Skip to main content
SpringerLink
Log in

Reasoning and mathematical skills contribute to normatively superior decision making under risk: evidence from the game of dice task

  • Research Report
  • Published:
Cognitive Processing Aims and scope Submit manuscript

Abstract

In this study, we assessed to what extent reasoning improves performance in decision making under risk in a laboratory gambling task (Game of Dice Task-Double, GDT-D). We also investigated to what degree individuals with above average mathematical competence decide better than those with average mathematical competence. Eighty-five participants performed the GDT-D and several numerical tasks. Forty-two individuals were asked to calculate the probabilities and the outcomes associated with the different options of the GDT-D before performing it. The other 43 individuals performed the GDT-D at the beginning of the test session. Both reasoning and mathematical competence had a positive effect on decision making. Different measures of mathematical competence correlated with advantageous performance in decision making. Results suggest that decision making under explicit risk conditions improves when individuals are encouraged to reflect about the contingencies of a decision situation. Interventions based on numerical reasoning may also be useful for patients with difficulties in decision making.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Notes

  1. In the cups task, taking a risk is advantageous in some trials, while it is disadvantageous in some other trials.

  2. Note that earlier studies report a normal distribution of GDT scores in the normal population. This was not the case in the present sample of highly educated participants.

References

  • Bechara A, Damasio H, Tranel D, Damasio AR (1997) Deciding advantageously before knowing the advantageous strategy. Science 275:1293–1295

    Article  CAS  PubMed  Google Scholar 

  • Bonatti E, Zamarian L, Wagner M, Benke T, Hollosi P, Strubreither W, Delazer M (2008) Making decisions and advising decisions in traumatic brain injury. Cogn Behav Neurol 21:164–175

    Article  PubMed  Google Scholar 

  • Brand M (2008) Does the feedback from previous trials influence current decisions? A study on the role of feedback processing in making decisions under explicit risk conditions. J Neuropsychol 2:431–443

    Article  PubMed  Google Scholar 

  • Brand M, Schiebener J (2013) Interactions of age and cognitive functions in predicting decision making under risky conditions over the life span. J Clin Exp Neuropsychol 35:9–23

    Article  PubMed  Google Scholar 

  • Brand M, Labudda K, Kalbe E, Hilker R, Emmans D, Fuchs G et al (2004) Decision-making impairments in patients with Parkinson’s disease. Behav Neurol 15:77–85

    Article  PubMed  Google Scholar 

  • Brand M, Fujiwara E, Borsutzky S, Kalbe E, Kessler J, Markowitsch HJ (2005) Decision-making deficits of korsakoff patients in a new gambling task with explicit rules: associations with executive functions. Neuropsychology 19:267–277

    Article  PubMed  Google Scholar 

  • Brand M, Labudda K, Markowitsch HJ (2006) Neuropsychological correlates of decision-making in ambiguous and risky situations. Neural Netw 19:1266–1276

    Article  PubMed  Google Scholar 

  • Brand M, Laier C, Pawlikowski M, Markowitsch HJ (2009) Decision making with and without feedback: the role of intelligence, strategies, executive functions, and cognitive styles. J Clin Exp Neuropsychol 31:984–998

    Article  PubMed  Google Scholar 

  • Brand M, Schiebener J, Pertl M-T, Delazer M (2014) Know the risk, take the win: how executive functions and probability processing influence advantageous decision making under risk conditions. J Clin Exp Neuropsychol 36:914–29

    Article  PubMed  Google Scholar 

  • Brevers D, Cleeremans A, Goudriaan AE, Bechara A, Kornreich C, Verbanck P, Noël X (2012) Decision making under ambiguity but not under risk is related to problem gambling severity. Psychiatry Res 200:568–574

    Article  PubMed  Google Scholar 

  • Chen Y, Wang J, Kirk RM, Pethtel OL, Kiefner AE (2014) Age differences in adaptive decision making: the role of numeracy. Educ Gerontol 40:825–833

