Typicality and Asymmetrical Similarity

Alaska is unusually far from the United States

Seeing as how Alaska is in the United States, I would say this makes it unusually close.

Has it been established that people who prefer "98 is approximately 100" to "100 is approximately 98" or "Mexico is like the US" to "the US is like Mexico" do so because, e.g., they think 98 is nearer to 100 than vice versa? It seems to me that "approximately 100" and "like the US" have an obvious advantage over "approximately 98" and "like Mexico": 100 is a nice-round-number, one that people are immediately familiar with the rough size of and that's easy to calculate with; the US is a nation everyone knows (or thinks they do).

I bet there really is a bias here, but that observation doesn't strike me as very good evidence for it. The rival explanations are too good. (The example about disease in ducks and robins is much better.)

g, as far as I can tell, what you described is a bias. Misapplied heuristic. Answering the wrong question.

but in a pragmatic sense, whatever difference separates a duck from a robin and would make a disease less likely to spread from a duck to a robin, must also be a difference between a robin and a duck, and would make a disease less likely to spread from a robin to a duck

What? No. It's not even vaguely reasonable to say that a transfer of a disease between two species is equally likely either way.

The differences between gray and red squirrels make it entirely certain that a particular disease will pass from gray to red, but not red to gray - grays carry the virus responsible in their DNA and are immune to it, but it kills reds.

Now, if you could show that people had a strong tendency to always assume that it would be easier to pass disease from something quite like the stereotypical example of a category to a non-stereotypical example than the other way around, you'd have something. As it is, you only have an anecdote.

Caledonian,

Your comments seem to me to increasingly be of the "gotcha" variety that focus on noncrucial details. There's value to keeping posters honest but you're on the slippery slope of irrelevancy. JMHO.

Your comments seem to me to increasingly be of the "gotcha" variety that focus on noncrucial details.

They're necessary to the arguments being made, which are necessary to the generation of conclusions.

If pointing out errors in the arguments isn't 'relevant' enough, what exactly would be?

The "errors" in the arguments are not relevant. When surveying people who aren't disease biologists, it doesn't matter if there are specific one-way paths in the cutting edge research, what matters are the processes that inform the decisions. In the absence of any biological information, there's no indication to tilt the scales one way or another. If these people were saying 'well, robins have gene XYZZY which causes etc.', but they aren't, they're functioning on categories as they don't have any real information on cross-species disease. Accidental cancellation is not an example of a lack of bias.

If all gray squirrels hold this "disease" DNA, and are completely unaffected by it, it doesn't seem any more a disease than mitochondria or stomach flora. If there are gray squirrels without it, and they can contract it from red squirrels, then the disease does indeed pass both ways even though gray squirrels are asymptomatic.

Pointing out why an error in an element of the argument matters would be relevant.

Thanks for the stuff on typicality, interesting. Just as a side thought, I suspect this has a bearing on Robin's recent post on complexity in political discourse. If one 'plank' of a candidate's position becomes 'typical' of his whole set of ideas, then that gives strength and coherence to Candidate X as a concept.

Tiiba, I don't think what I described is a bias, but perhaps I didn't explain it well. I'm proposing that in phrases like "X is approximately Y" and "X is like Y", the connectives are not intended to be taken as symmetrical relations like "differs little from"; rather, they mean something like "If you want to know about X, it may be useful to think about Y instead". And I don't see anything wrong with that, as such.

Let me give an analogy from a field where bias is quite effectively eliminated: pure mathematics. Mathematicians have various notations they use to express relationships of the form "this function is bigger than that one for large x". One of them, written something like "f ~ g", means "the ratio f/g tends to 1 in whatever limiting case we're interested in" (n -> oo, x -> 0, whatever). This really is a symmetrical relation; f ~ g if and only if g ~ f. But if you ask mathematicians which of "x^3+17x^2-25x+1 ~ x^3" and "x^3 ~ x^3+17x^2-25x+1" is more natural then I bet they'll quite consistently go for the former.

