Automatic Modeling of Personality Types

BA Thesis (Afstudeerscriptie)

written by

Douwe Oosterhout(born June 30th, 1985 in Ramotswa, Botswana)

under the supervision of Dr. Reinhard Blutner, submitted in partial fulfillment of therequirements for the degree of

BA Kunstmatige Intelligentie

at the Universiteit van Amsterdam.

Abstract

A model using two qubits to represent Jung’s personality types is compared to an exten-sion of Jung’s theory, the Myers-Briggs Type Indicator. The 2-qubit model can generateartificial personalities, which in turn can be compared to real world data. This data isgathered by a questionnaire. Conceptual advantages are the use of less variables and thebetter fitting of Jung’s theories by use of the shadow personality. An attempt is made tofind empirical differences. However, these are hard to find due to principal reasons of themodels.

Contents

1 Introduction 2

2 Personality types according to C.G. Jung 22.1 Thinking vs Feeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Sensation vs Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Introversion vs Extroversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4 The Shadow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 The MBTI 4

4 Singer-Loomis TDI 5

5 Two qubit approach 65.1 The Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65.2 Using two qubits to represent Jung’s personality types . . . . . . . . . . . . . . 85.3 Conceptual advantages of the 2 qubit model . . . . . . . . . . . . . . . . . . . 11

6 Questionnaire 12

7 Fitting the data to MBTI and the two Qubit model 12

8 Generating artificial personalities 13

9 Cronbach’s alpha and cluster analysis 13

10 Conclusion and further research 16

11 References 17

12 Appendix A : the questions used in German, English and Dutch 1812.1 Instructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1812.2 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

13 Appendix B : The personalities 25

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1 Introduction

For centuries psychologists and philosophers have tried to crack the code of human personality.The complexities of covering human personality has started a lot of debates what should andshould not be covered by a personality model, be it explanations about our behavior, or ourpsyche. This in turn ensured that many models spawned from brains of these psychologists andphilosophers. Two such widely used models are Jung’s personality type model by Carl GustavJung (1921) and the Big Five model. Where Jung’s model has four psychological functionsand two attitudes to express personality, the Five Factor Model, as the Big Five is also named,uses five personality traits or factors are used. The Big Five model is more empirically driventhan the MBTI or Jung’s model, although correlations have been found which suggests that themodels each models scales can be related to one another. (McCrae & Costa, 1989).

It is Jung’s personality type theories we shall be using in this paper. An adaptation toJung’s model, the Myers-Briggs Type Indicator (MBTI) is one the most used personality mod-els in western civilization. It is used in many applications such as relationship counseling,career planning and many more. Its widespread use makes it an important comparator whenintroducing a new model.

In this paper a two-qubit approach, to which Jung’s model fits very intuitively, is comparedto the MBTI. Jung himself never formalized his own model and introduced it purely from apsychological point of view. However using two qubits to express Jung’s theories lends itselfperfectly for formalization. It encompasses ideas of Jung that the MBTI does not, such as theshadow personality. Ambiguity however shadows over both models as both can reach certainstates where multiple personalities can be detected.

The two qubit model allows us to calculate expected values for the psychological functionsand attitudes, which in turn allows us to generate artificial personalities. The artificial personal-ities need to be compared to real world personalities. To obtain these a questionnaire was madewhich was filled in by 25 subjects. From this questionnaire the MBTI score was calculatedwhich could then be compared.

Besides a conceptual analysis of the two models, some empirical analysis is also performed.This is done in the form of analyzing the reliability of the questions by using Cronbach’salpha. Furthermore a cluster analysis is performed to see if each question clusters with it’scounterparts of the same type. A further task is to generate artificial personalities using the twoqubit model’s three parameters. These personalities can then be used to automatically fill inthe questionnaire. The simulation results can then be principally compared with the empiricalones. This is done by use of Cronbach’s alpha and a cluster analysis of the questions.

First off Jungian psychology will briefly be explained, together with some adaptations suchas the MBTI. After that the qubit will be explained, which uses formulas and theories fromquantum physics. After this the connection between Jung’s personality models and qubits willbe brought to light and the differences will be discussed.

2 Personality types according to C.G. Jung

Jung (1921) theorized that four psychological functions were needed to classify one’s per-sonality, namely sensation (S), thinking (T) , feeling (F) and intuition (N). Also two kinds ofpsychological attitudes were needed to specify one’s personality, introvert (I) and extrovert (E).Although everybody initially has access to the four psychological functions, what makes ev-eryone different is the various preferences people have to certain functions and there attitudetoward their preference. According to Jung, on the one hand we have thinking and feeling as

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rational functions and on the other hand we have sensing and intuition as non-rational func-tions. People rarely develop both rational (or non-rational) functions in their personalities,which leaves us to believe thinking and feeling and sensing and intuition should be opposites.Figure 1 gives us an intuitive look at the psychological functions. The result of having two axes,each with two psychological functions, combined with the two attitudes leaves us with eightdifferent personality types one can have. Each personality has a primary psychological func-tion and an auxiliary function, which have the same attitude, and are expressed the strongest.We experience these functions consciously. The two left over functions are the tertiary andinferior functions and are experienced unconsciously. Jung also specified that everyone alsohas a shadow personality which sits on the other side of the spectrum and can sometimes betriggered to take over. Naturally no personality type is better than another and no one fits per-fectly into one of the types. Jung suggested his model be used as a compass rather than a harddetermination of personality. Personality types are determined with questionnaires, where onecould choose from fixed answers.