    Article  PubMed  PubMed Central  Google Scholar 

  • Cokely ET, Kelley CM (2009) Cognitive abilities and superior decision making under risk: a protocol analysis and process model evaluation. Judgm Decis Mak 4:20–33

    Google Scholar 

  • Cokely ET, Feltz A, Ghazal S, Allan J, Petrova P, Garcia-Retamero R (2016) Decision making skill: from intelligence to numeracy and expertise. The Cambridge Handbook of Expertise and Expert Performance, 2nd edn. Cambridge University Press

  • Delazer M, Kemmler G, Benke T (2013) Health numeracy and cognitive decline in advanced age. Neuropsychol Dev Cogn B Aging Neuropsychol Cogn 20:639–59

    Article  PubMed  Google Scholar 

  • Donati MA, Panno A, Chiesi F, Primi C (2014a) A mediation model to explain decision making under conditions of risk among adolescents: the role of fluid intelligence and probabilistic reasoning. J Clin Exp Neuropsychol 36:588–595

    Article  PubMed  Google Scholar 

  • Donati MA, Primi C, Chiesi F (2014b) Prevention of problematic gambling behavior among adolescents: testing the efficacy of an integrative intervention. J Gambl Stud 30:803–818

    Article  PubMed  Google Scholar 

  • Estrada C, Barnes V, Collins C, Byrd JC (1999) Health literacy and numeracy. JAMA 282:527

    Article  CAS  PubMed  Google Scholar 

  • Euteneuer F, Schaefer F, Stuermer R, Boucsein W, Timmermann L, Barbe MT, Kalbe E (2009) Dissociation of decision-making under ambiguity and decision-making under risk in patients with Parkinson’s disease: a neuropsychological and psychophysiological study. Neuropsychologia 47:2882–2890

    Article  PubMed  Google Scholar 

  • Fagerlin A, Zikmund-Fisher BJ, Ubel PA, Jankovic A, Derry HA, Smith DM (2007) Measuring numeracy without a math test: development of the Subjective Numeracy Scale. Med Decis Making 27:672–680

    Article  PubMed  Google Scholar 

  • Figner B, Mackinlay RJ, Wilkening F, Weber EU (2009) Affective and deliberative processes in risky choice: age differences in risk taking in the Columbia Card Task. J Exp Psychol Learn Mem Cogn 35:709–730

    Article  PubMed  Google Scholar 

  • Galesic M, Garcia-Retamero R (2010) Statistical numeracy for health: a cross-cultural comparison with probabilistic national samples. Arch Intern Med 170:462–468

    Article  PubMed  Google Scholar 

  • Ghazal S, Cokely ET, Garcia-Retamero R (2014) Predicting biases in very highly educated samples: Numeracy and metacognition. Judgm Decis Mak 9:15–34

    Google Scholar 

  • Gigerenzer G, Gaissmaier W (2011) Heuristic decision making. Annu Rev Psychol 62:451–482

    Article  PubMed  Google Scholar 

  • Hecht SA, Vagi KJ, Torgesen JK (2007) Fraction skills and proportional reasoning. In: Berch DB, Mazzocco MM (eds) Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities. Paul H Brookes Publishing, Baltimore, pp 121–132

    Google Scholar 

  • Hoffrage U, Hertwig R, Gigerenzer G (2000) Hindsight bias: a by-product of knowledge updating? J Exp Psychol Learn Mem Cogn 26:566–581

    Article  CAS  PubMed  Google Scholar 

  • Hsee CK, Rottenstreich Y (2004) Music, pandas, and muggers: on the affective psychology of value. J Exp Psychol Gen 133:23–30

    Article  PubMed  Google Scholar 

  • Hsu M, Bhatt M, Adolphs R, Tranel D, Camerer CF (2005) Neural systems responding to degrees of uncertainty in human decision-making. Science 310:1680–1683

