Advertisement

Mind & Society

, Volume 16, Issue 1–2, pp 1–15 | Cite as

Randomness: off with its heads (and tails)

  • Aleksandar AksentijevicEmail author
Article
  • 103 Downloads

Abstract

Although widely investigated and used in psychology, the concept of randomness is beset with philosophical and practical difficulties. In this paper, I propose a resolution to a long-standing problem in psychological research by arguing that the inability to comprehend and produce random behavior is not caused by a defect on the part of the observer but is a consequence of conceptual confusion. Randomness describes a state of high complexity which defies analysis and understanding. The well-known biases in predictive behavior (e.g. hot-hand and gambler’s fallacy) are not caused by the observers’ inability to comprehend randomness but reflect a natural pattern-seeking response to high-complexity situations. Further, I address the circularity at the heart of the randomness debate. Replacing randomness with complexity in psychology and cognitive science would eliminate many of the current problems associated with defining, investigating and using this elusive term.

Keywords

Complexity Randomness Structure Change Hot hand Gambler’s fallacy 

Notes

Acknowledgments

The author wishes to thank Lisa Kainan for making available her unpublished doctoral dissertation and Ruma Falk for her encouragement and advice.

References

  1. Adami C, Cerf NJ (2000) Physical complexity of symbolic sequences. Phys D 137:62–69Google Scholar
  2. Aksentijevic A (2015a) Statistician, heal thyself: fighting statophobia at the source. Front Psychol. doi: 10.3389/fpsyg.2015.01558 Google Scholar
  3. Aksentijevic A (2015b) No time for waiting: statistical structure reflects subjective complexity. Proc Natl Acad Sci USA 112:E3159. doi: 10.1073/pnas.1507950112 Google Scholar
  4. Aksentijevic A, Gibson K (2012a) Complexity equals change. Cogn Syst Res 15–16:1–16Google Scholar
  5. Aksentijevic A, Gibson K (2012b) Complexity and the cost of information processing. Theor Psychol 22:572–590Google Scholar
  6. Alberoni F (1962) Contribution to the study of subjective probability: I. J Gen Psychol 66(2):261–264Google Scholar
  7. Alter AL, Oppenheimer DM (2006) From a fixation on sports to an exploration of mechanism: the past, present and future of hot hand research. Think Reason 12(4):431–444Google Scholar
  8. Attneave F (1959) Applications of information theory to psychology: a summary of basic concepts, methods, and results. Henry Holt, New YorkGoogle Scholar
  9. Ayton P, Fischer J (2004) The hot hand fallacy and the gambler’s fallacy: the two faces of subjective randomness? Mem Cogn 32(8):1369–1378Google Scholar
  10. Ayton P, Hunt A, Wright G (1989) Psychological conceptions of randomness. J Behav Decis Mak 2(4):221–238Google Scholar
  11. Bar-Eli M, Avugos S, Raab M (2006) Twenty years of “hot hand” research: review and critique. Psychol Sport Exerc 7:525–553Google Scholar
  12. Bar-Hillel M, Wagenaar W (1991) The perception of randomness. Adv Appl Math 12(4):428–454Google Scholar
  13. Boynton DM (2003) Superstitious responding and frequency matching in the positive bias and gambler’s fallacy effects. Organ Behav Hum 91(2):119–127Google Scholar
  14. Brown SG (1957) Probability and scientific inference. Longmans, Green, LondonGoogle Scholar
  15. Burns BD (2004) Heuristics as beliefs and as behaviors: the adaptiveness of the “hot hand”. Cogn Psychol 48(3):295–331Google Scholar
  16. Burns BD, Corpus B (2004) Randomness and inductions from streaks: “Gambler’s fallacy” versus “hot hand”. Psychon B Rev 11(1):179–184Google Scholar
  17. Calude CS (2000) Who is afraid of randomness? Report of the Centre of Discrete Mathematics and Theoretical Computer Science, University of Auckland, New ZealandGoogle Scholar
  18. Chaitin GJ (1969) On the length of the programs for computing finite binary sequences: statistical considerations. J Assoc Comput Mach 16:145–159Google Scholar
  19. Chaitin GJ (1975) Randomness and mathematical proof. Sci Am 232(5):47–52Google Scholar
  20. Chaitin GJ (2001) Exploring randomness. Springer, LondonGoogle Scholar
  21. Copeland BJ (ed) (2004) The essential Turing: the ideas that gave birth to the computer age. Clarendon Press, OxfordGoogle Scholar
  22. Coren RL (2002) Comments on “A law of information growth”. Entropy 4:32–34Google Scholar
  23. Cowan N (2001) The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav Brain Sci 24(1):87–114Google Scholar
  24. Coward A (1990) Pattern thinking. Praeger, New YorkGoogle Scholar
  25. Cutting JE (1998) Information from the world around us. In: Hochberg J (ed) Perception and cognition at century’s end: history, philosophy and theory. Academic Press, San Diego, pp 69–93Google Scholar
  26. Dawes RM (1988) Rational choice in an uncertain world. Harcourt, Brace & Jovanovich, New YorkGoogle Scholar
  27. Eagle A (2005) Randomness is unpredictability. Br J Philos Sci 56:749–790Google Scholar