Figure 1: Compass view of Jung’s psychological functions, taken from Jung et al. (1968, p.60)

I will now tell more about the different psychological functions and attitudes, as well as theshadow.

2.1 Thinking vs Feeling

As mentioned earlier, the thinking and feeling functions are the rational functions. Thinking isintuitively a rational function as it creates rational judgments of the perceived world, but feelingmight not be. Jung did not see the feeling function as a function for affection and emotion, buta function that performs value judgments. This requires thought and deduction and can thusbe seen as a rational function. When seeing another war on the news a person with a strongfeeling function would feel deeply sorrowful for the people suffering in that war, people losingtheir houses etc. Thinkers would feel less compassion and be more interested in hard facts,such as number of casualties, or the reasons of why the war started in the first place.

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2.2 Sensation vs Intuition

The sensation and intuition functions are the non-rational functions as they do not have any-thing to do with rationality. They are the perceptive functions and determine what one doeswith information that one gets from the world. Sensation creates a world view based on one’ssenses, so for example a person with a strong sensing function often perceives the colors of theflowers in the garden. This is in strong contrast with people with a stronger intuitive function,which perceives the relationships and possibilities of the information one receives. Flowersthat are all situated with equal distance to each other would cause an intuitionist to infer thatthey were planted there rather than sprouted by natural reproduction. Of course a sensationalistcould also perceive this, as no function binds exclusively to a person, but as one function runsstronger than the other, it will initially create a different perception of the world.

2.3 Introversion vs Extroversion

The four psychological functions introduced by Jung can all manifest in two attitudes, namelyintrovert and extrovert. This represents the orientation of one’s primary psychological function.If someone is extrovert, that person would reflect on the outer world, whereas an introvertwould reflect on his inner self. The result of this is for example that extroverts eagerly attachto others around them and don’t mind talking to strangers. This in great contrast to introvertswhom prefer to keep to themselves and would rather be left alone or be with people they reallytrust.

2.4 The Shadow

As mentioned earlier every person contains every psychological function and attitude. It is onlysomeone’s preference to use one, but not the other that makes every person unique. However,every person also contains a shadow personality. This shadow sits unconsciously in every per-son and its personality is the exact opposite of someone’s personality. So say, if someone is anextroverted thinker, his shadow will be an introverted feeler. A shadow there to counterbalanceour personality, in other words it is in superposition with our personality. A persons personalityis thus not wholly determined by their main personality, but in conjunction with their shadow.Jung finds that it is important for someone to understand their shadow, not only for personaldevelopment, but also for social harmony. (Stevens, 1994).

In the next three sections three extensions to Jung’s personality model will be discussed,namely the Myers-Briggs Type Indicator which introduces a new dimension, the Singer-LoomisType Deployment Instrument which is able to differentiate someone’s personality from hisor her shadow and an approach which implements two qubits to describe Jung’s personalitymodel.

3 The MBTI

MBTI stands for the Myers-Briggs Type Indicator and uses Jung’s theory of personality types,but adds an extra dimension. Myers and Briggs (1962,1980) theorized that a lifestyle functionwas needed to better capture the different personalities of the world. This lifestyle functionindicated which psychological axis one preferred, be it the judging function, which relates tothe thinking-feeling axis, or the perceiving function which relates to the sensing-intuition axis.To be more concrete, people who have a stronger preference for the judging function tend

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to plan their life more, whereas perceivers rather live their life unplanned. With this addeddimension we can now construct 16 different personality types. The MBTI has now becomeone of the most used personality type models in the world.

If we look at the MBTI from a statistical point of view, we can describe it with four pa-rameters. These are of course the four dimensions they use to describe someone’s personality:extrovert/introvert, sensing/intuition, thinking/feeling and judging/perceiving. These parame-ters can be seen as Boolean random variables, named E, S, T and J respectively. They map eachside of their dimension to {−1, 1}. For example, the random variable E maps the extrovert sideto 1 and the introvert side to −1. We define µ(E = 1) = e, µ(S = 1) = s, µ(T = 1) = t andµ(J = 1) = j. This gives us the following expectation values:

E = 2e− 1 (1)

S = 2s− 1 (2)

T = 2t− 1 (3)

J = 2j − 1 (4)

Here are some example personalities, with their appropriate values:

Name Personality type E e S s T t J jDaan INFP -1 0 -.6 .2 -.2 .4 -.4 .3Tim ISTP -1 0 .8 .9 1 1 -.2 .4Ruben ISFP -.2 .4 .6 .8 -.2 .4 -.8 .1Sanne ENTP .4 .7 -.2 .4 .8 .9 -.8 .1

In Daan’s case, using the MBTI description, being an INFP , shortly put, means that he isidealistic and loyal to his values and to people who are important to him. Sanne however, beingan ENTP, is in short a quick, ingenious, stimulating, alert, and outspoken person.

In stead of seeing an opposite complementary personality as a shadow, such as Jung de-scribed, Myers-Briggs see the inferior, least developed function as the shadow.

A problem with the MBTI is that it can sometimes be in an ambiguous state where a personcan have two personalities. Say e = 1

2 and t = 12 and s equals some small ε. This gives us

E = 0 and T = 0. Is this person then an extroverted thinker with an introverted feeling functionor an introverted thinker with an extroverted feeling function? It is this type of ambiguity thatcan wrongly give someone a opposite personality.

