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Cognitive dissonance is the stress that comes from holding two conflicting thoughts simultaneously in the mind, usually arising when people are asked to choose between two detrimental or two beneficial options. In view of the well-established role of emotions in decision making, here we investigate whether the conventional structural models used to represent the relationships among basic emotions, such as the Circumplex model of affect, can describe the emotions of cognitive dissonance as well. We presented a questionnaire to 34 anonymous participants, where each question described a decision to be made among two conflicting motivations and asked the participants to rate analogically the pleasantness and the intensity of the experienced emotion. We found that the results were compatible with the predictions of the Circumplex model for basic emotions.
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Neural Networks 32 (2012) 57–64
Contents lists available at SciVerse ScienceDirect
Neural Networks
journal homepage:
2012 Special Issue
A structural model of emotions of cognitive dissonances
José F. Fontanari a,, Marie-Claude Bonniot-Cabanac b, Michel Cabanac b, Leonid I. Perlovsky c,d
aInstituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos SP, Brazil
bDepartment of Psychiatry & Neurosciences, Faculty of Medicine, Laval University, Quebec, Canada
cHarvard University, 33 Oxford St, Rm 336, Cambridge MA 02138, United States
dAir Force Research Laboratory, Wright-Patterson Air Force Base, OH, United States
article info
Measure of emotions
Cognitive dissonance
Free-choice paradigm
Circumplex model
Cognitive dissonance is the stress that comes from holding two conflicting thoughts simultaneously in
the mind, usually arising when people are asked to choose between two detrimental or two beneficial
options. In view of the well-established role of emotions in decision making, here we investigate whether
the conventional structural models used to represent the relationships among basic emotions, such as
the Circumplex model of affect, can describe the emotions of cognitive dissonance as well. We presented
a questionnaire to 34 anonymous participants, where each question described a decision to be made
among two conflicting motivations and asked the participants to rate analogically the pleasantness and
the intensity of the experienced emotion. We found that the results were compatible with the predictions
of the Circumplex model for basic emotions.
©2012 Elsevier Ltd. All rights reserved.
1. Introduction
The notion of cognitive dissonance as the unpleasant motiva-
tional state that results from the inconsistency between people’s
behaviors and cognitions was put forward by the Stanford psychol-
ogist Leon Festinger about five decades ago (Festinger, 1957). As
first noted by Festinger, to reduce this dissonance people seek to
rationalize their behaviors by overvaluing their choices and under-
valuing the rejected alternatives.
The recognition that cognitive dissonance plays a key role
in people’s behavior when choosing between alternatives led to
the introduction of the so-called free-choice paradigm (Brehm,
1956): since the selected alternative is unlikely to be perfect,
and the rejected one is likely to have some desirable properties,
making an irreversible choice between them leads to the feeling
of discomfort associated to cognitive dissonance. Interestingly,
the literature on the free-choice problem has focused exclusively
on the post-decision changes in the assessment of the values of
the alternatives, i.e., overvaluing our choices (Brehm,1956;Chen
& Risen, 2010;Festinger,1964;Gerard & White, 1983;Shultz,
Léveillé, & Lepper, 1999), a finding that is closely related to the
basic human bias of overestimating what we own, the so-called
endowment effect (Kahneman, Knetsch, & Thaler, 1991).
Corresponding author. Fax: +55 16 33739877.
E-mail addresses: (J.F. Fontanari), (M.-C. Bonniot-Cabanac), (M. Cabanac),
(L.I. Perlovsky).
In this contribution we begin the exploration of a different
research vein, namely, the characterization of the emotions people
feel at the very moment they are prompted to make a decision
or to choose between two qualitatively different alternatives –
these are the emotions of cognitive dissonances. Of course, the
quantitative characterization of emotions – whether associated to
cognitive dissonances or not – is itself a major research problem
to which there is no consensual solution at the moment (Russell
& Feldman Barrett, 1999). Here we follow Russell’s suggestion
that whenever a measure of emotion is needed one should use
scales of pleasure–displeasure and arousal–sleepiness (Russell,
1989). Accordingly, we have presented a questionnaire containing
10 choice-questions to 34 participants and asked them to rate
the intensity and the hedonicity (pleasantness) of the emotions
elicited by those choices. In a second part of the experiment, we ask
the participants to write a single emotion word that best describes
the nature of the experienced emotion.
The main drawback of our experimental procedure is that
by registering the degrees of arousal and pleasantness only, we
discard a priori other dimensions that may also be important to
characterize the emotions of cognitive dissonance. Nevertheless,
even within this limited scenario we can test whether those
emotions can be described by the Circumplex model of affect,
in which emotions are arranged in a circular form with two
bipolar dimensions interpreted as the degree of pleasure and the
degree of arousal (Cabanac,2002;Russell,1980). In that sense,
emotions mix together in a continuous manner like hues around
the color circle (Russell, 1989). A reorientation and, consequently,
reinterpretation of the axes of the Circumplex model as positive
affect and negative affect has been suggested to correct for the fact
0893-6080/$ – see front matter ©2012 Elsevier Ltd. All rights reserved.
