Typicality and Asymmetrical Similarity

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.

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).