Posts tagged with human mathematics

The Cartesian products
{−,+} ⨉ {−,+}
 {−,+,0} ⨉ {−,+,0}
realised as faces and as theories of personality.

Isomorphic to what you get if you strip the lightswitch group of its relationships=mappings=arrows (forgetful functor →Set).

The Five Temperaments apparently thinks the Four Humours theory of personality is improved by adding 0. We could go all the way to fuzzy logic and make the dimension continuous. What would that do?


In game theory the word “strategy” means a fully specified contingency plan. Whatever happens—be it a sequence of things, a conditional branching of their responses and my responses—∃ a contingency.

I can’t prove this, but I do feel that sometimes people talk about others as constants rather than response functions.

(A function is a ≥1-to-1 association from elements of a source domain to elements of a target codomain. I’ll owe ya a post on how this is not the most intuitive way to think about functions. Because it depends which domains you’re mapping from and to. Think for example about automorphisms—turning something over in your hand—versus measures—assigning a size to something.)


For example, extraversion vs introversion. This is one of the less disputatious dimensions of human variation from the MBTI. We can observe that some people (like me) gain more energy by being around people and feel like sh*te when they spend too much time alone, whereas others (like my best friend) replenish their reserves by being alone and drain them when they go out in public.

So we observe one datum about you—but sometimes a discussion (eg, an economics debate) wants to veer over counterfactual terrain—in which case we need a theory about how things might else have been.

  • Maybe when you were young, your parents always made you do chores whenever they saw you, but didn’t particularly seek you out when you were out of sight. So you learned to hide in your room, avoid chores, and develop your personal life there. Hence became introverted as a response to environmental factors.
  • When I was young, I used to think I was introverted. Really I was just widely disliked and unpopular for being an ugly nerd. But later in life I developed social skills and had the fortune to meet people I liked, who liked me back. In response to who was around, I became extraverted.

I can think of other aspects of myself that are obviously responses to situational stimuli rather than innate constants.

  • If I were raised in a different culture, my sexuality would be different. In my culture, homosexuality is seen as “You boink / date / marry from your own sex”, but in ancient Sparta women all gayed on each other as a matter of ritual before the men came home from war. But they didn’t call themselves homos, and neither did the Roman men who sexually touched each other. It was just a different conception of sex (one I can’t fathom) where “Just because I regularly crave and do sexual stuff with people of my own sex, doesn’t mean I’m gay!”
    File:Pederastic erotic scene Louvre F85bis.jpg
    File:Banquet Euaion Louvre G467.jpg
    File:Pompeii - Terme Suburbane - Apodyterium - Scene V.jpg
    File:Nisos Euryalos Louvre LL450 n2.jpg
    Point being this is all the result of inputs; born Puritan, think sex = evil. Born Roman, "sexuality is a behaviour, not an identity".
  • If I ate more food and exercised less, my fat:muscle ratio would increase.
  • If I meditated more, I would feel more at peace.
  • If I read more maths, I would know more maths. More people would think of me as a mathematician—but not because it was inevitable or inherent in me to be a mathmo, rather because I chose to do maths and became the product of my habits.
  • If I fixed more bikes, I would be able to fix bikes faster.
  • If I made more money, I would go to different places, meet different people, be exposed to their response functions to their own pasts and presents and anxieties and perceptions, a vector field of non-Markovian baggage, and all of this history and now-ness would sum up to some stimuli-complex that would cause some response by me, and change me in ways I can’t now know.
  • Our friendship could have been so much more, but we sort of let it fall off. Not for any reason, but it’s not so strong now.
  • Our love could have been so much less volatile, but I slept around, which had repercussions for your feelings toward me, which repercussed to my feelings toward you, which repercussed …. (multiplier effect / geometric series)

Besides being motivation for me to learn more maths to see what comes out of this way of thinking about people when you layer abstract algebra over it, this view of people is a reminder to

  1. release the egotism, and
  2. not take too literally what I think I’m seeing of whomever I’m interacting with.

Someone who piss me off may not be “a jerk”, it may not be about me whatever, s/he may be lag-responding to something from before I was there. Or s/he may not have adapted to a “nice guy” equilibrium of interacting with me. Who knows. I’m not seeing all of that person’s possibility, just a particular response to a particular situation.