4 Singer-Loomis TDI

The Singer-Loomis model (Singer & Loomis, 1984) is another adaptation to Jung’s. TDI standsfor Type Deployment Instrument. The SL-TDI changed the way subjects could respond toquestions by implementing a one-to-five scale. This way a subject can indicate how often he orshe would give a certain response, resulting in more dynamic results. Also, in stead of askingquestions about a psychological function they ask questions about psychological functions in acertain attitude. This is because they think that the attitudes are inseparable from the functions,because they are always used in a introverted or extroverted way. (Dugan & Wilson, 2002) Theyalso assume that the functions do not cancel each other out. In other words, one can have astrong thinking function, but this does not mean that you have a weak feeling function. Askingquestions in the Singer-Loomis TDI way takes care of the ambiguity problem the MBTI has,as it is now clear which attitude each function works with. However by asking questions in a

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certain attitude and thus relieving people from giving answers to bipolar questions, Singer andLoomis have created a way where a single dimension can emerge as the primary and secondaryfunction. This is in disagreement with Jung’s ideas where the inferior function is always theopposite of the primary function.

When formalizing the Singer-Loomis TDI we can use the same random variables as de-fined in the MBTI case, excluding the random variable J of coarse, because it is not used bythe model. Now because they assume that every psychological function is used in an intro-verted or extroverted manner the probabilities are calculated as combined probabilities, e.g.µ(E = 1, T = 1). These dependencies do however enlarge the number of parameters neededto express the model formally. The three random variables and eight dependency relations sumup to 11 parameters and this is only in the simpler bipolar case. Of course, the chosen randomvariable can be connected to form a Bayesian network as a formal expression of the full model.However, because of the high number of free parameters this can form a descriptive model onlywithout any explanatory value.

5 Two qubit approach

A 2-qubit model to Jung’s methodology has recently been introduced (Blutner & Hochnadel,2009). This model makes use of certain formulas and ideas from quantum theory such as qubits,Pauli’s spin matrices. It is this model I will be researching in this paper. It will primarily becompared to the MBTI. It will be introduced formally in the next section.

To formally introduce the 2-qubit model, we must first introduce some formalisms fromquantum physics which are necessary to understand the approach.

5.1 The Qubit

A qubit is in a sense similar to a computer bit in that they both have two states, 0 and 1. Thebiggest difference however is that a qubit has the possibility to be in a superposition of the twostates, whereas a bit can be only one or the other.

A qubit can be represented by a Bloch sphere. This allows us to represent a qubit with thetwo parameters θ and ϕ. Here θ is the superposition parameter and ϕ indicates the phase factorof the qubit. An example can be found in figure 2.

Figure 2: Bloch sphere, taken from http://en.wikipedia.org/wiki/File:Bloch sphere.svg underthe Creative Commons Attribution ShareAlike 3.0 licence.

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In the two qubit model the phase factor is ignored, leaving us with one parameter to rep-resent our psychological functions. Without parameter ϕ we are left with a circle, namely thecircle of figure 3.

Figure 3: A Bloch sphere representation where the phase factor is 0

A qubit state is called pure when the superposition is linear. This means that the qubit canbe represented with the following formula, using the bra-ket notation:

|Ψ〉 = α|0〉+ β|1〉 (5)

where |0〉 and |1〉 are orthogonal unit vectors representing state 0 and 1 mentioned above andα2 + β2 = 1.

It is intuitive to view a qubit as polarized light. If light is polarized in one direction, po-larizing it again in a direction which is perpendicular to the previous polarization will blockany light of coming through. Thus the polarizations are mutually exclusive. Similarly it couldbe viewed as a photon, as photons can also be polarized. This is visualized in figure 4. Allintermediate lines from the x-axis to the z-axis are possible states the photon can be in. As thispicture can also be seen as two vectors spanning a two-dimensional space it is in agreementwith formula 5.

Figure 4: Visualization of possible photon states

As Bloch spheres operate on the Hilbert space it is useful to define states on such a space.Here we use Pauli’s spin matrices, because these (together with the identity matrix I) form anorthogonal basis for the Hilbert space. They are defined as follows:

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σx =

(0 11 0

)(6)

σy =

(0 −ii 0

)(7)

σz =

(1 00 −1

)(8)

Looking back at figure 4 we see that given a certain vector, the angle θ can be attained.This gives us the means to determine the state our photon is in:

ψ =

(cos θ2sin θ

2

)(9)

Formula 9 relates directly to our Bloch sphere representation, only there our pure statesoppose each other 180◦ in stead of the 90◦ here, so the angles have to be multiplied by 2. Nowthe cosine gives us our location on the z-axis and the sinus function gives us our location on thex-axis. Because they both use only one and the same variable, formula 9 gives us the possibilityto represent two photons with one variable as seen in figure 3.

The state of the first photon can thus be calculated with the formula cos θ. The state of thesecond photon can be calculated with sin θ, giving us:

ψ′ =

(cos θsin θ

)(10)

We can now easily determine the expected value of a function by using the standard formulafor expected values in quantum physics:

σz = ψ′Tσzψ′ (11)

this gives us

σz =(

cos θ sin θ)( 1 0

0 −1

)(cos θsin θ

)= cos 2θ (12)

Similarly we find

σx = sin 2θ (13)

σy has been omitted because we will not be using it further on.So if we take θ = π

4 we get σz = 0 and σx = 1, or if θ = π8 we find σz = 1√

2and σx = 1√

2This is to give us an intuition to what is possible when using this representation. We will

now implement these theories to model Jungs personality types by using two qubits.