    Article  CAS  PubMed  Google Scholar 

  • Ibrahimovic N, Bulheller S (2008) Mathematiktest: Grundkenntnisse für Lehre und Beruf [Mathematical Test: basic knowledge for apprenticeship and career], 3rd edn. Pearson, Frankfurt am Main

    Google Scholar 

  • Iuculano T, Butterworth B (2011) Understanding the real value of fractions and decimals. Q J Exp Psychol (Hove) 64:2088–2098

    Article  Google Scholar 

  • Jasper JD, Bhattacharya C, Levin IP, Jones L, Bossard E (2013) Numeracy as a predictor of adaptive risky decision making. J Behav Decis Mak 26:164–173

    Article  Google Scholar 

  • Lehrl S (1999) Mehrfach-Wortschatz-Intelligenztest [Multiple choice vocabulary intelligence test], 4th edn. Spitta Verlag, Balingen

    Google Scholar 

  • Liberali JM, Reyna VF, Furlan S, Stein LM, Pardo ST (2012) Individual differences in numeracy and cognitive reflection, with implications for biases and fallacies in probability judgment. J Behav Decis Mak 25:361–381

    Article  PubMed  Google Scholar 

  • Lipkus IM, Peters E (2009) Understanding the role of numeracy in health: proposed theoretical framework and practical insights. Health Educ Behav 36:1065–1081

    Article  PubMed  PubMed Central  Google Scholar 

  • Lipkus IM, Samsa G, Rimer BK (2001) General performance on a numeracy scale among highly educated samples. Med Decis Mak 21:37–44

    Article  CAS  Google Scholar 

  • Mack NK (1995) Confounding whole-number and fraction concepts when building on informal knowledge. J Res Math Educ 26:422–441

    Article  Google Scholar 

  • Obrecht NA, Chesney D (2016) Prompting deliberation increases base-rate use. Judgm Decis Mak 11:1–6

    Google Scholar 

  • Pertl M-T, Benke T, Zamarian L, Martini C, Bodner T, Karner E, Delazer M (2014) Do patients with mild cognitive impairment understand numerical health information? J Alzheimers Dis 40:531–540

    PubMed  Google Scholar 

  • Pertl M-T, Benke T, Zamarian L, Delazer M (2015) Decision making and ratio processing in patients with mild cognitive impairment. J Alzheimers Dis 48:765–779

    Article  PubMed  Google Scholar 

  • Peters E (2012) Beyond comprehension: the role of numeracy in judgments and decisions. Curr Dir Psychol Sci 21:31–35

    Article  Google Scholar 

  • Peters E, Bjalkebring P (2015) Multiple numeric competencies: when a number is not just a number. J Pers Soc Psychol 108:802–822

    Article  PubMed  Google Scholar 

  • Peters E, Vastfjall D, Slovic P, Mertz CK, Mazzocco K, Dickert S (2006) Numeracy and decision making. Psychol Sci 17:407–413

    Article  PubMed  Google Scholar 

  • Reyna VF (2004) How people make decisions that involve risk: a dual-processes approach. Curr Dir Psychol Sci 13:60–66

    Article  Google Scholar 

  • Reyna VF (2008) A theory of medical decision making and health: fuzzy trace theory. Med Decis Mak 28:850–865

    Article  Google Scholar 

  • Reyna VF, Nelson WL, Han PK, Dieckmann NF (2009) How numeracy influences risk comprehension and medical decision making. Psychol Bull 135:943–973

    Article  PubMed  PubMed Central  Google Scholar 

  • Schiebener J, Brand M (2015) Decision making under objective risk conditions: a review of cognitive and emotional correlates, strategies, feedback processing, and external influences. Neuropsychol Rev 25:171–198

    Article  PubMed  Google Scholar 

  • Schiebener J, Wegmann E, Pawlikowski M, Brand M (2013) Supporting decisions under risk: explicit advice differentially affects people according to their working memory performance and executive functioning. Neurosci Decis Mak 1:9–18