On the other hand, if they really are acting wrong, it’s up to me to address the issue reasonably right away, rather than let my frustration passive-aggressively fester. Wait ten years for revenge and they’ll be a different person by then.

The final suggestion of people-as-functions is that there’s always something buried, something untapped—like part of a wavefunction that will never be measured, or a button on a machine that never gets pressed. You may see one version of yourself or someone else, but there’s more latent in you and in them—if you’re thrown into a war, a divorce, the Jazz Age, the Everglades, a hospice, a black-tie dinner, poverty, wealth, a band, a reality show about life under cruel premodern conditions—that may bring out another part of them.


UPDATE: peacemaker points out the similarity between people-as-response functions and the nature/nurture debate. I think this viewpoint subsumes both the nature and the nurture side, as well as free will.

  1. Evolution shaped our genes in response to environmental pressures (see for example the flies’ eyes chart above).
  2. My assumptions & predilections are a response to a more immediate “environment” than the environment of evolutionary adaptation.
  3. And I exercise free will over how I respond to the most immediate “environment” which is just the stimuli I get from you and the Wu Tang Clan.

UPDATE 2: As I think through this again, I feel quantum measurement really is a great metaphor for interacting with people. You only evoke one particular response-complex from a person on that particular time. And the way you evoke it perturbs the “objective” underlying thing. For example if yo’re introduced to someone in a flirtatious way versus in a business setting.

Is it possible to describe Human Beings with Mathematics?

  • isomorphisms: I hope that one day people will figure out the "perfect formula" for a constitution (balanced incentives / structure).
  • gsx002: I doubt it. Formulas belong to the math and logic realm.
  • isomorphisms: There is some logic to human interactions.
  • gsx002: That's using the word loosely. :)
  • isomorphisms: The promise of using maths to describe people is what got me interested in economics. I also do mathpsych.
  • isomorphisms: This is why I have high hopes for Acemoglu stuff. Also spatial voting theory, game theory, applications to constitutional design.
  • gsx002: I so have to follow these things more...I used to once upon a time.
  • gsx002: It's always fascinated me, but I still haven't met a really good Bayesian...and Newcomb's paradox is still tricky for me.
  • isomorphisms: I'm not saying a currently existing model [like Bayesian rationality]. Just that in theory a correct mathematical model of human behaviour seems (to me) possible.
  • isomorphisms: Not saying it would be super specific either. The difficulty in convincing people to my point of view is that few people know how loose abstract mathematics is. Cobordisms, homology, homotopy, topology are all very loose. Results in category theory are also quite loose.
  • isomorphisms: You can construct huge equivalence classes of things. Then you don't distinguish between very different things (famously, a coffee mug and a donut have the same topological equivalence class).
  • isomorphisms: Some abstract maths (like coalgebras) is actually criticised because "There are no calculations!"
  • gsx002: Hmm. . . i'd take the opposite bet . . . that there's a proof that there isn't or that there can't be such a model #Gödel
  • isomorphisms: Gödel is off-topic. His result was about pure maths.
  • isomorphisms: Even Arrow's Theorem has things fairly nailed down.
  • gsx002: Tarski then?
  • isomorphisms: Tarski also unrelated. Says ℝ is fuktup. I agree: especially for economics.
  • isomorphisms: I actually got Stan Wagon (a Tarski ball scholar) into a discussion on how ℝ is inappropriate for econ.
  • gsx002: ok, you forced me to bring out the big guns: sartre and camus! "we refuse to be modeled," or something like that :)
  • isomorphisms: They didn't know how loose abstract mathematics is either. =)
  • isomorphisms: Lacan thought there were applications of topology to psychoanalysis. Also there's a postmodernist at Ball State who says topology may be an appropriate tool for cultural analysis.
  • gsx002: I was talking about Tarski's Truth paradox.
  • isomorphisms: Oh. That's a linguistic problem. We don't have natural language logically figured out yet. However that's not a problem for behavioural modelling.