5.2 Using two qubits to represent Jung’s personality types

As mentioned we will be using two qubits to represent Jungs personality model. We can quicklysee the analogy between Jungs personality functions and a qubit when we look at figures 1 and3. The compass like structure makes for a perfect analogy. This allows us to use the previouslyintroduced formulas for the calculation of expected values to determine someones personality.As our Thinking-Feeling function (T) is situated on the z-axis on the Bloch sphere it is σz

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(formula 8) that is the observable for this function. As the thinking function T = σz , theopposite function, feeling, can be represented by F = −σz . The Sensing-Intuition (S) functionsits on the x-axis and is thus represented by σx (formula 6).

When using the formulas for calculation the expected values (formulas 12 and 13) andfilling in θ for values between −π and π we find figure 5.

Figure 5: The eight Jungian personality types represented by their expected values

In figure 5, if one would draw a vertical line at each of the numbers, the eight Jungianpersonality types emerge. So at number 1 we find a dominant Feeling function, a secondaryintuition function, a tertiary sensing function and an inferior thinking function.

The second qubit expresses the attitudes. Here we choose for the z-axis to represent theExtroversion-Introversion attitudes. This is also represented by σz . However, because we arein another qubit we do not use θ as our variable, but α. The x-axis is not used in the two qubitmodel and is simply an intermediate state, which has no effect on the personality types.

In stead of using the angle θ from our Bloch sphere representation in the two qubit model,we will be using θ′ = θ

2 . This way our representation looks like figure 6.

Figure 6: Alternate representation of our qubit.

Two such qubit are now combined using the tensor product. As we will be using the modelas described by equation 9, where opposite functions are perpendicular, we can describe a stateor personality type as the following:(

cos α2sin α

2

)⊗(

cos θ2sin θ

2

)(14)

Here the left vector describes a persons attitude and the right vector a persons psychologicalfunctions.

We also wish to include the shadow of one’s personality type in its state vector. For thisreason we superpose the state vector 14 with a state vector perpendicular to it. This is:

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(sin α

2− cos α2

)⊗(

sin θ2− cos θ2

)(15)

In the two qubit model, the shadow is entangled with someones personality. In the presentcase, this means that a psychological function is inseparably connected with a certain attitude.Since more than one attitude is possible for each personality, the superposition of attitude-psychological function pairs accounts for the description of the full personality. This gives usthe the general state representation of the two qubit model:

ψ = τ

(cos α2sin α

2

)⊗(

cos θ2sin θ

2

)−√

(1− τ2)

(sin α

2− cos α2

)⊗(

sin θ2− cos θ2

)(16)

Where τ is the entanglement factor and −√

(1− τ2) is needed for normalization.We now define the basic observables in this 2-qubit model, which are our two opposing per-

sonality types and opposing attitudes. However, because a personality type is now representedby a qubit with personality types and the attitude qubit we get the following formulas:

E =

(1 00 −1

)⊗ I (17)

T = I ⊗(

1 00 −1

)(18)

S = I ⊗(

0 11 0

)(19)

Where I is the identity matrix.Now once again, with the states and observables we can calculate the expected values. For

complexity purposes all parts of the equation where a matrix multiplication results to 1 have

been omitted (i.e.

(cos θ2sin θ

2

)I = 1).

E = ψTEψ = τ(

cos θ2 sin θ2

)( 1 00 −1

)τ

(cos θ2sin θ

2

)+ (20)

−√

(1− τ2)(

sin α2 − cos α2

)( 1 00 −1

)−√

(1− τ2)

(sinα2− cos α2

)+ (21)

τ(

cos θ2 sin θ2

)( 1 00 −1

)−√

(1− τ2)

(sinα2− cos α2

)+ (22)

−√

(1− τ2)(sinα2 − cos α2

)( 1 00 −1

)τ

(cos θ2sin θ2

)= (23)

(2τ2 − 1) cosα− 2τ√

1− τ2sinα (24)

In the same way we find

T = (2τ2 − 1) cos θ − 2τ√

1− τ2sinθ (25)

S = (2τ2 − 1) sin θ − 2τ√

1− τ2 cos θ (26)

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In a similar fashion we can calculate µ(E = 1), represented further on as E+. µ(E = 1)is the chance that a personality will answer the extrovert answer when given a question about

the extrovert-introvert attitude. Here the observable is

(1 00 0

)⊗ I . We find:

ψTE+ψ = sin2 α

2+ τ2 cosα− τ

√(1− τ2) sinα (27)

And similarly:

ψTT+ψ = sin2 θ

2+ τ2 cos θ − τ

√(1− τ2) sin θ (28)

ψTS+ψ =12

(1− sin θ) + τ2 sin θ − τ√

(1− τ2) cos θ (29)

With these expectations in place we can use these formulas to create our own personali-ties. These can then be compared to some self obtained personalities. The outcome will bediscussed further on. However, we must be cautious. Some values of our parameters can leadto ambiguous results, just like in the MBTI. Figure 7 shows us formula 25 for different fixedτ and a variable θ from −π to π. If we look at the central curve with value −1 at θ = 0 (hereτ = 0, we see that the value 0.5 for example can be achieved by multiple θ.

Figure 7: Function T as a function of theta for different tau.