    Google Scholar 

  • Schiebener J, Wegmann E, Gathmann B, Laier C, Pawlikowski M, Brand M (2014) Among three different executive functions, general executive control ability is a key predictor of decision making under objective risk. Front Psychol 5:1386

    Article  PubMed  PubMed Central  Google Scholar 

  • Schwartz LM, Woloshin S, Black WC, Welch HG (1997) The role of numeracy in understanding the benefit of screening mammography. Ann Intern Med 127:966–972

    Article  CAS  PubMed  Google Scholar 

  • Siegler RS, Fazio LK, Bailey DH, Zhou X (2013) Fractions: the new frontier for theories of numerical development. Trends Cogn Sci 17:13–19

    Article  PubMed  Google Scholar 

  • Sinz H, Zamarian L, Benke T, Wenning GK, Delazer M (2008) Impact of ambiguity and risk on decision making in mild Alzheimer’s disease. Neuropsychologia 46:2043–2055

    Article  CAS  PubMed  Google Scholar 

  • Starcke K, Tuschen-Caffier B, Markowitsch HJ, Brand M (2009) Skin conductance responses during decisions in ambiguous and risky situations in obsessive-compulsive disorder. Cogn Neuropsychiatry 14:199–216

    Article  PubMed  Google Scholar 

  • Starcke K, Pawlikowski M, Wolf OT, Altstotter-Gleich C, Brand M (2011) Decision-making under risk conditions is susceptible to interference by a secondary executive task. Cogn Process 12:177–182

    Article  PubMed  Google Scholar 

  • Tobler PN, Weber EU (2014) Valuation for risky and uncertain choices. In: Glimcher PW, Fehr E (eds) Neuroeconomics: decision making and the brain, 2nd edn. Elsevier, Amsterdam, pp 149–172

    Chapter  Google Scholar 

  • Zamarian L, Sinz H, Bonatti E, Gamboz N, Delazer M (2008) Normal aging affects decisions under ambiguity, but not decisions under risk. Neuropsychology 22:645–657

    Article  PubMed  Google Scholar 

  • Zamarian L, Weiss EM, Delazer M (2011) The impact of mild cognitive impairment on decision making in two gambling tasks. J Gerontol B Psychol Sci Soc Sci 66:23–31

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

We would like to thank all participants for their contribution to the study as well as Franziska Foldenauer, Julia Horn, and Lisa-Marie Neier for their help with data collection. We also thank Prof. Matthias Brand for providing the GDT-D. This work is part of the first author’s (M.-T. P.) doctoral thesis and was supported by a fellowship granted by the “Vizerektorat für Forschung” of the Leopold Franzens University, Innsbruck, 2014/3/PSY-15. The second and corresponding author (L. Z.) receives research support from TWF-2010-1-993 and MUI-Start 2014-05-001.

Author information

Authors and Affiliations

  1. Department of Neurology, Medical University Innsbruck, Anichstraße 35, 6020, Innsbruck, Austria

    Marie-Theres Pertl, Laura Zamarian & Margarete Delazer

  2. Department of Psychology, Leopold Franzens University, Innrain 52, 6020, Innsbruck, Austria

    Marie-Theres Pertl

Authors
  1. Marie-Theres Pertl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laura Zamarian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Margarete Delazer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laura Zamarian.

Additional information

Handling editor: Don Ross (University of Cape Town); Reviewers: Matthias Brand (University of Duisburg-Essen), Edward Cokely (University of Oklahoma), Ellen Peters (Ohio State University).

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 16 kb)

Supplementary material 2 (TIFF 119 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pertl, MT., Zamarian, L. & Delazer, M. Reasoning and mathematical skills contribute to normatively superior decision making under risk: evidence from the game of dice task. Cogn Process 18, 249–260 (2017). https://doi.org/10.1007/s10339-017-0813-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10339-017-0813-x

Keywords

Search

Navigation