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58 J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64
that there were few emotions in the neutral middle region of the
pleasantness–unpleasantness axis (Watson & Tellegen, 1985).
We found that the measures of arousal Eand pleasantness H
obtained from the questionnaires are not independent quantities,
contrary to the prediction of the Circumplex model. Most
remarkably, however, we found that the axes determined by the
directions of the first and second principal components of the
matrix of data were in fact associated to actual dimensions of
pleasantness and arousal according to the emotion words used by
the participants. In addition, the central region of the (E,H)plane
where the Circumplex model predicts emotions should be absent
is fittingly described by the word indecision by the majority of the
participants. Hence in the context of the experiment reported here
we conclude that our characterization of the emotions of cognitive
dissonance is consistent with the predictions of the Circumplex
The rest of this paper is organized as follows. In Section 2we
describe the procedure used to apply the questionnaires with the
choice questions to the participants. The items of the question-
naires are presented in the Appendix A. In Section 3we present a
statistical study of the answers to the choice questions, emphasiz-
ing the differences due to the gender of the participants. The corre-
spondence between emotion words and the regions in the (E,H)
plane is obtained using a clustering algorithm and the suitability
of the Circumplex model to represent our data is discussed in that
section too. Finally, Section 4summarizes our main conclusions. An
abridged version of the present paper was published in Fontanari,
Bonniot-Cabanac, Cabanac, and Perlovsky (2011).
2. Method
As is previous studies (Balaskó & Cabanac, 1998;Bonniot-
Cabanac & Cabanac, 2009, 2010;Cabanac, Pouliot, & Everett,
1997;Cabanac, Guillaume, Balaskó, & Fleury, 2002;Cabanac &
Bonniot-Cabanac, 2007;Perlovsky, Bonniot-Cabanac, & Cabanac,
2010;Ramírez, Bonniot-Cabanac, & Cabanac, 2005;Ramírez,
Millana, Toldos-Romero, Bonniot-Cabanac, & Cabanac, 2009),
mental experience was explored in interviews where participants
answered printed questionnaires (see also Botti & Iyengar, 2004;
Rachlin, Logue, Gibbon, & Frankel, 1986;Raufaste, da Silva Neves,
& Mariné, 2003). Thirty-four anonymous participants (who were
referred to by numbers only), 17 men (age 49 ±17 yr.) and 17
women (age 50 ±17 yr.) were presented two questionnaires
each containing ten items. Both questionnaires presented the
same items, but the participant was asked to rate experienced
pleasantness or hedonicity (H) from one and intensity (E) from
the other. All items described a decision to be made among two
conflicting motivations and the participant was to rate analogically
the magnitude of her/his experience.
Questionnaire E explored emotion: a horizontal line was
present below the item with a zero mark on its left end. The
participant was to pencil a small vertical mark at that line rating
the intensity of the experienced feeling. The distance from the zero
mark would indicate the magnitude of the experience, denoted
by E. After rating the magnitude of the emotion, the participant
wrote one word describing the nature of the experienced emotion,
e.g., curiosity, surprise, joy, indifference, anger, etc. We were able
to obtain the emotion words from 33 of the 34 participants.
Questionnaire H explored hedonicity: as before, a horizontal
line was present below the item but with a zero on its middle, a
minus () sign at the left end and a plus (+) sign at the right end.
The participant was to pencil a small vertical mark on the right
side of that line if the feeling was pleasant, or on the left side if
unpleasant. The distance from the middle (zero mark) of the line
would indicate the magnitude of the experienced hedonic feeling,
denoted by H.
Thus, the hedonic and magnitude feelings were measured quan-
titatively in millimeters, as well as recorded semantically. In order
to minimize a possible influence of answering one questionnaire
on the response to the other questionnaire, Questionnaires E and H
were presented separately over time spans that varied from about
one hour to half a day, depending on the availability of the partici-
pant; 17 of them received Questionnaire E first, then Questionnaire
H and the other 17 started with Questionnaire H. The first question-
naire was presented in the morning period with the care to keep
the gender of the participants balanced, and the second question-
naire was presented in the afternoon.
The ten items describing decisions to be made covered a
broad range of motivations, from minor decisions in the daily
life (e.g., how about movie or theater for tonight?) to clear but
non-vital problems (e.g., would you go for a high-gain but risky
investment or for a low-gain but secure one?) and finally to vital
problems (e.g., would you go for radical surgery or for life-long
therapy to treat a severe illness?). The ten items are presented in
the Appendix A.
