Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations
This paper has two aims. First, we investigate how often people make choices conforming to Bayes’ rule when natural sampling is applied. Second, we show that using Bayes’ rule is not necessary to make choices satisfying Bayes’ rule. Simpler methods, even fallacious heuristics, might prescribe correc...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2015-08-01
|
| Series: | Frontiers in Psychology |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2015.01194/full |
| _version_ | 1818199546935640064 |
|---|---|
| author | Artur eDomurat Olga eKowalczuk Katarzyna eIdzikowska Zuzanna eBorzymowska Marta eNowak-Przygodzka |
| author_facet | Artur eDomurat Olga eKowalczuk Katarzyna eIdzikowska Zuzanna eBorzymowska Marta eNowak-Przygodzka |
| author_sort | Artur eDomurat |
| collection | DOAJ |
| description | This paper has two aims. First, we investigate how often people make choices conforming to Bayes’ rule when natural sampling is applied. Second, we show that using Bayes’ rule is not necessary to make choices satisfying Bayes’ rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were to be inferred from a set of pictures, followed by a choice between the data which was made to maximize a chance for a preferred outcome. Using Bayes’ rule was deduced indirectly from choices.Study 1 (N=60) followed a 2 (gender: female vs. male) x 2 (education: humanities vs. pure sciences) between-subjects factorial design with balanced cells, and a number of correct choices as a dependent variable. Choices satisfying Bayes’ rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N=76) choices conforming to Bayes’ rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes’ rule to apply. It does not require inversing conditions (transforming P(H) and P(D|H) into P(H|D)) when computing chances). Study 3 examined efficiency of the three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes’ rule. Computer-simulated scenarios revealed that the heuristics produce correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling leads to most choices conforming to Bayes’ rule. However, people tend to replace Bayes’ rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient. |
| first_indexed | 2024-12-12T02:23:29Z |
| format | Article |
| id | doaj.art-1ccba6107ef04b01a5ec672c9991be1e |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-12-12T02:23:29Z |
| publishDate | 2015-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-1ccba6107ef04b01a5ec672c9991be1e2022-12-22T00:41:37ZengFrontiers Media S.A.Frontiers in Psychology1664-10782015-08-01610.3389/fpsyg.2015.01194130369Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situationsArtur eDomurat0Olga eKowalczuk1Katarzyna eIdzikowska2Zuzanna eBorzymowska3Marta eNowak-Przygodzka4University of WarsawUniversity of WarsawKozminski UniversityNencki Institute of Experimental BiologyUniversity of WarsawThis paper has two aims. First, we investigate how often people make choices conforming to Bayes’ rule when natural sampling is applied. Second, we show that using Bayes’ rule is not necessary to make choices satisfying Bayes’ rule. Simpler methods, even fallacious heuristics, might prescribe correct choices reasonably often under specific circumstances. We considered elementary situations with binary sets of hypotheses and data. We adopted an ecological approach and prepared two-stage computer tasks resembling natural sampling. Probabilistic relations were to be inferred from a set of pictures, followed by a choice between the data which was made to maximize a chance for a preferred outcome. Using Bayes’ rule was deduced indirectly from choices.Study 1 (N=60) followed a 2 (gender: female vs. male) x 2 (education: humanities vs. pure sciences) between-subjects factorial design with balanced cells, and a number of correct choices as a dependent variable. Choices satisfying Bayes’ rule were dominant. To investigate ways of making choices more directly, we replicated Study 1, adding a task with a verbal report. In Study 2 (N=76) choices conforming to Bayes’ rule dominated again. However, the verbal reports revealed use of a new, non-inverse rule, which always renders correct choices, but is easier than Bayes’ rule to apply. It does not require inversing conditions (transforming P(H) and P(D|H) into P(H|D)) when computing chances). Study 3 examined efficiency of the three fallacious heuristics (pre-Bayesian, representativeness, and evidence-only) in producing choices concordant with Bayes’ rule. Computer-simulated scenarios revealed that the heuristics produce correct choices reasonably often under specific base rates and likelihood ratios. Summing up we conclude that natural sampling leads to most choices conforming to Bayes’ rule. However, people tend to replace Bayes’ rule with simpler methods, and even use of fallacious heuristics may be satisfactorily efficient.http://journal.frontiersin.org/Journal/10.3389/fpsyg.2015.01194/fullBayesian inferenceHeuristicschoicesecological rationalityBayes’ ruleBinary hypothesis |
| spellingShingle | Artur eDomurat Olga eKowalczuk Katarzyna eIdzikowska Zuzanna eBorzymowska Marta eNowak-Przygodzka Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations Frontiers in Psychology Bayesian inference Heuristics choices ecological rationality Bayes’ rule Binary hypothesis |
| title | Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations |
| title_full | Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations |
| title_fullStr | Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations |
| title_full_unstemmed | Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations |
| title_short | Bayesian probability estimates are not necessary to make choices satisfying Bayes’ rule in elementary situations |
| title_sort | bayesian probability estimates are not necessary to make choices satisfying bayes rule in elementary situations |
| topic | Bayesian inference Heuristics choices ecological rationality Bayes’ rule Binary hypothesis |
| url | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2015.01194/full |
| work_keys_str_mv | AT arturedomurat bayesianprobabilityestimatesarenotnecessarytomakechoicessatisfyingbayesruleinelementarysituations AT olgaekowalczuk bayesianprobabilityestimatesarenotnecessarytomakechoicessatisfyingbayesruleinelementarysituations AT katarzynaeidzikowska bayesianprobabilityestimatesarenotnecessarytomakechoicessatisfyingbayesruleinelementarysituations AT zuzannaeborzymowska bayesianprobabilityestimatesarenotnecessarytomakechoicessatisfyingbayesruleinelementarysituations AT martaenowakprzygodzka bayesianprobabilityestimatesarenotnecessarytomakechoicessatisfyingbayesruleinelementarysituations |