A Perfect Formula for Constitutions

  • moiracathleen: People today think there is a one size fits all constitution. This is perhaps the greatest tragedy to constitutionalism in history.
  • isomorphisms: How many sizes do you think there are?
  • moiracathleen: The Constitution is not to be used to impose a particular form of government, but rather expresses boundaries between the Government and the People.
  • moiracathleen: Those boundaries ought be drawn by the people living under the Constitution; rather than people from other countries.
  • isomorphisms: I hope that one day people will figure out the "perfect formula" for a constitution (balanced incentives / structure).
  • isomorphisms: Which is not to say that particular instantiations wouldn't vary.
  • isomorphisms: Like a line bundle.
  • isomorphisms: The lines in the bundle vary from point to point. The ideal constitution, according to a formula, could also vary from place to place (and time to time and history to history and people to people).

This week I posted different viewpoints on The Self.

Particularly I’m interested in self as a function of inputs. Just as the size of eyes a fly is born with is a function of the temperature of the eggs, so too, many facets of ourselves are a function of the environment, other people’s behaviour toward us, game-theoretic strategy, incentives, and so on.

Other people’s theories of us can be seen as functions as well. (For example, a hiring manager’s view of employee performance may assume school quality or GPA to be positively related to human capital.)

  • Economics: I didn’t get to Jean Tirole’s theory of money-saving as bargains among multiple selves.
  • Psychology: Jim Townsend found that self-versus-other dichotomies can be expressed as a negatively curved metric space.
  • Personality: I’ve already written that the MBTI is too restrictive a theory of self. It maps from habits to [0,1]⁴.
  • Douglas Hofstadter's thoughts on the extension of the pronoun “we”. ‘We’ went to the moon, ‘we’ share a common ancestor with other primates, ‘we’ are overcrowding the planet, ‘we’ have a nice theory of quantum chromodynamics, ‘we’ do not know if ‘we’ are experiencing a simulation or actual reality, ‘we’ don’t really know what makes an economy grow.
  • Criminology: My criminal output is a function of the crime level in the neighbourhood I’m raised in. Except when it’s a function of strongly held beliefs.
  • Sociology: In contemporary OECD places, ‘we’ are coerced by our cultures to play roles. “There are” certain scripts — modifiable but still requisite or recommended in some sense; at the very least influential, even if only because benefits and rewards are socially tied to role performance.
  • The topic of cultural coercion … is something I’ll return to.
  • The concept of people-as-functions is one I want to return to later, in discussing historyeconomics, and a couple different ways of talking about human behaviour mathematically.

I can think of several other mathematics-inspired questions about ourselves. The difference between habit and personality; the yogic metaphor of a river cutting deeper as related to habituation; choice & free will; Markovian and completely-the-opposite-of-Markovian choices (how constrained we are by our past choices); … and a lot more. But you know what, writing is hard. So I do only a little at a time.

Update, 25 September 2013: I’ve written more on this topic now:

OKCupid is using the wrong mathematics to match potential dates together. But before I critique them, let me compliment them on what they’re doing right:

  • "Our" mutual score is the geometric average of your score of me, and my score of you.
  • They low-ball the match % until they have enough statistical confidence in the number of questions we’ve both answered.
  • Questions come from users as well as staff. So they avoid some potential blind spots. (crowdsourcing)
  • OKCupid prompts you with questions that have the greatest chance of distinguishing you as quickly as possible. (maximally separating hyperplanes) If OKC already knows you want your date to shower at least once a day, keep a clean room, and that picking food from the trashcan is unacceptable, it won’t ask if you prefer crustpunks or gutterpunks.
  • You don’t have to be the same as me for us to match. I get to specify what answers I want from you.
  • They use a logarithmic scale of importance. Logs are the natural way we perceive levels or categories of importance. (For example “categories” of how big a war was, emerge naturally when you take the log of number of deaths.)
  • It’s simple. At least they’re not using a non-linear Bayesian splitting tree didactogram or some other hunky machine-learning jiu jitsu.

But, there’s still room for improvement. Particularly the following critique, originally made by Becky Russoniello. Currently, OKCupid is set up to award high scores just for being not-a-terrible match. That’s bad.