3. Results
Our analysis of the answers to the questionnaire items is
greatly facilitated by the fact that they can be represented in a
two dimensional arousal–pleasantness (E,H)graph. So we begin
our study by presenting a scatter plot showing the raw data
(Section 3.1) and then proceed to a more detailed account of
the gender-dependent distribution of answers for each choice
question (Section 3.2). In Section 3.3 we use a Self-Organizing Map
to reduce the two-dimensional scatter plot representation of the
data to a one-dimensional neural representation. The assignment
of emotion names to each item of the questionnaire allows us to
use those names to tag points in the (E,H)plane and then define
the distances between emotion words as the Euclidean distance
between points in that plane. Given these distances we use a
hierarchical clustering algorithm to partition the emotion names
into 8 categories (Section 3.4). A summary of the main results is
presented in Section 3.5.
3.1. Scatter plot
Our first task is to turn the analogical measures Eand Hinto
dimensionless quantities. Recalling that the degree of arousal E
takes on positive values only and the degree of pleasantness H
takes on positive as well as negative values, we can rescale these
measures by their maximum and minimum values so that E
[0,1]and H[0.5,0.5], without loss of generality. In order to
facilitate the visual inspection of the spread of these quantities in a
two dimensional graph, we have equated the sizes of the domains
of Eand H.
In Fig. 1 we show that two-dimensional graph (scatter plot)
where the symbols indicate the values of the properly rescaled
degrees of arousal Eand pleasantness Hfor the 340 points
associated to the 10 choice questions of the 34 participants, as
described in the previous section. We have separated the answers
– for simplicity we will refer to a coordinate (E,H)as an answer to
a corresponding choice question – according to the gender of the
participants so that the crosses in Fig. 1 represent men’s answers
and the circles, women’s. In particular, the mean degrees of arousal
and pleasantness associated to men’s answers are ¯
(standard deviation σE
m=0.257) and ¯
Hm=0.038 (standard
deviation σH
m=0.245), respectively, whereas for women’s we
find ¯
Ef=0.454 (standard deviation σE
f=0.270) and ¯
0.021 (standard deviation σH
f=0.275). Regardless of gender,
these statistical measures yield ¯
E=0.417 (standard deviation
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J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64 59
Fig. 1. Scatter plot of the degrees of arousal and pleasantness. The crosses indicate
the arousal–pleasantness coordinates obtained from men’s rates and the open
circles from women’s. The horizontal straight line indicates the location of the mean
value ¯
H=0.029, whereas the vertical indicates the location of ¯
Table 1
Mean degree of arousal for men ( ¯
Em), women ¯
Efand gender-independent (¯
E) for the
ten choice questions. The last column shows a sample of the null model.
ENull model
1 0.275 0.314 0.294 0.514
2 0.300 0.470 0.385 0.636
3 0.412 0.581 0.496 0.434
4 0.501 0.545 0.523 0.541
5 0.418 0.497 0.457 0.561
6 0.233 0.407 0.320 0.467
7 0.411 0.393 0.402 0.550
8 0.495 0.597 0.546 0.549
9 0.356 0.273 0.314 0.522
10 0.399 0.461 0.430 0.456
σE=0.260) and ¯
H=0.029 (standard deviation σH=0.260),
which are also presented in the scatter plot of Fig. 1. Interestingly,
in the average, women exhibited a higher degree of arousal but a
lower degree of pleasantness than men. The histograms exhibiting
the distribution of Eand Hvalues were presented in Fontanari
et al. (2011); here we just mention that about 18% of the Hvalues
are very close to its mean value so ¯
His actually the most likely
value of H(visual inspection of the scatter plot confirms this claim),
whereas only about 5% of the values of Eare very close to its
mean ¯
3.2. Characterization of the choice questions answers
In order to better acquaint the readers with the participants
answers to the ten choice questions, we present in Figs. 2 and 3the
degrees of arousal and pleasantness separated by gender for each
question. In addition, Tables 1 and 2exhibit the mean values of
those degrees; the standard deviations can be estimated by visual
inspection of the figures. To appreciate the underlying structure
of the participant answers we compare them with a null model in
which Eand Hare chosen randomly and uniformly in the ranges
[0,1]and [0.5,0.5]. In this case the null model mean degree
of arousal associated to a given item is a sum of 34 independent
random variables uniformly distributed in [0,1]and so it has mean
0.5 and standard deviation 1/34 ×12 0.05. The same is
true for the null model mean degree of pleasantness except that
its mean is zero. Inspection of Tables 1 and 2indicate that for
some items the range of variation of the participants’ answers is
far greater than that predicted by the null model.