Now, if you want to call it a "bias" every time some term that looks symmetrical is used asymmetrically as a matter of convention or convenience, fair enough. I'd prefer to reserve "bias" for cases where the asymmetrical usage actually causes, or is a symptom of, error. As I say, I'm sure there's plenty of error caused by typicality heuristics; but I don't see that the asymmetry in the use of phrases like "is like" is, or indicates, an error.

(What "wrong question" do you think is being answered here?)

Kansas is unusually close to the center of the United States, and Alaska is unusually far from the United States;

anon & Eliezer, I think there's a 'the centre of' missing there. Easy typo to make.

Good post.

Caledonian's comments are increasingly annoying/irrelevant, taking cheap shots against Eliezer's posts and adding no useful information. There should be a way to filter his trollish comments.

They can moderate comments, but Cal occasionally makes a (cantankerously phrased) good point, so I doubt that they will.

In the absence of any biological information, there's no indication to tilt the scales one way or another.

Ah, but we're dealing with people who call everything even incidentally related to the subject 'evidence' and suggest that it should change the outcome of a Bayesian evaluation.

The statement about how disease transmission from one species to another should be just as likely as the reverse is simply logically wrong, period. Now, the post could have made a statement that we had no reason to presume the relationship would be of any particular form, and thus people should have favored one as much as the other - but that's not what was said.

Furthermore, one datapoint does not suffice to demonstrate a tendency. Citing multiple examples is necessary for even an informal claim to be taken seriously.

Furthermore, this is part of a tendency on the part of the authors to make incredibly sloppy, poorly-supported, and often necessarily invalid or factually incorrect arguments. I am willing to cut reasonable people some slack, especially since everyday language is so imprecise, but a pattern of serious error burns through the grace leeway very rapidly.

Caledonian: I am afraid I have to agree with Bob, Sean and Pyramid Head. Contrary to what you just said, you have not cut Eliezer the slack that every reader should cut every author before publishing a critical comment.

Were you hurt in a lasting way by someone Eliezer reminds you of? Someone, say, with a grand program to change the world? Someone claiming extremely high intelligence? Someone with many lectures on the right way to think?

I hate to say this, but technically 98 is closer to 100 than 100 is to 98. The difference between 98 and 100 is (100-98)/100 or 2%. The difference between 100 and 98 is (98-100)/98 or 2.04%. True, the difference between is only 2, but the percentage differences are, um, different. With this idea in mind, is this a type of bias that can carry over to other comparisons? (e.g. Mexico could theoretically be closer to the US (politics, standard of living, etc.) than the US is to Mexico (currency, language, etc.)) Or have I missed something important here?

anon and Ben, fixed.

Lee,

I'd assume we can do other experiments to find this out... maybe they've been done? Instead of {98,100}, try all pairs of two numbers from 90-110 or something?

Lee, I'm confident that you'd find that "97 is approximately 100" seems more natural to most people than "100 is approximately 99". As for the percentage differences, (1) why should the percentage difference be the thing to focus on rather than the absolute difference, and (2) why do it that way around? (Only, I think, because of the effect I mentioned above: when you say "X is approximately Y" you're implicitly suggesting Y as a standard of comparison, because it's useful for that purpose one way or another.)

Lee, you're confusing the map with the territory, to borrow Eli's phrasing. Percentages are just a convenient way to label the ratio, or difference, between values, but they are not precisely the difference, just an arbitrary representation.

Lee, if we're going to talk technically, then "percentage difference" is technically not a valid measure of distance or "closeness", because distance is something that happens in a metric space, and a metric has to be symmetrical.

Also, I think you'd find subjects saying that "102 is approximately 100" sounds more natural than "100 is approximately 102".

An approximation is something less accurate than the original. 100 looks less accurate because it looks like it's been rounded to the hundreds column.

Contrary to what you just said, you have not cut Eliezer the slack that every reader should cut every author before publishing a critical comment.

Critical comments are the natural result of critical thinking. They do not imply rejection or necessarily contain negative opinions. There is no threshold that must be met before readers can critically comment, because that's what they're supposed to be doing.

The validity of an argument has nothing to do with the correctness of the conclusion. The arguments being presented here are wrong. Why are you more concerned with whether you agree with the conclusion than with the methods used to generate it?