To show why I need to first detail how your score of me is calculated:

  1. You answer questions like, “Is homosexuality a sin?” Your answer consists of: (a) what you think, (b) what answer/s are acceptable for me to give, and (c) how important it is for me to get this question “right” per your definition.
  2. The question’s importance draws from {Mandatory, Very Important, Somewhat Important, A Little Important, Irrelevant} which biject to the numbers {250, 50, 10, 1, 0}.
  3. If I get a Very Important question “right”, I get 50/50 points, and if I get a Very Important question “wrong”, I get 0/50 points. If I haven’t answered the Very Important question, I get 0/0 points — neither penalised nor rewarded.

For more details, see their FAAAQ.



Here’s the important flaw: the denominator grows as long as we’ve answered the same question. In practice, the Mandatory questions both

  1. crowd out more interesting differentiators, and
  2. inflate the scores of people who merely have tolerable political views.

To demonstrate this, I’ll share some of the Mandatory questions from my own OKCupid profile.

  • Do you think homosexuality is a sin?
  • How often are you open with your feelings? (can’t be Rarely or Never)
  • Would it bother you if your boss was minority, female, or gay?
  • Would you write your child’s college entry essay?
  • What volume level do you prefer when listening to music? (can’t be “I prefer not to listen to music”)
  • Would you try to control your mate with threats of suicide?
  • Gay marriage — should it be legal?
  • Are you married, engaged to be married, or in a relationship that you believe will lead to marriage?
  • How important to you is a match’s sense of humor? (can’t be Not Important)
  • Would the world be a better place if people with low IQ’s were not allowed to reproduce?

Some other doozies which I might wrongly make Mandatory include:

  • Which is bigger? The Earth, or the Sun?
  • How many continents are there?
  • Do you consider astrology to be a legitimate science?

The problem with all of these filters, is that I mean them to act only in a negative direction. (Could I call them “quasi-filters”?)



In other words, someone doesn’t become a great potential match simply because they’re not

  • a bigot,
  • a cheat,
  • a eugenicist,
  • or a depressive manipulative.

You need to receive those check-marks just to get to zero with me. You also need to be not-married-to-someone-else. That doesn’t win you plus points, it’s just a requirement. But under the current OKCupid schema, you do win 250/250 from me for simply being available. Oops.

Likewise, knowing basic facts from grade-school seems, like, uh, necessary. But, even if somebody thinks there are 6 or 8 continents, do you really think you won’t be able to tell once they message you?

Few people will be culled by the Continents question, and if you make 10 such easy questions Mandatory, then everybody else will start with 2500/2500 points — so the rest of your match questions will barely distinguish one from the other. Even the Very Important questions (50 points apiece) will only budge the score a little below a default of 100%. And the Somewhat Important questions, which tend to be the more discriminative ones, are mowed down by the juggernaught of Easy Questions.

EDIT (23 NOV): According to the comments, the number of continents is not a universal fact, but rather varies from culture to culture (and within cultures). So that’s a really terrible question to make Mandatory! I should have said above Few people will be culled by asking whether the Earth is bigger than the sun, and if you make 10 such easy questions Mandatory, then everybody else will start with 2500/2500 points.

OKCupid asks other, more useful questions, like:

  • Are you annoyed by people who are super logical?
  • Do you like abstract art?
  • Do you spend more money on clothes, or food?
  • Could you tolerate a ___________________ [my political / religious views] ?
  • Do you like dogs?

which would actually distinguish among potential dates for me. Let’s face it: I write a blog about mathematics, so someone who is annoyed by super logical people is probably going to dislike me. And, I like abstract art. Maybe we could go to a gala for our first date.

Although everyone knows there are 7 continents the Sun is bigger than the Earth, not everyone is bothered by “logical” personalities. So those questions better sort the available dates.

want to go on a cruise on us stevenf?


The worst side effect of the current scoring system, is that a spammer could easily answer only the questions with obvious answers (basic facts and display of non-bigotry) and get a decently high match percentage with a lot of people. At which point, the spammer uploads a picture of an attractive guy/girl, writes some generic profile text, and scams away.



I think a better model oft how people evaluate potential dates can be found within economics. Specifically, Kahneman & Tversky's Prospect Theory:


The main lessons I draw from prospect theory, as a theory of psychology, are:

  1. We evaluate things based on a reference point (“zero”).
  2. Small perceived negatives are twice as bad, as small perceived positives are good (“local kink at zero”).
  3. Really bad or really good, we lose our ability to coherently measure how far from zero (“log-like at great distances”).

