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Typicality and Asymmetrical Similarity

25 Post author: Eliezer_Yudkowsky 06 February 2008 09:20PM

Followup toSimilarity Clusters

Birds fly.  Well, except ostriches don't.  But which is a more typical bird—a robin, or an ostrich?
Which is a more typical chair:  A desk chair, a rocking chair, or a beanbag chair?

Most people would say that a robin is a more typical bird, and a desk chair is a more typical chair.  The cognitive psychologists who study this sort of thing experimentally, do so under the heading of "typicality effects" or "prototype effects" (Rosch and Lloyd 1978).  For example, if you ask subjects to press a button to indicate "true" or "false" in response to statements like "A robin is a bird" or "A penguin is a bird", reaction times are faster for more central examples.  (I'm still unpacking my books, but I'm reasonably sure my source on this is Lakoff 1986.)  Typicality measures correlate well using different investigative methods—reaction times are one example; you can also ask people to directly rate, on a scale of 1 to 10, how well an example (like a specific robin) fits a category (like "bird").

So we have a mental measure of typicality—which might, perhaps, function as a heuristic—but is there a corresponding bias we can use to pin it down?

Well, which of these statements strikes you as more natural:  "98 is approximately 100", or "100 is approximately 98"?  If you're like most people, the first statement seems to make more sense.  (Sadock 1977.)  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.  (Tversky and Gati 1978.)

And if that still seems harmless, a study by 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.

Yes, you can come up with rationalizations, like "Well, there could be more neighboring species of the robins, which would make the disease more likely to spread initially, etc.," but be careful not to try too hard to rationalize the probability ratings of subjects who didn't even realize there was a comparison going on.  And don't forget that Mexico is more similar to the United States than the United States is to Mexico, and that 98 is closer to 100 than 100 is to 98.  A simpler interpretation is that people are using the (demonstrated) similarity heuristic as a proxy for the probability that a disease spreads, and this heuristic is (demonstrably) asymmetrical.

Kansas is unusually close to the center of the United States, and Alaska is unusually far from the center of the United States; so Kansas is probably closer to most places in the US and Alaska is probably farther.  It does not follow, however, that Kansas is closer to Alaska than is Alaska to Kansas.  But people seem to reason (metaphorically speaking) as if closeness is an inherent property of Kansas and distance is an inherent property of Alaska; so that Kansas is still close, even to Alaska; and Alaska is still distant, even from Kansas.

So once again we see that Aristotle's notion of categories—logical classes with membership determined by a collection of properties that are individually strictly necessary, and together strictly sufficient—is not a good model of human cognitive psychology.  (Science's view has changed somewhat over the last 2350 years?  Who would've thought?)  We don't even reason as if set membership is a true-or-false property:  Statements of set membership can be more or less true.  (Note:  This is not the same thing as being more or less probable.)

One more reason not to pretend that you, or anyone else, is really going to treat words as Aristotelian logical classes.

 

Part of the sequence A Human's Guide to Words

Next post: "The Cluster Structure of Thingspace"

Previous post: "Similarity Clusters"


Lakoff, George. (1986). Women, Fire and Dangerous Things: What Categories Tell Us About the Nature of Thought. University of Chicago Press, Chicago.

Rips, Lance J. (1975). "Inductive judgments about natural categories."  Journal of Verbal Learning and Verbal Behavior. 14:665-81.

Rosch, Eleanor and B. B. Lloyd, eds. (1978).  Cognition and Categorization.  Hillsdale, N.J.: Lawrence Erlbaum Associates.

Sadock, Jerrold. (1977).  "Truth and Approximations."  In Papers from the Third Annual Meeting of the Berkeley Linguistics Society, pp. 430-39.  Berkeley: Berkeley Linguistics Society.

Tversky, Amos and Itamar Gati. (1978).  "Studies of Similarity".  In Rosch and Lloyd (1978).

Comments (66)

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Comment author: anonymous9 06 February 2008 10:05:51PM 16 points [-]

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.

Comment author: g 06 February 2008 10:46:35PM 8 points [-]

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.)

Comment author: Tiiba2 07 February 2008 12:52:15AM 1 point [-]

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

Comment author: Caledonian2 07 February 2008 01:05:38AM -1 points [-]

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.

Comment author: Bob3 07 February 2008 05:16:31AM 4 points [-]

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.

Comment author: Caledonian2 07 February 2008 05:36:26AM 1 point [-]

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?