An even better question: why do the people who are so enthusiastic about eliminating others' bias so unconcerned about dealing with their own?

Caledonian,

I'm suggesting that you ask yourself "does this really matter?" before you post. You've made contributions to past threads but now we get comments like "a tendency on the part of the authors to make incredibly sloppy, poorly-supported, and ..." that signal an attack dog mentality. Why is "incredibly" part of this sentence? Does it add anything except flame? Do you really find the "errors" you comment on incredible?

You may care more about the methods than the conclusions but, personally, I visit OB more for the questions than the answers.

Sorry to highjack the thread but I think that increased civility warrants attention.

I agree with Bob.

And I am curious about something, Caledonian: can you name 3 authors you consider less biased or more likely to make valid arguments than Eliezer is? The reason I ask is, I am curious whether you think most authors' arguments are incredibly sloppy (which is how you describe Eliezer's arguments).

Do you really find the "errors" you comment on incredible?

In the sense of 'nearly unable to believe them'? Yes. I am flabbergasted that rudimentary errors are made by people with a reputation for great intelligence.

In this post, on this topic alone, Eliezer presumed that: 1) the prototype model is correct, 2) that robins are closer to the prototype than ducks, 3) the reason people thought a disease transfer would be more likely from robins to ducks was because of this, 4) the same pattern applies generally, and 5) that is also because of how we reason from generalities to specifics. All of these things are assumptions, none of which were given even the sketchiest support within this post.

He also said some things which were simply wrong.

Quite a lot of people here seem to be giving Our Hosts so much benefit of the doubt that they're filling in holes in their arguments for them. I mean, really, what is it with you people? The point is to overcome biases, not wallow in them.

Caledonian,

May I just say that I'm enjoying the fact that you're actually taking the time to explain your thoughts in greater depth than you have typically done to date. It was clear that you have a high opinion of your own intelligence, but I was finding it difficult to form my own opinion on the value of your comments based on your previous rather telegraphic style.

It was clear that you have a high opinion of your own intelligence

No, I have a very low opinion of other people's intelligence. I'm a fool. But a fool surrounded by morons starts to look pretty clever after a while.

Not that this is relevant to the question here: why is Eliezer's audience not concerned with finding or even looking for his errors in reasoning and argument? They're not hard to find. It doesn't take a great deal of intelligence or rhetorical experience to identify them. I can only presume that there is no interest. (Lack of interest in being correct seems to be one of the biggest, if not the biggest, reasons people are wrong.)

Cal, the whole point of the post is to introduce the idea of the prototype model versus Aristotelian model of cognition. The stated purpose of the blog is to be at least 50% accessible to the public, and the posts are headed toward amalgamation into a popular book, not a technical book. The point wasn't to rigorously support or defend the prototype model as such -- I would imagine that that has been done in many other places (maybe Eli could post some sources for your research). The point here was to expose it to a larger audience.

In the light of the larger audience, the bird prototype doesn't have to be defined with any particular level of technical accuracy -- robins versus ducks is true a priori; it's accessible to an average reader. It would hurt the overall work to beat that horse, because it's not aimed at a professional, it's not a dissertation, it's an explanation aimed at the lowest common denominator.

My point is that you're missing the point here, Cal. Rip apart falsity here, by all means, but don't think you're the only reader who realizes that it's perfectly plausible that a robin could spread a disease to a duck but not visa versa -- I realize that, and I bet most of the people who read the post also realized that, but it's ridiculous to think that a statistically significant proportion of the population, randomly selected to answer a question like that, would have any knowledge of the specific disease pathways between robins and ducks that would skew the results in any given way. Even if by some magical coincidence, enough people even realized there COULD be different pathways, there is no reason to expect that knowledge to skew the results toward one bird over another, without further explanation. Clearly there is a bias at work. If you don't think the evidence points toward the bias Eli was talking about, then explain why and offer a different hypothesis.

You keep saying we're blind to the errors and biases written here, but I think you don't realize that everyone sees most of what you post, but we choose not to post it, because we don't want to be pedantic. We're trying to digest the meat of the information, and we understand who the intended audience is.