5.3 Conceptual advantages of the 2 qubit model

The MBTI is formally defined by four random variables, so it thus takes four variables toproduce result. It can get even worse if there are dependencies between these random variables,which in the case of the EI and TF can be determined by seeing if the following holds.

P (E|T ) 6= P (E) (30)

If this would be the case another variable would need to be added to capture this depen-dency. This means that the MBTI hold at least four variables. The 2-qubit approach howeveruses three variables only, namely τ , θ and α to describe all personalities. The three parametersdescribe the full distribution without the need for additional parameters. This provides us witha more elegant solution than say the Singer-Loomis TDI which uses at least 11 parameters.The incorporation of the shadow and the entanglement of the shadow with a personality makesthe 2-qubit model fit better to Jung’s theories, as opposed to the MBTI which does not use ashadow. Also the notion of superposition result in far more dynamic personality types than the

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generic 16 types of the MBTI. Jung’s theories tell us that opposing functions should be used,so thinking should oppose feeling, however the Singer-Loomis TDI ignores this, allowing op-posing functions to become the primary and auxiliary functions. This part of Jung’s theory isfollowed in the 2-qubit model.

6 Questionnaire

The self obtained personalities were obtained by asking subjects 24 questions. There werefour categories of six questions each. Each category was one of the MBTI dimensions. Thequestions were given in random order. After each question the subject was asked to indicatehow certain he or she was of their answer. This was done on a scale from 1 to 5, where 1 wascompletely uncertain and 5 was completely certain. All the questions where taken from theMyers Briggs test. The MBTI uses far more questions, but most had to be removed to keepwithin the time frame of this thesis. An example question, which was part of determining theThinking-Feeling value, is:

Are you swayed more by :(1) convincing evidence

(2) a touching appeal

After receiving an answer the following was asked:

How certain are you about your answer? (1 to 5)

Say someone would answer 2 here with certainty 3, this would then result in an answervalue of -3, because the feeling function to which the answer refers sits on the opposite side ofthe thinking function. After the test the answers were stored in a file. 25 people were asked tovoluntarily participate in the questionnaire.

7 Fitting the data to MBTI and the two Qubit model

For each person a Myers-Briggs type could then be determined. This was simply done byscaling all answers to the interval [−1, 1]. Now for each group of questions, each representinga function or attitude, the mean value could be determined. In the thinking-feeling case thismeant that if the value was bigger than 0 the thinking function was appointed to the personality.Obviously, if the value was smaller than zero the feeling function was appointed.

To get the parameters τ , α and θ for the 2-qubit model a χ2-fit was used. As mentionedearlier, and as depicted in figure 7, sometimes multiple solutions are possible. The χ2-fithowever only finds one solution, when appointing personality types. Due to time constrictions,looking for the other solutions was not possible and could be subject for further research.

To incorporate the Myers-Briggs lifestyle function (J), we simply looked at the dominantpersonality function. If the sensing or intuition function was dominant, the lifestyle functionwould become the perceiving function (P). Otherwise we would use the judgment function (J).All personalities, both MBTI and 2-qubit, can be found in the appendix.

In the MBTI case the psychological functions and attitudes are represented reasonablyequal. However the thinking function was represented significantly within the first ten subjects.

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This could be because these subjects were Artificial Intelligence students. This study asks fora lot of logical and causal reasoning skills, which in turn makes this outcome logical.

In the 2-qubit case we also see the dominance of the thinking function in the first tensubjects. Furthermore we find a change of primary function in 52% of the time. Dugan andWilson found a 46% change when comparing the Singer-Loomis model to the MBTI. (2002,p. 3) To what extent these changes are the same is yet to be determined.

In the 2-qubit case there were three subjects with a τ value of over 0.95, which indicatesthat they have a weak shadow. In these cases we find what we would expect, a (near) matchwith the MBTI case, as the MBTI does not incorporate a shadow function. If we look at asubject with a lower τ , such as subject 16, we find MBTI personality INTJ. In the 2-qubitcase we find the ESTJ personality which is entangled with it’s shadow INFJ. The strength ofthe entanglement, as stated by the variable τ , is 62%. This means that the shadow takes up38% of the personality. If the shadow were to ’intervene’ in some of the questions asked in thequestionnaire, approximately 38% of the time in this case, it could be the reason why the MBTIpersonality differs from the 2-qubit personality. In the MBTI case there is no explanation towhy someone who is an introvert according to the MBTI would give extrovert answers to someof the questions, as the MBTI does not use any shadows or forms of superposition. The 2-qubit model does do this which, if you believe in Jung’s theories, makes it the richer, moreexplanatory model of the two.

8 Generating artificial personalities

Simulations give people an easy way of testing hypotheses. A car simulator gives people thechance to learn to drive without having to worry about making mistakes and simulations ofmodels give scientists the possibility to gather data that might be time consuming or difficultto gather in the real world. In this case personalities many can be generated to be tested upon,for example by psychologists or people with a background in Artificial Intelligence. Alsorobots could later be given random personalities, which makes having a model for accuratelygenerating them useful.

