, and I don't have any siblings, by the way.

But it's also possible that the nature of the question I asked simply doesn't match the questions in the study.

Yes, but is it as possible as the boss knowing about you and the intern?

I voted for the second, as like Cecil I'd say the coworker wouldn't raise such a subject unless she had a very strong belief in that being the case. Also from what I've seen, doctors usually dodge the issue where probabilities are raised instead of trying to convert them into qualitative terms! I wonder if working in a litigatious environment influences this process...

I voted for the brother statement because it seemed most likely to be based on first hand knowledge, whereas the boss/affair statement seemed like it was based on rumor or second/third/etc. hand knowledge, and therefore more suspect.

Sorry to have voted in contradiction to the theory... it's a nice theory in other ways, I'm sure. Very clean.

Duhh,what was the question again??!!?....

By Anotherbrick (not verified) on 06 Nov 2007 #permalink

I selected #2. #1 speculated about a future event that had not happened, #2 speculated about one's knowledge of an event that already taken place.

In a hypothetical and highly complex process with unstated subjective frameworks are results meaningful in objective reality?

By kevin armstrong (not verified) on 06 Nov 2007 #permalink

Like Alejandro, I focused on the implied consequences of the statments. If the probability of two events happening are equal, but the consequence of one is more serious, how will that change the conversation?

I suggest that a person, for any given probability, is more likely to raise the more serious event. Conversely, if both events receive equal weight, (e.g., It's possible that...") I would assume the probability of the inocuous event would higher than the serious event.

I'll apologize if I'm repeating someone, I didn't make it through all the previous comments. I do think that you have a good point here about 'face-saving' with the use of 'possible', but I think the first poll has a problem.

If your coworker suggests that it's possible that her brother is coming into town, that is one, independent, event. Her brother will either come to town or not. If your coworker suggests that it's possible that your boss knows about your affair, that is two events. The affair has to happen and the boss has to know. Which one do I think my coworker believes is true? Depends on what I think she knows about my affair (it may or may not exist or she I may or may not have told her) and about my boss' suspicion (he may or may not know or she may or may not know that he is suspicious).

I still answered #2...but it took a bit of thinking until I decided i was having the affair and that I had told her. She and I are very close friends.

Interesting phenomenon.

For what it's worth, I voted (1) because I reckoned she'd feel more confident in the quality of her information about something like her brother's plans (presumably, she knows this because he told her he had had tentative plans to visit) than about something like her boss' knowledge of an affair (presumably, she knows this because of hints he dropped or inferences she otherwise drew from his behavior).

I voted #2. I felt the speaker was trying to cushion the negative event with the word "possible".

Although, when evaluating the first example (brother and affair), I found myself reflecting on my relationship and communication with my own brother, which I don't think was the point? Also, the brother statement wasn't just less negative, it wasn't negative at all.

Whereas in the second example (medical statements) both possibilities were in a similar vein and both were negative.

I voted for the brother coming into town. It's more likely than an affair, and more common. What does that say about me? Oh wait, I guess I should read the remainder of the article.

My reasons for picking one are a combination of Dan's and Peter Turney's.

I heard the word "possible" as having completely different meanings in the two cases:

In the brother's case, it meant that he had apparently expressed the intention of coming, but the uncertainty was located in his inability to completely predict events.

In the case of the affair, I located the uncertainty in the fact that the co-worker was making an inference on less than solid grounds.

So I heard "possible" in the second case as meaning, "I've got a feeling that maybe", and in the first case as meaning, "If everything goes as planned."