Comment author: Sean4 07 February 2008 09:12:25AM 6 points [-]

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.

Comment author: epigeios 11 May 2012 07:19:53PM *  -1 points [-]

The errors are relevant. So what if the person who mentions an error doesn't have the capacity to deduce the relevancy? It's still possible that someone on here will deduce the relevancy.

Your post, by contrast, as well as Bob3's just above, are making the assumption that the only argument to be found is the one that was stated. Caledonian2 is right, and if you weren't focused on the irrelevancy of his argument, you might have been able to find the relevancy of his point.

Granted, Caledonian2 did his best to find an argument fitting his idea, and the argument he picked isn't necessarily relevant. He probably did this because of the scientific bias of this message board, where I myself have previously succumbed to the fear that I need to have a valid argument to back up my point, lest others attack me for not having one. But none of that diminishes the potential relevancy of his idea

Comment author: tcpkac 07 February 2008 09:19:05AM 0 points [-]

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.

Comment author: g 07 February 2008 11:58:34AM 5 points [-]

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?)

Comment author: Ben_Jones 07 February 2008 12:41:43PM 0 points [-]

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.

Comment author: Pyramid_Head2 07 February 2008 02:22:11PM 0 points [-]

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.

Comment author: LG 07 February 2008 02:37:54PM 1 point [-]

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

Comment author: Caledonian2 07 February 2008 03:16:52PM -2 points [-]

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.

Comment author: Richard_Hollerith2 07 February 2008 05:04:51PM 2 points [-]

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?

Comment author: Lee_Turpin 07 February 2008 05:48:50PM 1 point [-]

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?

Comment author: Kenny 04 February 2013 09:28:59PM 0 points [-]

I'm guessing people would agree with "100 is approximately 102" less often than "102 is approximately 100".

Comment author: PetjaY 01 May 2015 07:40:48PM 0 points [-]

When you count percentages, you always count percentages of something. In this case you count percentages of 100 in one case, and percentages of 98 in the other, which explains why you get different numbers

Comment author: Eliezer_Yudkowsky 07 February 2008 06:13:51PM 0 points [-]

anon and Ben, fixed.

Comment author: GreedyAlgorithm 07 February 2008 07:04:02PM 0 points [-]

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?

Comment author: g 07 February 2008 08:56:44PM 4 points [-]

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.)

Comment author: LG 07 February 2008 09:17:41PM 0 points [-]

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.

Comment author: Eliezer_Yudkowsky 07 February 2008 09:44:21PM 8 points [-]

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".

Comment author: inemnitable 15 June 2012 01:50:41AM 1 point [-]

I think in certain contexts it makes sense to think about the closeness of two quantities in terms of percentage difference. For example, let's say we're not just talking about the numbers 98 and 100, but the rates 98 mph and 100 mph. When we talk about speed, what we're actually interested in is usually not the speed itself but rather the amount of time it takes to cover a certain distance when traveling that speed.

So in this context, it makes sense to say that 98 mph is about 100 mph to the same degree that 980 mph is about 1000 mph--because they have the same marginal relation in the time required to cover a certain distance at those speeds.

Comment author: Kindly 15 June 2012 11:31:49AM 0 points [-]

But the relation you're describing is itself percentage-based! If you go from the rates to, say, the time it takes to cover a distance of 100 miles, then you get (roughly) 102 and 100 hours in the first case, and 10.2 and 10 hours in the second case. These only have the same relation if we use percentage differences or ratios to think about how close two times are.

Comment author: Vaniver 15 June 2012 01:47:39PM 0 points [-]

It looks to me like that was iemnitable's goal.

Comment author: Kindly 15 June 2012 05:47:01PM 1 point [-]

I thought that iemnitable was trying to justify the use of ratios when comparing speeds (as an example), and I pointed out that this requires us first to justify the use of ratios when comparing times.

Comment author: Vaniver 15 June 2012 05:51:34PM 0 points [-]

Ah; I got a different impression from the great-grandparent. I agree with your point in the parent.

Comment author: inemnitable 15 June 2012 09:20:49PM 1 point [-]

I was thinking of it more like: if there's a certain place I can get to in (roughly) 102 hours going 98 mph, and I want to get there in 100 hours, I need to speed up to 100 mph. Similarly, if there's a another place that I can get to in roughly 102 hours going 980 mph, and I want to get to that place in 100 hours, I need to speed up to 1000 mph.