Using a formalized model to Jung’s psychology has this advantage, we can now generateartificial personalities. Given some random value for the parameters τ , α and θ we can createa personality. This is done by filling in the variables into formulas 24, 25 and 26. Now thispersonality can fill in the questionnaire. Again, using the variables we can determine the chancethat a personality will answer the extrovert answer by using formula 27. Using a randomnumber generator artificial answers could be generated, returning 1 if the answer was extrovertand -1 if the answer was introvert with the chance given by the parameters. The same can bedone for the psychological functions T and S using formulas 28 and 29 respectively. To fullysimulate the questionnaire, where answers can be given with a certainty level scaling from 1 to5, for each question the random answer generator ran 5 times where after the returned valueswere summed up.

9 Cronbach’s alpha and cluster analysis

A fairly common way to evaluate the reliability and consistency of a questionnaire is the use ofCronbach’s Alpha. It measures the internal consistency reliability, in other words how well aset of questions or items measure the same concept. In our case we can measure how well eachset of questions measure the same set of psychological functions or attitudes (e.g. the questions

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for the Feeling vs the Thinking function). The definition of Cronbach’s Alpha (Cronbach, 1951,p. 321) is as follows:

α =N

N − 1

(1−

∑Ni=1 σ

2Yi

σ2X

)(31)

Where N is the number of components, σ2X is the variance of the total test scores and σ2

Yi

is the variance of component i.As an example, we can use Cronbach’s alpha to get an impression of how good the Intro-

vert/Extrovert questions relate to one another. If they all genuinely measure the same conceptwe will get a alpha score of around 1. A score of 0.7 and above is generally accepted as reliableand means that the questions are related to each other and measure the same concept. Howeverthe threshold of 0.7 is only a guideline as Cronbach’s alpha can be influenced by multiple fac-tors (Spiliotopoulou, 2009), such as the distribution of the data, the sample size and the widthof the scale. In our case we have a uniform distribution in our data which causes an underesti-mate of the alpha value. A low alpha value would prevent us from being able to make any validassessments about the outcome of our data.

Values of Cronbach’s alpha can also be negative. This happens when the average covari-ance between the variables is negative (Nichols, 1999). According to Nichols the most probablecause of finding a negative alpha with a small sample size is “that while the true population co-variances among items are positive, sampling error has produced a negative average covariancein a given sample of cases”. (1999)

For our questionnaire we find the following results:

Type α

E -19.3T -24,4S -12,5

When filling in the questionnaire with generated personalities we can also calculate Cron-bach’s alpha. We find:

Type α

E -1,3T -13,2S 0

In both cases we find very bad alpha values, even when we take the influencing factorsinto account no decent score is achieved. This could be related to the small sample size of 25people. Another reason could be that there is something wrong with the questions and that theyindeed don’t measure the same concept. However, we also find bad values in the artificiallygenerated case. Here we know we are measuring the same concept, but we still get low (andeven negative) scores. Therefore there must be a principal reason that the alpha values are sobad. A reason for this may be found in figure 5. Here we see that if a personality has a strongprimary function, the auxiliary and tertiary functions will always be situated very close to eachother and thus have approximately the same chance of answering a question. This generates alot of variance in the data which in turn lowers the alpha value.

Additionally to calculating Cronbach’s alpha a cluster analysis was performed. One wouldexpect that questions that measure the same thing would cluster together. When performingthis on the answers of the questionnaire, we find figure 8. Here we only used the first 18

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questions because the 2-qubit model cannot fill in the final six questions about the judgmentand perception axis the MBTI contains. The three groups of six have been colored in to get aquick intuitive look of how the data is clustered.

Figure 8: Cluster analysis performed on the results of the questionnaire

When we perform the same cluster analysis on the data we get from the artificially filled inquestionnaire, we find figure 9.

Figure 9: Cluster analysis performed on the results of the questionnaire with artificial person-alities

In both cases we see that no true clusters are found. The three sets of questions overlapeach other and each question is almost evenly divided over the space. As we find no clusteringand as the origin of the questions are from the MBTI and were carefully selected that theydo measure the same concept, we again must conclude that there must be principal reason forthese results. Using Cronbach’s alpha and cluster analysis can therefor at this time not be used

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to determine empirical differences between the MBTI and the 2-qubit case. This could be asubject for further research.

10 Conclusion and further research

A first step has been made in the comparison between the 2-qubit model and the MBTI. Al-though only 25 subjects were compared to a Myers-Briggs test with only 24 questions, the fullMBTI has about 73 questions, some conclusions can be made. Conceptually the 2-qubit modelseems better because of the use of less variables than the MBTI. Also it follows Jung’s theoriesmore accurately by implementing a shadow which is entangled with someones personality. Inthe results found, people with a weak shadow showed a near perfect match with the MBTI,indicating some correlation. Although the use of the shadow makes the 2-qubit model moredivers and descriptive. Also the first attempts to find some empirical evidence of which modelsmight perform better need further research. Cronbach’s alpha and the cluster analysis showedus some bad results, but this is however probably to some innate properties of the models. Inthe future more subjects should be used to ensure that a small sample size is not the problemwith Cronbach’s alpha. Also using the full MBTI questionnaire should lead to better MBTIresults for comparison.

Further research could also make a comparison with the Singer-Loomis TDI. The modelcan partly mimic the Singer-Loomis TDI, which always uses psychological functions in com-bination with a attitude, by defining some new operators. If we would want to combine thethinking-feeling function with the extroversion-introversion attitudes we simply take E ⊗ T asthe new operator.

The curse of ambiguity that resides in this model is a big problem for the model. Theambiguity makes it difficult to conclude anything concretely when you know that the fitted per-sonalities could have another solution. The the full extent of it’s effect needs further research.

