Confirmation bias is rational when hypotheses are sparse

摘要: Confirmation bias is rational when hypotheses are sparse Amy F. Perfors (amy.perfors@adelaide.edu.au) School of Psychology, University Adelaide Adelaide, SA 5005 Australia Daniel J. Navarro (daniel.navarro@adelaide.edu.au) Abstract We consider the common situation in which a reasoner must induce rule that explains an observed sequence data, but hypothesis space possible rules not explicitly enumer- ated or identified; example this number game (Wason, 1960), “twenty questions.” present math- ematical optimality results showing as long hypothe- ses – is, rules, on average, tend to be true only for small proportion entities world then confirmation near-optimal strategy. Experimen- tal evidence suggests at least domain numbers, sparsity assumption reasonable. Keywords: analysis; decision making; bias; information Introduction Humans constantly confronted with situations they underlying process generated data see. Children learning language infer grammar basis sentences hear; scientists theories ob- serve; and people trying understand explanations experience have. One might expect learners would approach situa- tion by evaluating both confirming disconfirming evidence. However, one most well- studied well-supported science demon- strates that, variety situations, seek after evidence; known (see Nickerson (1998) overview). The can cover situations. It includes times motivated support be- lieve pet theory, perhaps emotional reasons, thus discount falsify it (e.g., Matlin & Stang, 1978). also overweight con- firmatory Gilovich, 1983) let their prior bi- ases affect see Kuhn, 1989). focus here selection aspect bias: tendency who determine correct ask questions will get “yes” response if currently un- der consideration Mynatt, Doherty, Tweney, 1978; Wason, 1960, 1968). This more precisely called positive test strategy, following Klayman Ha (1987). classic strategy occurs task Wason Selection task, participants shown four cards letters side numbers other 1968) asked evaluate truth form IF P , THEN Q . Participants out confirm components (p q), even though whole, confir- matory disconfirmatory relevant. Although ameliorated under some conditions Cosmides, 1989), rarely completely eliminated. How- ever, (Oaksford Chater, 1994) have argued Task seen rational, assumes properties described p q rare goal testers perform queries (i.e., select cards) maximize expected informa- gain. provocative result, applies sub- set interesting cases people. For chil- dren language, forming theories, peo- ple causal well many constrained p, q. In different ini- tially invented (1960), were try guess defines three numbers. suggested triads received feedback about whether those acceptable rule, was NUMBERS ARE INCREASING (such 2-4-6 4-2-6 not). They often failed whilst still finding consistent all had POWERS OF TWO ). Notably, identified sort “subset rule” disconfirm suggesting unacceptable case 2-4-6), instead predicted 2-4-8). Other analyses rationality general than Oaksford Chater (1994). instance, (1987) demonstrate effective heuristic falsifying “minor- ity phenomena” events, Austerweil Griffiths (2008) showed deterministic predict result any given query yields max- imum experimental conditions, people’s gathering has been congruent Bayesian maximization (Nelson, Tenenbaum, Movellan, 2001). Underlying these what we call require-