1) the prototype model is correct,

He cites five papers that fairly well establish the prototype model within the domain of this discussion. If you don't like this sort of "presumption", and don't offer any sort of counter argument before calling it an "incredibly sloppy mistake", you've gone beyond the point of reasonable discussion.

2) that robins are closer to the prototype than ducks,

This is indeed the general finding, at least for Americans and presumably many other groups.

3) the reason people thought a disease transfer would be more likely from robins to ducks was because of this,

Can you give a good reason why the general public would think this? Can you support it non-anecdotally with high school biology that everyone remembers? Can you even defend more thoroughly the gray/red squirrel "disease" without hedging your definitions of disease?

4) the same pattern applies generally,

This was the finding when performed with numbers, states, and cities. Quick, describe the properties of the set {birds, numbers, states, cities}, and why the pattern doesn't apply outside of here.

The "errors" in the argument do little to diminish the fact that people, when given the option, favored robins over ducks. It's unlikely a "robin bias" exists.

"Why is Eliezer's audience not concerned with finding or even looking for his errors in reasoning and argument?"

The torture vs dust specks discussions showed that there are quite a number of people here who would like to show that Eliezer is wrong, on the occasions when they believe that he is.

However, it isn't helpful to look at every post and start by saying, "What's wrong with that?" Start by seeing what's right, and you're much more likely to see what's wrong.

It doesn't take specialist expertise to recognize that Eliezer's statement is nonsense. Anyone with some basic general knowledge about disease transmission would recognize it as incorrect - that would include most people who briefly scanned a Newsweek article about bird flu within the past six years. All he had to say was that there was no good reason for people to presume transmission from robin to duck would be harder than the other way around. It would even have been shorter and more elegant! He went out of his way to make an untrue statement, one that either makes him look foolish or possibly adds a false 'fact' to his readers' datastore.

Sean, I think you've become confused. #3 isn't my point, it's Eliezer's. I have no need to defend it - I'm attacking it.

His overall argument contains multiple interlocking assumptions that aren't labeled as such, but simply presumed to be true. In addition, he wrote statements that (in the most generous possible reading) poorly illustrated his actual point or (in more hard-nosed evaluations) were both wrong and blatantly so.

It is always, always more important to look for what has gone wrong than to recognize what is correct. There will be crowds of flattering sycophants and yesmen to sing praises and seek out the weakest virtue of the thing for adoration; more aren't needed. The best creators are their own worst critics. Mediocre creators let their critics find their errors. Bad ones surround themselves with praise and abhor criticism.

"It is always, always more important to look for what has gone wrong than to recognize what is correct."

Yes - as long as you are attacking the main thrust of the argument, not some insignificant side issue. People have a right to be annoyed when others constantly ignore the main part of what they are saying on instead pick on them for getting some triviality wrong.

And this medium is not an academic volume, it's more informal than that, so people will publish incomplete thoughts and/or grasping attempts to understand new things, and posts should be read in that context, not as if you are critiquing a journal article.

If people were perfectly rational, it wouldn't matter much whether you first looked for what was right or for what was wrong.

The problem is this: empirically it turns out that when people first look for what is wrong with something, they tend to distort it. If they first look for what is right, they get a better view of it, and so are better able to judge what is wrong.

One reason for the above (the empirical fact), perhaps, might be that understanding and seeing truth are closely related; it has even been argued that in order to understand something, we have to accept it in some way, and only as a secondary step apply skepticism to it. So if the skepticism is applied in advance, it will impede understanding.

The problem is this: empirically it turns out that when people first look for what is wrong with something, they tend to distort it. If they first look for what is right, they get a better view of it, and so are better able to judge what is wrong.

That's a very interesting finding. Can I get a source?

Excellent, Unknown!

If the point wasn't relevant to the argument, it shouldn't have been there. If it was relevant to the argument, its validity is of central importance to the argument.

And if the point was wrong, it definitely shouldn't have been there whether it was relevant or not.

Skepticism is only possible when we do not accept a thing as true. Looking at our own beliefs skeptically requires putting aside our acceptance and returning them to a state of uncertainty - it's a trick not many people have mastered.

The idea that we have to accept things before we can critically examine them is so... deeply wrong that I cannot think of words that adequately encompass the nature of the error.