The future should however be met with some optimism. The use of few variables to de-scribe personalities and the ability generate more accurate personalities gives it the upper hand,for now.

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11 References

Blutner, R & Hochnadel, E. (Yet unpublished) Two Qubits for C.G. Jung’s Theory of Person-ality.Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika,16(3), 297-334.Dugan, S., & Wilson, K. (2002). Singer-Loomis TDI: The next generation of psychologicaltype instrument: University of Calgary, Haskayne School of Business, Working Paper 2002-07.Jung, C. G. (1921). Psychologische Typen. Zurich: Rascher.McCrae, R R & Costa, P T (1989). ”Reinterpreting the Myers-Briggs Type Indicator From thePerspective of the Five-Factor Model of Personality”. Journal of Personality 57: 17-40Myers, I. B. (1962). The Myers-Briggs Type Indicator. Palo Alto, Cal.: Consulting Psycholo-gists Press.Myers-Briggs, I., & Myers, P. B. (1980). Gifts Differing: Understanding Personality Type.Palo Alto, Cal.: Davies-Black Publishing.Singer, J., & Loomis, M. E. (1984). The Singer-Loomis Inventory of Personality. Palo Alto,Cal.: Consulting Psychologists Press.Spiliotopoulou. (2009) Reliability reconsidered: Cronbach’s alpha and paediatric assessmentin occupational therapy. Australian Occupational Therapy JournalNichols, D. P. (1999). My Coefficient a is Negative!. SPSS Keywords, Number 68.http://www.ats.ucla.edu/stat/spss/library/negalpha.htmStevens, A. (1994). Jung - A very short Introduction. Oxford: Oxford University Press.

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12 Appendix A : the questions used in German, English and Dutch

12.1 Instructions

InstructionMark the answers which you think most valid. Next, indicate for how certain you take thisanswer:

1. completely uncertain

2. uncertain but with a week preference for the given answer

3. moderately uncertain with a clear preference fort he given answer

4. moderately certain

5. absolutely certain

InstruktionWhlen Sie die jenige Antwort, die Sie fr zutreffend halten.Nachdem Sie die Antwort gewhlt haben, geben Sie an, wie sicher Sie sich bei der Entscheidungwaren:

1. vollig unentschieden

2. unsicher mit nur leichter Prferenz fr die angekreuzte Antwort

3. relativ unsicher mit deutlicher Prferenz fr die angekreuzte Antwort

4. einigermaen sicher

5. sehr sicher

InstructiesGeef het antwoord dat het meest bij jou past. Geef vervolgens aan hoe zeker je bent van jeantwoord:

1. volledig onzeker

2. onzeker, maar je hebt een zwakke voorkeur voor het gegeven antwoord

3. gematigd onzeker, maar wel met een duidelijke voorkeur voor het gegeven antwoord

4. gematigd zeker

5. absoluut zeker

EXAMPLECommon sense iso usually reliableo frequently questionable

BEISPIEL

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Gesunder Menschenverstand isto oft vertrauenswrdigo oft fragwrdig

VOORBEELDGezond verstand iso over het algemeen betrouwbaaro regelmatig twijfelachtig

12.2 Questions

E/I

1. Verhalten Sie sich in Gesellschaft so, dass Sieo den ersten Schritt tun, die Unterhaltung in Gang zu bringeno warten, bis Sie angesprochen werden

At a party,o do you take the first step in order to start a conversationo do you wait until somebody else starts talking to you

Op een feestje,o neem jij de eerst stap om een gesprek te beginneno wacht je af totdat iemand met jou gaat praten

2. Wie verhalten Sie sich beim Luten des Telefons:o Sie beeilen sich, um als erster den Hrer abzunehmeno Sie hoffen, dass ein anderer den Hrer abnehmen wird

When the phone rings, do you:o hurry to get to it firsto hope someone else will answer it

Als de telefoon gaato neem je hem meteen als eerste opo hoop je dat iemand anders opneemt

3. Haben Sie liebero viele Freunde mit kurzzeitigem Kontakto einige Freunde mit lnger andauerndem Kontakt

Do you prefer to haveo many friends with short-living contactso only a few friends with long-standing contact

Heb je lievero veel vrienden waar je kortdurend contact mee hebto alleen een paar vrienden waar je langdurig contact mee hebt

4. Ist es so, da

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o es Ihnen leichtfllt, sich eingehend mit Fremden zu unterhalteno Sie Fremden gegenber wenig zu sagen wissen

Is it the case thato it is simple for you to speak with people you don’t knowo you have less to say to people you don’t know

In het geval dat je een onbekende tegen komto praat je er toch makkelijk meeo heb je eigenlijk niets te zeggen

5. Suchen Sie bei einer Party den Kontakt mito mglichst vielen, einschlielich Fremdeno nur wenigen, die Sie kennen

At a party do youo interact with many people, even strangerso interact with a few friends

Op een feestjeo ga je om met veel mensen, ook onbekendeno ga je alleen om met een paar vrienden

6. Sind Sie meistenso leicht ansprechbaro etwas reserviert

Do you consider yourselfo rather talkativeo somewhat reserved

Zie jij jezelf also praatgraago ietwat teruggetrokken

T/F

1. Treffen Sie Entscheidungen lieber auf der Grundlage vono Normeno Gefhlen

Are you more comfortable in making your judgements based ono Normso Feelings

Waar baseer je liever je oordelen op?o Normeno Gevoelens

2. Fllt es Ihnen leichter,o Urteile auf logischer Basis zu treffen

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o Werturteile zu treffen

Are you more comfortable in makingo Judgements on a logical basiso Value judgements