  28. Falk R (1991) Randomness—an ill-defined but much needed concept (commentary on “Psychological Conceptions of Randomness”). J Behav Decis Mak 4(3):215–218Google Scholar
  29. Falk R (2010) The infinite challenge: levels of conceiving the endlessness of numbers. Cogn Instruct 28(1):1–38Google Scholar
  30. Falk R, Konold C (1997) Making sense of randomness: implicit encoding as a basis for judgment. Psychol Rev 104(2):301–318Google Scholar
  31. Feynman RP, Leighton RB, Sands M (1963) The Feynman lectures on physics. Addison-Wesley, ReadingGoogle Scholar
  32. Gardner M (1989) Mathematical carnival, chap 13—random numbers. The Mathematical Association of America, Washington, DCGoogle Scholar
  33. Garner WR (1962) Uncertainty and structure as psychological concepts. Wiley, New YorkGoogle Scholar
  34. Gell-Mann M (1994) The quark and the jaguar: adventures in the simple and the complex. Freeman, New YorkGoogle Scholar
  35. Gell-Mann M (1995) What is complexity? Complexity 1(1):1–9Google Scholar
  36. Gilden DL, Wilson SG (1995) On the nature of streaks in signal detection. Cogn Psychol 28(1):17–64Google Scholar
  37. Gilovich T, Vallone R, Tversky A (1985) The hot hand in basketball: on the misperception of random sequences. Cogn Psychol 17:295–314Google Scholar
  38. Glanzer M, Clark WH (1962) Accuracy of perceptual recall: an analysis of organization. J Verb Learn Verb Behav 1(4):289–299Google Scholar
  39. Grassberger P (1986) How to measure self-generated complexity. Phys A 140(1–2):319–325Google Scholar
  40. Hahn U, Warren P (2009) Perceptions of randomness: why three heads are better than four. Psychol Rev 116(2):454–461Google Scholar
  41. Hammond KR, Householder JE (1962) A model of randomness. In: Hammond KR, Householder JE (eds) Introduction to the statistical method: foundations and use in the behavioral sciences. Alfred A. Knopf, New York, pp 238–286Google Scholar
  42. Ichikawa S (1985) Quantitative and structural factors in the judgment of pattern complexity. Percept Psychophys 38(2):101–109Google Scholar
  43. Jaditz T (2000) Are the digits of π an independent and identically distributed sequence? Am Stat 54(1):12–16Google Scholar
  44. Kahneman D, Tversky A (1972) Subjective probability: a judgment of representativeness. Cogn Psychol 3(3):430–454Google Scholar
  45. Keren G, Lewis C (1994) The two fallacies of gamblers: type I and type II. Organ Behav Hum 60(1):75–89Google Scholar
  46. Koffka K (1935) Principles of Gestalt psychology. Lund Humphries, LondonGoogle Scholar
  47. Kolmogorov AN (1965) Three approaches to the quantitative definition of information. Probl Inf Transm 1(1):1–7Google Scholar
  48. Li M, Vitanyi P (1997) An introduction to Kolmogorov complexity and its applications. Springer, New YorkGoogle Scholar
  49. Lopes LL (1982) Doing the impossible: a note on induction and the experience of randomness. J Exp Psychol Learn 8(6):626–636Google Scholar
  50. Lordahl DS (1970) An hypothesis approach to sequential prediction of binary events. J Math Psychol 7(2):339–361Google Scholar
  51. MacKay D (1950) Quantal aspects of scientific information. Philos Mag 41:289–311Google Scholar
  52. Matthews WJ (2013) Relatively random: context effects on perceived randomness and predicted outcomes. J Exp Psychol Learn 39(5):1642–1648Google Scholar
  53. Miller GA (1956) The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol Rev 63(2):81–97Google Scholar
  54. Nickerson R (2002) The production and perception of randomness. Psychol Rev 109(2):330–357Google Scholar
  55. Noether G (1987) Mental random numbers: perceived and real randomness. Teach Stat 9:68–70Google Scholar
  56. Oskarsson AT, Van Boven L, McClelland G, Hastie R (2009) What’s next? Judging sequences of binary events. Psychol Bull 135(2):262–285Google Scholar
  57. Péter R (1957/1976) Playing with infinity: mathematical explorations and excursions. Dover, LondonGoogle Scholar
  58. Rapoport A, Budescu DV (1997) Randomization in individual choice behavior. Psychol Rev 104(3):603–617Google Scholar
  59. Roney CJR, Trick LM (2003) Grouping and gambling: a Gestalt approach to gambler’s fallacy. Can J Exp Psychol 57(2):69–75Google Scholar
  60. Shannon C (1948) A mathematical theory of communication. Bell Labs Tech J 27:623–656Google Scholar
  61. Solomonoff RJ (1964) A formal theory of inductive inference, part 1 and part 2. Inform Control 7:224–254Google Scholar
  62. Tune GS (1964) Response preferences: a review of some relevant literature. Psychol Bull 61(4):286–302Google Scholar
  63. Tversky A, Kahneman D (1971) The belief in the law of small numbers. Psychol Bull 76(2):105–110Google Scholar
  64. Tyzska T, Zielonka P, Dacey R, Sawicki P (2008) Perception of randomness and predicting uncertain events. Think Reason 14(1):83–110Google Scholar
  65. Volchan SB (2002) What is a random sequence? Am Math Mon 109:46–63Google Scholar
  66. Wagenaar WA (1991) Randomness and randomizers: maybe the problem is not so big. J Behav Decis Mak 4(3):220–222Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Psychology, Whitelands CollegeUniversity of RoehamptonLondonUK

Personalised recommendations