How does P.T. apply to dating and OKCupid?

Amos Tversky

Bigots, cheats, eugenicists, and depressive manipulatives are way off in negative land. I’m not even interested in meeting them. I don’t care whether OKC gives them a 0% or a 10%, because those are effectively the same to me: ignore. I only need OKCupid to accurately score people who are somewhere north of my reference point.

  • What if the scoring system simply binned everyone below 50%? They could all be labelled “non-match” and then twice as many numbers would be available to grade the remaining candidates.

    That’s a mathematically good idea, but doesn’t address the issue of dilution. And, it seems to ignore an aspect of “numbers psychology”: people like using only the upper half of the scale. Think about how people use the hotness scale: they would never be comfortable dating a 4.
  • What if OKCupid revamped their whole framework along the lines of Prospect Theory? Try to establish a reference point, do some research into psychology papers that bear on the topic, and so on.

    Well, it might be cool. But that’s a lot of work, and OKC is already successful. Big changes alienate users.

Here’s the simplest solution I can think of — which requires no UI changes and no research. In fact an OKC developer should only need to amend one line of code.

  • Mandatory questions can only give out negative points for answering wrong. No plus points for right answers to Mandatory.

Mathematically this is ugly because you introduce a discontinuity — but, so what? I think this is what the broad majority of people mean when they say something is mandatory. If you have a mandatory employee meeting, do people get a bonus for showing up? Does HM Revenue pat you on the back for paying tax?

In the eloquent phrasing of Chris Rock:

If OKC ends out giving some negative (or I guess imaginary, under the square root from the geometric average) scores, so what? I was ignoring everybody under 60% anyway.


If you use OKCupid, there is a way to improve your matches even if they never change their matching algorithm:

  • Lower the importance of questions with obvious answers. I bet you won’t start matching with people who believe the Earth is larger than the Sun. And you will pick up extra precision in matches with other people.
  • Even if something is mandatory for you to date someone, don’t use the Mandatory category like that. Maybe you can have a few mandatory questions, but overall it just dilutes the scoring.

The act of writing is like the collapse of a quantum waveform. So many things are in your mind, interacting with each other, unsaid. Many truths — some at odds with others — could be spun into a thread. But whatever you write crystallizes as the story. The other ephemera die.

Since speech is serial, it’s hard to portray the composite quality of real-time motivations, perceptions, emotions, impulses, sentiments, choices, …. I’ve heard that Chinese poetry can multi-track — and perhaps many great writers can — but not me. 

Quantum Quacks

Even Roger Penrose was roundly mocked for suggesting that quantum interactions in the brain relate to free will. Going the other direction, What the bleep do we know? draws several intellectually limp conclusions from quantum mechanics, e.g. that QM implies the possibility of telekinesis. (I would say that the authors must have leapt to conclusions from blurbs & pamphlets, except that Niels Bohr and Wolfgang Pauli also took spiritualistic and parapsychological views on QM.)

So it would seem that connections between QM and psychology are limited to quackery.



However, QM is just an abstract mathematical theory. You don’t have to plug physical parameters into the formalism. In that sense you can abscond the superposition-and-collapse metaphor out of the subatomic realm where it was invented and apply it to other things — like thought.

In other words, you don’t have to talk about quantum superposition. You can talk about emotional superposition, opinion superposition, mood superposition, colour superposition (like, are these images green? red? blue? 1 2 3 4 5), personality superposition, guilt superposition, … and more.

If I say: “I had a superposition of thoughts during the bear attack which collapsed into a 1-D sequence when I told the story,” that is valid.

It’s neither what-the-bleep nor relying on quantum effects on my brain. I just appropriated the mathematical metaphor of superposition and the mathematical metaphor of collapse, to express how I can’t really tell you the whole story of the bear attack, and how the telling perverts the story itself.

Some day I want to read all of Daron Acemoglu’s work. What in here isn’t interesting?