Maak je lievero Oordelen op een logische basiso Waarde oordelen

3. Welches ist das grere Kompliment:o ”er ist ein sehr logischer Mensch”o ”er ist ein sehr sentimentaler Mensch”

Which is more of a complimento ”There’s a logical person”o ”There’s a sentimental person”

Wat krijg je liever als compliment?o ”Jij een verstandig persoon”o ”Jij bent een gevoelsmatig ingesteld persoon”

4. Fhlen Sie sich mehr hingezogen zu dem, was Sieo berzeugto berhrt

Are you swayed (attracted) more byo convincing evidenceo a touching appeal

Wordt je meer aangetrokken dooro overtuigend bewijso een emotioneel pleidooi

5. Sind Sie mehr beeindruckt vono Prinzipieno Emotionen

Are you more impressed byo principleso emotions

Wordt je meer overtuigd dooro principleso emoties

6. Was wnschen Sie sich selbst mehr:o einen klaren Verstando starkes Mitgefhl

What do you wish more for yourself

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o a pretty clear braino strong sympathy

Wat heb je liever?o Gezond verstando Veel symapahtie kunnen tonen

S/N

1. Schriftsteller sollten sicho klar und unmissverstndlich ausdrckeno mehr unter Zuhilfenahme von Analogien ausdrcken

Do you like writers whoo say what they meano use metaphors and symbolism

Hou je meer van schrijvers dieo zeggen wat ze bedoeleno metaforen en symbolismen gebruiken

2. Wodurch lassen Sie sich eher leiten:o durch Fakteno durch Prinzipien

Are you more often leado by factso by principles

Word je vaker geleid dooro feiteno principes

3. Verlassen Sie sich eher auf Ihreo Erfahrungeno Ahnungen

Do you prefer to trusto your experienceo your intuition

Vertrouw je liever op jeo Ervaringeno Intutie

4. Was schtzen Sie an sich selbst mehr:o einen ausgeprgten Sinn fr Realitto ein lebhaftes Vorstellungsvermgen

Do you prize in yourselfo a strong hold on reality

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o a vivid imagination

Beschrijf jij jezelf meer als iemand meto beide benen op de grondo een levendige fantasie

5. Welche Art von Geschichten bevorzugen Sieo Action- und Abenteuergeschichteno Phantasie- und Heldengeschichten

In stories do you prefero action and adventureo fantasy and heroism

Wat prefereer je in verhalen?o actie en avondtuuro fantasie en heldhaftigheid

6. Nehmen Sie sprachliche uerungen ehero wrtlicho bertragen/metaphorisch

Are you inclined to take what is saido more literallyo more figuratively

Neem je gesproken uitlatingen eerdero figuurlijko letterlijk

J/P

1. Treffen Sie eine Wahlo eher berlegto eher impulsiv

Do you tend to make your choiceso well thought outo rather spontaneous

Maak je je keuzeso goed doordachto nogal spontaan

2. Welche Situation sagt Ihnen mehr zu:o die strukturierte und planmigeo die unstrukturierte und unplanmige

What situation do you prefero structured and plannedo unstructured and unplanned

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Welke situatie staat je meer aan:o een geplande gestructureerdeo een ongeplande en ongestructureerde

3. Was zieht Sie mehr an:o vernnftige Menscheno einfallsreiche Menschen

Are you more attracted too reasonable peopleo creative and unconventional people

Voel je je meer aangetrokken toto verstandige menseno creatieve en onconventionele mensen

4. Neigen Sie mehr dazu,o eher vorstzlich als spontan zu handelno eher spontan als vorstzlich zu handeln

Do you have a tendencyo to act planned rather than spontaneouso to act spontaneous rather than planned

Heb je de neiging omo gepland te handeleno spontaan te handelen

5. Neigen Sie mehr dazu,o eher rasch zu entscheideno grndlich und eher langsam zu entscheiden

Is it your way too make up your mind quicklyo pick and choose at some length

Neem je je beslissingeno snelo doordacht en langzaam

6. Neigen Sie dazu, Ihre Arbeitsaufgaben,o gut geplant zu erledigeno eher spontan und ungeplant zu erledigen

On the job, do you want your activitieso scheduledo unscheduled

Wil je op je werk dat al je activiteiteno gepland zijno ongepland zijn

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13 Appendix B : The personalities

# MBTI 2-qubit1 ISTJ 60% ESFP2 ISTP 66% ISFP3 INTJ 76% INTP4 ESTP 75% ESTP5 ENFP 73% ENTP6 ESTJ 62% ESFP7 ESTP 94% ESTJ8 ISTJ 53% ENTP9 INTP 70% ESTP10 ENTJ 74% ESTJ11 ESFJ 58% ESFP12 INFP 62% ENFP13 ESFP 90% ESFP14 INTJ 69% ESTP15 ISTJ 66% ISFJ16 INTJ 62% ESTJ17 ESTJ 94% ESTJ18 ESTP 75% ESFP19 ESFJ 55% ESTP20 INFJ 55% ENTJ21 ESTJ 75% ISTP22 ENTJ 75% INTJ23 ESFJ 83% ESFP24 ESFP 72% ESTP25 ENFP 59% INTP

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