Study examines common cognitive biases (have you tried this brain teaser?) and ways to mitigate them

Pic: Get­ty Images

A fas­ci­nat­ing new study, Tver­sky and Kahneman’s Cog­ni­tive Illu­sions: Who Can Solve Them, and Why?, probes into the cog­ni­tive “heuris­tics and bias­es” researched by Daniel Kah­ne­man and Amos Tver­sky since the late 1960s.

If you have nev­er encoun­tered the “Lin­da brain teas­er” before, please give it a try:

Lin­da is 31 years old, sin­gle, out­spo­ken, and very bright. She majored in phi­los­o­phy. As a stu­dent, she was deeply con­cerned with issues of dis­crim­i­na­tion and social jus­tice, and also par­tic­i­pat­ed in anti-nuclear demonstrations.

Which state­ment is more probable?

(a) Lin­da is a bank teller.

(b) Lin­da is a bank teller and is active in the fem­i­nist movement.


Quick! What’s your answer?

Solution and Explanation

If you said b) is more prob­a­ble, you are in good com­pany … and wrong.

Answer b) is what most peo­ple answer the first time they face this par­tic­u­lar brain teas­er, reflect­ing the per­va­sive cog­ni­tive bias called a “con­junc­tion fal­la­cy.” Sta­tis­ti­cal­ly speak­ing, it is more prob­a­ble that Lin­da is a bank teller–feminist or not–that she is both a bank teller AND also active in the fem­i­nist move­ment, which is obvi­ous­ly a sub­set of the whole cat­e­go­ry of bank tellers.


As the researchers elab­o­rate in the new study (key por­tions bolded):

The prob­a­bil­i­ty of the simul­ta­ne­ous occur­rence of two events—for exam­ple, p(Bank teller And Feminist)—can be math­e­mat­i­cal­ly obtained by mul­ti­ply­ing the two involved sin­gle prob­a­bil­i­ties, that is, p(B) And p(F), or—in the case of the sto­chas­ti­cal depen­den­cy of B and F—p(B) And p(F|B). How­ev­er, the prod­uct of two num­bers between 0 and 1 always becomes small­er than each of both fac­tors, which is why (a) is the cor­rect option. The descrip­tion of Lin­da turns out to be irrel­e­vant here, since it is always more unlike­ly that two events will hap­pen simul­ta­ne­ous­ly than that only one of both con­stituents will (thus the con­tent of the events is irrel­e­vant here, too). All that counts are the terms “prob­a­bil­i­ty” and “and,” which the con­junc­tion rule inter­prets, respec­tive­ly, as math­e­mat­i­cal prob­a­bil­i­ty and the log­i­cal oper­a­tor “and” (Her­twig, 1995; Gigeren­z­er and Regi­er, 1996; Her­twig et al., 2008).

Yet Tver­sky and Kah­ne­man (1983) found that about 80–90% of par­tic­i­pants judged the sec­ond option (B and F) to be more prob­a­ble than the first option (B). In terms of the heuris­tics and bias­es pro­gram, the Lin­da prob­lem is anoth­er instance of the rep­re­sen­ta­tive­ness heuris­tic, since the sec­ond option seems to be more rep­re­sen­ta­tive of Lin­da than the first. The so-called “con­junc­tion fal­la­cy” in the form of the Lin­da task or sim­i­lar prob­lems has also been exam­ined exten­sive­ly since then (e.g., Fiedler, 1988; Reeves and Lock­hart, 1993; Dono­van and Epstein, 1997; Her­twig et al., 2008; Wedell and Moro, 2008; Char­ness et al., 2010). Her­twig and Chase (1998), for instance, found that the pro­por­tion of con­junc­tion fal­lac­i­es could be sub­stan­tial­ly reduced (from 78% to 42%) by chang­ing the response for­mat from rank­ing to con­crete prob­a­bil­i­ty esti­ma­tion. Inter­est­ing­ly, although there is no con­crete prob­a­bil­i­ty giv­en, the Lin­da prob­lem can also be under­stood more eas­i­ly using the nat­ur­al fre­quen­cy con­cept intro­duced in the con­text of Bayesian rea­son­ing prob­lems (see above). When par­tic­i­pants are sim­ply instruct­ed to imag­ine 200 women who fit Linda’s descrip­tion, they real­ize that there must be more women who are bank tellers than women who are both bank tellers and fem­i­nists (for details see, e.g., Fiedler, 1988; Her­twig and Gigeren­z­er, 1999).

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SHARPBRAINS is an independent think-tank and consulting firm providing services at the frontier of applied neuroscience, health, leadership and innovation.
SHARPBRAINS es un think-tank y consultoría independiente proporcionando servicios para la neurociencia aplicada, salud, liderazgo e innovación.

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