I kind of wanted to clarify that in the original post but I hadn't really thought of a good way to express it at the time.

Furthermore, I think that your interpretation of the example even makes it more clear that it makes sense to think of it in terms of a ratio. In the first case, you've sped up by 2 mph and gotten a gain of about 2 hours, straightforward enough. But in the second case, you've sped up by 20 mph, and only gotten a gain of about 0.2 hours. Here's where I think most people's intuition is probably screaming "whaaaaaaat!?"

But if we think of it in terms of the ratios, then everything fits together nicely again and the screaming intuition voice shuts up. Plus the math we have to do to get to the right answer is a lot easier.

Comment author: Kindly 15 June 2012 10:40:13PM 0 points [-]

Oh, I see what you mean now.

(Incidentally, Eliezer's original objection can be resolved by taking logs. Suddenly although the ratios 102/100 and 100/102 are not symmetrical, log(102/100) and log(100/102) are.)

Comment author: Ian_C. 07 February 2008 10:33:07PM 3 points [-]

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.

Comment author: Bob3 08 February 2008 02:55:57AM 6 points [-]

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.

Comment author: Richard_Hollerith2 08 February 2008 03:45:27AM 2 points [-]

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).

Comment author: Cyan2 08 February 2008 05:17:13AM 2 points [-]

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.

Comment author: LG 08 February 2008 02:16:00PM 13 points [-]

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.

Comment author: Sean4 08 February 2008 02:44:47PM 6 points [-]

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.

Comment author: Unknown 08 February 2008 05:30:07PM 3 points [-]

"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.

Comment author: Ian_C. 09 February 2008 02:40:49AM 5 points [-]

"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.

Comment author: Unknown 09 February 2008 04:19:24AM 1 point [-]

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.

Comment author: Cyan2 09 February 2008 04:57:45AM 5 points [-]

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?

Comment author: Richard_Hollerith2 09 February 2008 05:59:52AM -1 points [-]

Excellent, Unknown!

Comment author: Caledonian2 09 February 2008 03:48:36PM -2 points [-]

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.

Comment author: Eliezer_Yudkowsky 09 February 2008 06:13:13PM 4 points [-]

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.

Comment author: Caledonian2 09 February 2008 06:46:13PM -2 points [-]

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.

Comment author: Richard_Hollerith2 09 February 2008 08:17:43PM 0 points [-]

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.

Comment author: tcpkac 09 February 2008 10:18:33PM 3 points [-]

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

Comment author: Richard_Hollerith2 10 February 2008 12:02:22AM 1 point [-]

Ouch.

Comment author: TGGP4 10 February 2008 03:32:54AM 0 points [-]

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.

Comment author: Caledonian2 10 February 2008 04:45:30AM 1 point [-]

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.

Comment author: TGGP4 10 February 2008 05:17:26AM 1 point [-]

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?

Comment author: Tim_Mensch 10 February 2008 07:59:51PM 2 points [-]

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.

Comment author: [deleted] 12 September 2011 08:26:41PM 2 points [-]

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”.

Comment author: RobertLumley 24 October 2011 07:40:23PM 2 points [-]

"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...

Comment author: timtyler 11 January 2012 12:55:11PM *  0 points [-]

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.

Comment author: gwern 11 January 2012 05:51:25PM 0 points [-]

Reasonable, but wouldn't such reasoning make Duck->Robin much more likely than Robin->Duck, since ducks seem to migrate further than robins (which at least in America don't go further south than Florida) -- the exact opposite of what people said?

Comment author: timtyler 11 January 2012 10:27:28PM -2 points [-]

You disagree with their collective intellligence?

Maybe you know something they don't. Or maybe they know something you don't...

Comment author: gwern 11 January 2012 11:27:29PM 0 points [-]

I disagree with collective intelligences all the time. Problem?

Comment author: shminux 12 January 2012 12:45:06AM 0 points [-]

Not a problem, provided you turn out to be right and the "collective intelligences" wrong more often than not. Do you?

Comment author: gwern 12 January 2012 01:18:34AM 0 points [-]

I think I do. My calibration is pretty good so far, and that's on many collectively sourced predictions like Intrade.

Comment author: shminux 12 January 2012 01:19:53AM 0 points [-]

"If you are so smart, why aren't you rich?"

Comment author: gwern 12 January 2012 01:55:04AM 0 points [-]

Akrasia and lack of capital.

Comment author: epigeios 11 May 2012 07:05:39PM 3 points [-]

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.