Ludic fallacy
Encyclopedia
The ludic fallacy is a term coined by Nassim Nicholas Taleb in his 2007 book The Black Swan. "Ludic
" is from the Latin ludus, meaning "play, game, sport, pastime." It is summarized as "the misuse of game
s to model real-life situations." Taleb explains the fallacy as "basing studies of chance on the narrow world of games and dice."
It is a central argument in the book and a rebuttal of the predictive mathematical models used to predict the future – as well as an attack on the idea of applying naïve and simplified statistical models in complex domains. According to Taleb, statistics only work in some domains like casino
s in which the odds are visible and defined. Taleb's argument centers on the idea that predictive models are based on platonified forms
, gravitating towards mathematical purity and failing to take some key ideas into account:
. There are two people:
A third party asks them, "assume a fair coin is flipped 99 times, and each time it comes up heads. What are the odds that the 100th flip would also come up heads?"
The ludic fallacy here is to assume that in real life the rules from the purely hypothetical model (where Dr John is correct) apply. Would a reasonable person bet on black on a roulette
table that has come up red 99 times in a row (especially as the reward for a correct guess are so low when compared with the probable odds that the game is fixed)?
In classical terms, highly statistically significant (unlikely) events should make one question one's model assumptions. In Bayesian statistics
, this can be modelled by using a prior distribution for one's assumptions on the fairness of the coin, then Bayesian inference
to update this distribution.
. The interviewee has already learned statistics
and utility
theory in college and performed well in the exams. Considering whether to take the interview, he tries to calculate the probability
he will get the job versus the cost of the time spent.
The young job seeker here forgets that real life has more variables than the small set he has chosen to estimate. Even with a low probability of success, a really good job may be worth the effort of taking the interview. Will he enjoy the process of the interview? Will his interview technique improve regardless of whether he gets the job or not? What strategic value might he win or lose in the process? Even the statistics of the job business are non-linear. What other jobs could come the man's way by meeting the interviewer? Might there be a possibility of a very high pay-off in this company that he has not thought of?
based on a fixed universe or model of possible outcomes ignores and minimizes the impact of events which are "outside model." For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday (1987)
but might not model the market breakdowns following the recent Japanese Tsunami and subsequent fallout. A fixed model considers the "known unknowns," but ignores the "unknown unknowns."
Ludic
Ludic derives from Latin ludus, "play," and is an adjective meaning "playful." The term is used in philosophy to describe play as an act of self-definition; in literary studies, the term may apply to works written in the spirit of festival.-Homo ludens:...
" is from the Latin ludus, meaning "play, game, sport, pastime." It is summarized as "the misuse of game
Game
A game is structured playing, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements...
s to model real-life situations." Taleb explains the fallacy as "basing studies of chance on the narrow world of games and dice."
It is a central argument in the book and a rebuttal of the predictive mathematical models used to predict the future – as well as an attack on the idea of applying naïve and simplified statistical models in complex domains. According to Taleb, statistics only work in some domains like casino
Casino
In modern English, a casino is a facility which houses and accommodates certain types of gambling activities. Casinos are most commonly built near or combined with hotels, restaurants, retail shopping, cruise ships or other tourist attractions...
s in which the odds are visible and defined. Taleb's argument centers on the idea that predictive models are based on platonified forms
Platonic realism
Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato , a student of Socrates. As universals were considered by Plato to be ideal forms, this stance is confusingly also called...
, gravitating towards mathematical purity and failing to take some key ideas into account:
- it is impossible to be in possession of all the information.
- very small unknown variations in the data could have a huge impact. Taleb does differentiate his idea from that of mathematical notions in chaos theory, e.g. the butterfly effectButterfly effectIn chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...
. - theories/models based on empirical data are flawed, as events that have not taken place before cannot be accounted for.
Example 1: Suspicious coin
One example given in the book is the following thought experimentThought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
. There are two people:
- Dr John, who is regarded as a man of science and logical thinking.
- Fat Tony, who is regarded as a man who lives by his wits.
A third party asks them, "assume a fair coin is flipped 99 times, and each time it comes up heads. What are the odds that the 100th flip would also come up heads?"
- Dr John says that the odds are not affected by the previous outcomes so the odds must still be 50:50.
- Fat Tony says that the odds of the coin coming up heads 99 times in a row are so low (less than 1 in 6.33 × 1029) that the initial assumption that the coin had a 50:50 chance of coming up heads is most likely incorrect.