I need to spend some quality time with an unabridged thesaurus and dictionary set.

Given that y'all allowed Caledonian to succeed in derailing the conversation, I'm surprised that none of you pointed out that Caledonian's original 'objection' - "It's not logically necessary for ducks' and robins' disease transmissions to be symmetrical!" - was explicitly pointed out by me in the original text. Did you reread the original article? Or did you unwittingly take Caledonian's word for what I had or had not said, assuming that if he attacked me at point X, I must be there defending at point X?

Anyway, if you allow Caledonian to derail another thread, I will withdraw my lone objection (among the Overcoming Bias editors) to banning him. You're not doing him any favor by responding to his trolls.

I'm surprised that none of you pointed out that Caledonian's original 'objection' - "It's not logically necessary for ducks' and robins' disease transmissions to be symmetrical!" - was explicitly pointed out by me in the original text.

That's probably because that wasn't my original point.

My original point - which was the first three sentences of my very first post in this thread - is as follows: "What? No. It's not even vaguely reasonable to say that a transfer of a disease between two species is equally likely either way."

The point is correct. We would in fact expect it to be quite likely for any disease transfer to function far more effectively in one direction than equally well in both.

The reason favoring a robin->duck transfer over a duck->robin transfer is irrational is that we have no justification for saying which way the preferential transfer would occur. That was the correct point which you should have made, instead of the incorrect one that you did.

none of you pointed out that Caledonian's original 'objection' - "It's not logically necessary for ducks' and robins' disease transmissions to be symmetrical!" - was explicitly pointed out by me in the original text

I noticed, went back to your post to check my recollection and would have pointed it out, but my memory is not good enough to eliminate the possibility that you changed the post after Caledonian's erroneous criticism.

Comments on this page by Bob, Sean, Pyramid Head, Eliezer and I all present a common description of Caledonian's behavior: he raises objections that do not contribute anything because they are either trivial and ought to be corrected silently by the reader in the normal process of blog reading or are not valid at all. Not all his objections are this way, but more than half of them are. Also, the shrillness of his objections and his generalizations from those objections have caused me to go back and check the original post not only on this page but on many other pages, and I am a little angry that I wasted my time that way. My guess is that other people feel the same way. Also, I worry that his continuing this way will encourage other sloppy shrill comments from other individuals with the result that the comments on this blog will become less worth reading.

To prevent the perception that I am ignoring contrary evidence, I point out that in one recent exchange Caledonian retracted an invalid objection to something Eliezer wrote. I hope he learns to do that more often. Of course the ideal would be for him to do it silently before posting the original objection.

To summarise : A storm in a teacup between a pot and a kettle.

Ouch.

Perhaps you should get a blog of your own, Caledonian. Or you could e-mail me at aljaynock AT hotmail DOT com and I'll make you a contributing author at my blog.

That's very kind of you, TGGP. But I suspect dealing with the positive feedback loop of commentators' 'creative' interpretations would be terminally exhausting for both of us.

You always have the option of disabling comments and/or pingbacks for any post, although of course you can't do anything about meanies at Overcoming Bias saying nasty things over there.

Eliezer, you've been going on concerning talking about things as if people considered them Aristotelian classes, but isn't it also the case that people don't think of things in a Bayesian sense? Shouldn't it be enough simply to say that essentialism is a faulty way to look at the world?

On a completely different note about ducks vs. robins (pretending the above flame war didn't happen): I can't say whether average folks would make this connection, but it seems to me that robins sit in trees and don't walk around on the ground very often, whereas ducks tend to hang out on the ground (or in the water). Since robin droppings (a typical disease vector) would work their way to the ground, whereas duck droppings would just stay there, it seems like robins would be more likely infect ducks. Again, I don't KNOW this to be the case, but that's not the point--the point is that this belief (whether or not it's true) immediately popped into my head when reading the question, and therefore would have skewed my own answer.