  • Social Structure and Development - A Legacy of the Holocaust in Russia
  • Theory, General Equilibrium, Political Economy and Empirics in Development Economics
  • Experimentation, Patents and Innovation Spread of (Mis)Information in Social Networks
  • Political Selection and Persistence of Bad Governments
  • Emergence and Persistence of Inefficient States
  • Vertical Integration and Technology: Theory and Evidence
  • Skills, Tasks and Technologies: Implications for Employment and Earnings
  • Persistence of Civil Wars
  • Dynamic Mirrless Taxation Under Political Economy Contraints
  • Institutions, Factor Prices and Taxation: Virtues of Strong States?
  • Political Limits to Globalization Price and Capacity Competition Foundations of Social Inequality (alternate access)
  • When Does Policy Reform Work - The Case of Central Bank Independence
  • A Theory of Military Dictatorships
  • Reevaluating the Modernization Hypothesis
  • Do Juntas Lead to Personal Rule?
  • Productivity Differences Between and Within Countries
  • Determinants of Vertical Integration: Financial Development and Contracting Costs
  • Economic and Political Inequality in Development: The Case of Cundinamarca, Colombia
  • Input and Technology Choices in Regulated Industries - Evidence from the Health Care Sector
  • Coalition Formation in Non-Democracies Income and Democracy
  • Capital Deepening and Nonbalanced Economic Growth
  • Local Indices for Degenerate Variational Inequalities Political Economy of Mechanisms
  • Persistence of Power, Elites and Institutions Oligarchic vs. Democratic Societies Markets Versus Governments
  • Incentives in Markets, Firms and Government Disease and Development: The Effect of Life Expectancy on Economic Growth
  • Disease and Development: The Effect of Life Expectancy on Economic Growth Appendices B and C
  • On the Stability of P-Matrices
  • Competition in Parallel-Serial Networks Partially Optimal Routing
  • Competition and Efficiency in Congested Markets
  • Generalized Poincare-Hopf Theorem for Compact Nonsmooth Regions
  • Equilibrium Bias of Technology Contracts and Technology Adoption
  • Technology, Information and the Decentralization of the Firm
  • Appendix to Technology, Information and the Decentralization of the Firm
  • A Simple Model of Inefficient Institutions
  • De Facto Political Power and Institutional Persistence
  • Did Medicare Induce Pharmaceutical Innovation? Modeling Inefficient Institutions
  • Efficiency and Braess’ Paradox under Pricing in General Networks
  • Price Competition in Communication Networks Competition in Parallel-Serial Networks Distance to Frontier, Selection, and Economic Growth
  • Economic Backwardness in Political Perspective
  • Politics and Economics in Weak and Strong States Institutions as the Fundamental Cause of Long-Run Growth
  • Constitutions, Politics and Economics: A Review Essay on Persson and Tabellini’s “The Unbundling Institutions The Rise of Europe: Atlantic Trade, Institutional Change and Economic Growth”
  • From Education to Democracy?
  • Market Size in Innovation: Theory and Evidence from the Pharmaceutical Industry
  • Women, War and Wages: the Effect of Female Labor Supply on Labor Market Outcomes
  • Kleptocracy and Divide-and-Rule: A Model of Personal Rule (The Alfred Marshall Lecture)
  • The Marginal User Principle for Resource Allocation in Wireless Networks
  • Why Not a Political Coase Theorem? Social Conflict, Commitment and Politics
  • Disease and Development in Historical Perspective
  • Patterns of Skill Premia Labor- and Capital-Augmenting Technical Change
  • An African Success Story: Botswana
  • Factor Prices and Technical Change: from Induced Innovations to Recent Debates
  • The Labor Market and Corporate Structure Institutional Causes, Macroeeconomic Symptoms: Volatility, Crises and Growth
  • Reversal of Fortune: Geography and Institutions in the Making of the Modern World
  • Directed Technical Change
  • The World Income Distribution Technical Change, Inequality, and The Labor Market
  • The Colonial Origins of Comparative Development: An Empirical Investigation
  • Inefficient Redistribution
  • A Theory of Political Transitions
  • Consequences of Employment Protection? The Case of the Americans with Disabilities Act
  • Deunionization, Technical Change and Inequality
  • Credit Market Imperfections and Persistent Unemployment
  • Changes in the Wage Structure, Family Income, and Children’s Education
  • Productivity Differences
  • Good Jobs Versus Bad Jobs
  • Wage and Technology Dispersion
  • Why Did the West Extend the Franchise? Democracy, Inequality and Growth in Historical Perpective
  • Political Losers as a Barrier to Economic Development
  • How Large Are Human Capital Externalities Evidence? Evidence from Compulsory Schooling Laws
  • The Choice between Market Failures and Corruption Productivity
  • Gains from Unemployment Insurance
  • Democratization or Repression? Certification of Training and Training Outcomes
  • Efficient Unemployment Insurance
  • Changes in Unemployment and Wage Inequality: An Alternative Theory and Some Evidence
  • Holdups and Efficiency Search Frictions
  • The Structure of Wages and Investment in General Training
  • Information Accumulation in Development
  • Beyond Becker: Training in Imperfect Labour Markets
  • Why Do New Technologies Complement Skills? Directed Technical Change and Wage
  • Property Rights, Corruption and the Allocation of Talent: A General Equilibrium Approach
  • Why Do Firms Train? Theory and Evidence
  • Credit Market Imperfections and the Separation of Ownership from Control
  • Asymmetric Business Cycles: Theory and Time Series Evidence
  • Was Prometheus Unbound by Chance? Risk, Diversification, and Growth
  • Training and Innovation in an Imperfect Labour Market
  • Matching, Heterogeneity, and the Evolution of Income Distribution
  • A Microfoundation for Social Increasing Returns in Human Capital Accumulation
  • Asymmetric Information, Bargaining, and Unemployment Fluctuations
  • Reward Structures and the Allocation of Talent