The ludic fallacy here is to assume that in real life the rules from the purely hypothetical model (where Dr John is correct) apply. Would a reasonable person bet on black on a roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
table that has come up red 99 times in a row (especially as the reward for a correct guess are so low when compared with the probable odds that the game is fixed)?
In classical terms, highly statistically significant (unlikely) events should make one question one's model assumptions. In Bayesian statistics
Bayesian statistics
Bayesian statistics is that subset of the entire field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities...
, this can be modelled by using a prior distribution for one's assumptions on the fairness of the coin, then Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
to update this distribution.
Example 2: Job interview
A man considers going to a job interviewJob interview
A job interview is a process in which a potential employee is evaluated by an employer for prospective employment in their company, organization, or firm. During this process, the employer hopes to determine whether or not the applicant is suitable for the job.-Role:A job interview typically...
. The interviewee has already learned statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and utility
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
theory in college and performed well in the exams. Considering whether to take the interview, he tries to calculate the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
he will get the job versus the cost of the time spent.
The young job seeker here forgets that real life has more variables than the small set he has chosen to estimate. Even with a low probability of success, a really good job may be worth the effort of taking the interview. Will he enjoy the process of the interview? Will his interview technique improve regardless of whether he gets the job or not? What strategic value might he win or lose in the process? Even the statistics of the job business are non-linear. What other jobs could come the man's way by meeting the interviewer? Might there be a possibility of a very high pay-off in this company that he has not thought of?
Example 3: Stock returns
Any decision theoryDecision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
based on a fixed universe or model of possible outcomes ignores and minimizes the impact of events which are "outside model." For instance, a simple model of daily stock market returns may include extreme moves such as Black Monday (1987)
Black Monday (1987)
In finance, Black Monday refers to Monday October 19, 1987, when stock markets around the world crashed, shedding a huge value in a very short time. The crash began in Hong Kong and spread west to Europe, hitting the United States after other markets had already declined by a significant margin...
but might not model the market breakdowns following the recent Japanese Tsunami and subsequent fallout. A fixed model considers the "known unknowns," but ignores the "unknown unknowns."
Relation to Platonicity
The ludic fallacy is a specific case of the more general problem of Platonicity defined by Taleb as:the focus on those pure, well-defined, and easily discernible objects like triangles, or more social notions like friendship or love, at the cost of ignoring those objects of seemingly messier and less tractable structures.
See also
- map-territory relation
- Congruence biasCongruence biasCongruence bias is a type of cognitive bias similar to confirmation bias. Congruence bias occurs due to people's overreliance on direct testing of a given hypothesis, and a neglect of indirect testing.-Examples:...
- Déformation professionnelle
- Focusing effect
- Hindsight biasHindsight biasHindsight bias, or alternatively the knew-it-all-along effect and creeping determinism, is the inclination to see events that have already occurred as being more predictable than they were before they took place. It is a multifaceted phenomenon that can affect different stages of designs,...
- Quasi-empiricism in mathematicsQuasi-empiricism in mathematicsQuasi-empiricism in mathematics is the attempt in the philosophy of mathematics to direct philosophers' attention to mathematical practice, in particular, relations with physics, social sciences, and computational mathematics, rather than solely to issues in the foundations of mathematics...
- We (novel)We (novel)We is a dystopian novel by Yevgeny Zamyatin completed in 1921. It was written in response to the author's personal experiences during the Russian revolution of 1905, the Russian revolution of 1917, his life in the Newcastle suburb of Jesmond, and his work in the Tyne shipyards during the First...
- Demarcation problemDemarcation problemThe demarcation problem in the philosophy of science is about how and where to draw the lines around science. The boundaries are commonly drawn between science and non-science, between science and pseudoscience, between science and philosophy and between science and religion...
- Relevance paradoxRelevance ParadoxThe relevance paradox describes an attempt to gather information relevant to a decision, which fails because the elimination of information perceived as distracting or unnecessary and thus detrimental to making an optimal decision, also excludes information that is actually crucial.-Definition:In...
Further reading
- The Ludic Fallacy. Chapter from the book "The Black Swan"
- Medin, D. & Atran, S. (2004) The native mind: Biological categorization and reasoning in development and across cultures. Psychological Review.111, 960–98
- Fodor, J. (1983) Modularity of mind. Cambridge, MA: MIT Press.
- Tales of the Unexpected, Wilmott Magazine, June 2006, pp 30–36
- "A misplaced question". Taleb at Freakonomics blog