But I'm also willing to accept that I think about these kinds of things way more than the average person, so my own answer (or prejudice?) may not be at all relevant. :)

On Mexico vs. the US: Here I'm not quite convinced that this is the same phenomenon--though it certainly is an asymmetric comparison, I'm not convinced that it's because one is a more "typical" country, unless I misunderstand the definitions. I'd say that each country has a set of generalized qualities that it's known for: The U.S. may be known for "freedom", "opportunity", "multicultural", whereas when you think of Mexico you think of "poverty", "don't drink the water", "warm beaches." I'm speaking in broad generalities of subject's potential perceptions on both counts; please no one take offense.

When you're comparing the first to the second, (my hypothesis is that) you look for similarities in the first to the generalities in the second, so Mexico->US means you're looking for freedom, opportunity, and multicultural aspects of Mexico, all of which exist to some degree, whereas US->Mexico you're looking for poverty, poor water, and warm beaches in the US (in my brief example), which don't fit nearly as well (though all three exist, of course).

This may be your exact point, but it feels different than the other examples, in that the others refer to the compared object's distance from an archetypal category (100 is a round number, robins are more like "bird" than ducks). Is it that the US is simply familiar because the subjects are here? What happens then when you ask Americans about Mexico vs. Canada or Canada vs. Mexico? I would bet there's a similar asymmetry to the answers, for the reasons I gave. But that's just a guess.

The statement “x approximately equals 98” and the statement “x approximately equals 100” will likely be interpreted in different ways. I'd normally interpret the former to mean that x is likely between 97.5 and 98.5, and unlikely to be less than 96 or more than 100; whereas I'd usually interpret the latter more broadly (e.g. between 90 and 110). In particular, if the latter was rephrased to “x approximately equals 10^2”, I wouldn't object to it being used to mean something as vague as “x is very likely to be somewhere between 30 and 300”.

"For similar reasons, people asked to rate how similar Mexico is to the United States, gave consistently higher ratings than people asked to rate how similar the United States is to Mexico."

I assume this was done in the United States...

Rips (1975) showed that people were more likely to expect a disease would spread from robins to ducks on an island, than from ducks to robins. Now this is not a logical impossibility, but in a pragmatic sense, whatever difference separates a duck from a robin and would make a disease less likely to spread from a duck to a robin, must also be a difference between a robin and a duck, and would make a disease less likely to spread from a robin to a duck.

Alas, the same argument shows that diseases are equally likely to spread from Spaniards to native Americans as the other way around. However, that turned out to be completely wrong: the Spaniards had an extended symbiosis with domestic animals, and had developed immunity to most of their diseases - while the native Americans had no such symbiosis with large animals. They were vulnerable to the germs the Spaniards brought with them, without their germs causing the Spaniards any problems.

The flaw in the argument is that a difference involving a host with a full pathogen reservoir is asymmetric - it makes the pathogens spread away from the reservoir, but not towards it.

It seems to me that diseases would be more likely to spread from robins to ducks than from ducks to robins. The reason I am thinking this is the case is that robins fly around more than ducks, and ducks rest in water. This means that ducks are fairly likely to come in contact with traces of past robins, but robins are unlikely to come in contact with traces of past ducks.

The idea that the spread of disease between species is equally likely not only ignores differences in immunity, as Caledonian2 said; it also assumes direct contact between the species. Indirect contact, but contrast, can be one-way.

Even the concept of Alaska being far and Kansas being close is easily explained by calling into question the wording of the question in the experiment. Kansas is close to Alaska, compared to the average of everywhere else. Alaska however, is far from Kansas, compared to the average of the rest of the US. It's definitely a bias as a result of categorization, but it's not because of the properties of the categories. It instead seems to be a bias in how the question is interpreted: in which category the question refers to. And this, obviously, is a result of contextual inference making. Kansas is in a different context than Alaska.

I had to look up whether robins are migratory.

"98 is closer to 100 than 100 is to 98"

Geometrically, this is literally true. I would like to see if the same applies for how close 98 is to 100 vs 100 to 101. I suspect we get the same result, but for me, at least, it "feels" different. My innate comparison is multiply/divide, then add/subtract, then other things. I bet I'm more likely to add/subtract weird multiples of 12 and 24 and 100 (like 3, 6, 8, and 25), and more likely to multiply/divide "round" numbers like 1, 5, 10, 20, 100.