People make a big deal over how humans are too complicated to ever be described by mathematics. (I don’t agree.  Topic for another time.) So it’s astonishing that so many people give credence to the Myers-Briggs Type Indicator test.


The MBTI classifies people into sixteen categories, based on their proclivity to:

  1. Extraversion
  2. Facts vs. Ideas
  3. Heart vs. Head
  4. Like things settled vs. Like things open-ended

Each dimension varies on a sliding scale, so one’s score on a 100-question test is like [0,1] × [0,1] × [0,1] × [0,1] (actually it’s sparser in practice and could be several dimensions smaller, due to overlap).

MBTI < [0,1]^4 ... how bad is it?

Now that’s a shocker!  I know that we’re supposed to stick to simple models to describe things, but four parameters is the same as a bloody electron!  How are these four static numbers supposed to capture such a large chunk of human complexity?

Measures the Wrong Stuff, and Measures Unreliably

The model discards many characteristics that could be relevant—nice, creative, clever, honest, hard-working, religious, favorite sandwich—that’s a hack list but the point is, I don’t think they’re measuring the principal components of personality.

Not only that — but the test isn’t even sound.  One, MBTI asks people to describe themselves, with no external check.  Two, the best validation of it is a 90% consistency only if testing the same people soon after.  Let’s turn that around and say that in 10% of cases the test fails a basic scoff test.  Three, Wikipedia claims (with citation) that merely 36% of adults remain the same type after more than nine months.

I’m being harsh, but there really are some people who take the MBTI too far — using it to plan corporate teams, screening job candidates because they “don’t fit” according to a far-out extrapolation of the theory.

I remember in my first sales job the trainer used a stripped-down version of MBTI (4 types) to help us characterize customers quickly.  It was fine for that task—but shouldn’t be used for serious stuff like career counseling.  I’m thinking of books like Do What You Are — as if who you are doesn’t change over time, or wouldn’t be influenced by the job market!  Jeesh.


So where does the MBTI come from, anyway?  The first three parameters come from schlockmeister Jung, the same one who gave us “cultural memory” and the book Synchronicity.  Well my trust in those is blown.  [Persi Diaconis, the statistician’s statistician (and magician), refuted the improbable nature of the coincidences that comprise Synchronicity.] 

Read the Wikipedia article for more of this history.  But essentially the practical purpose that brought MBTI typology into common use was its application in the US during WW II, to match women to jobs while the men were at war.  It wasn’t intended to find them a fulfilling career for life — merely to point people who had worked exclusively at home toward a factory or office that they were more likely to enjoy.

Now that is an appropriate sized job for the MBTI.  It shouldn’t be used for important stuff like screening employees, managing them, choosing a career, or making definitive judgments about anyone.  The typology is too small, people change, the test is unreliable, and these four factors probably aren’t the principal components.