A more useful piece of information is the correlation between
the degrees of arousal and pleasantness for each question. This
Fig. 2. The degree of arousal Efor each of the i=1,...,10 choice questions. The
crosses are men’s answers and the open circles, women’s. The filled circles indicate
the mean degree of pleasantness of each question regardless of gender.
Fig. 3. The degree of pleasantness Hfor each of the i=1,...,10 choice questions.
The crosses are men’s answers and the open circles, women’s. The filled circles
indicate the mean degree of arousal of each question regardless of gender.
Table 2
Mean degree of pleasantness for men ( ¯
Hm), women ¯
Hfand gender-independent ( ¯
for the ten choice questions. The last column shows a sample of the null model.
HNull model
1 0.172 0.152 0.162 0.009
2 0.129 0.107 0.118 0.014
3 0.178 0.253 0.215 0.048
4 0.228 0.139 0.183 0.069
50.077 0.121 0.099 0.034
6 0.076 0.158 0.117 0.072
70.043 0.197 0.120 0.043
80.191 0.091 0.141 0.019
90.132 0.086 0.109 0.039
10 0.036 0.108 0.036 0.042
quantity can be calculated by introducing the item-dependent
with i=1,...,10 and is Xi=34
i/34 is an item-
dependent expected value. Hence the measured correlation
coefficient for item iis
Table 3 exhibits these correlations together with a sample of
correlations generated by the null model described before. Of
course, the choice questions have no influence on the correlation
values for the null model.
To facilitate the comparison with the null model we consider
the mean correlation regardless of the choice question, which
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60 J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64
Table 3
Correlation between the degrees of arousal and pleasantness
for each choice question. The third column is a sample of the
null model.
i Cori(E,H)Null model
1 0.393 0.178
2 0.318 0.176
3 0.527 0.247
4 0.209 0.169
50.157 0.278
6 0.559 0.304
70.003 0. 013
8 0.112 0.138
9 0.061 0.067
10 0.009 0.001
is obtained by adding up the correlations in the second column
of Table 3 and dividing the result by the number of items.
We find that the final result Cor (E,H)=0.203 is about four
standard deviations apart from the result predicted by the null
model. More importantly, the finding that this correlation is
significantly different from zero shows that Eand Hare not
independent quantities as assumed in the Circumplex model of
affection. In fact, we recall that Questionnaires E and H were
applied in different periods of the day exactly to minimize the
influence of the answering one questionnaire on the response to
the other questionnaire. Hence the correlation reported here is not
an artifact of the experimental setup. We will return to this point
in Section 3.5.
3.3. The Self-Organizing Map
The main utility of the Self-Organizing Map (SOM) is to visualize
high-dimensional data by mapping them into a low-dimensional
space (usually a two-dimensional space) using a neighborhood
function that preserves the topological properties of the input
space (Kohonen, 2001). However, as we will show next, even in our
case for which the data is two-dimensional already (see Fig. 1) the
use of SOM to reduce it to a one-dimensional space can produce
relevant information to understand the organization of the input
data. The self-organizing map we consider here consists of a chain
of 200 components, which we will call neurons. Associated with
each neuron is a weight vector of the same dimension as the input
data vectors and a position in the (one-dimensional) chain. The
procedure for placing a vector from data space onto the chain is
to find the neuron with the closest weight vector to the vector
taken from data space and to assign the location in the chain of
this neuron to our vector. The goal of learning in the self-organizing
map is to cause different parts of the chain to respond similarly to
certain input patterns.
In Fig. 4 we show the resulting SOM. In particular, for a neuron
located at position n=1,...,200 in the chain we show the
values of degree of arousal and degree of pleasure to which it
responds more strongly. Actually, these neurons are tuned to the
strength (modulus) of the two-dimensional vector whose entries
are Eand H. There are two ways to interpret this figures or a SOM
in general. First, since during training the weights of the whole
neighborhood are moved in the same direction, similar input data
tend to excite adjacent neurons. Hence, SOM forms a semantic map
where similar samples are mapped close together and dissimilar
samples are mapped apart. Second, the neuronal weights may
be thought of as a discrete approximation of the distribution of
training samples. More neurons point to regions with high training
sample concentration and fewer where the samples are rare.
Recalling that the degree of arousal Eis said to be above
average if E>E⟩ = 0.417 whereas an above average degree
of pleasantness is one such that |H|>⟨| H|⟩ = 0.211, we can
Fig. 4. Representation of the input data using a one-dimensional self-organizing
map composed of 200 neurons. The locations nof the neurons in the chain are
shown in the x-axis, whereas the y-axis shows the values of Eand Hto which these
neurons are most sensitive.
begin interpreting the SOM results displayed in Fig. 4. About 25%
of the neurons (n=1,...,50) are sensitive to high, i.e., above
average, arousal and pleasantness degrees indicating that this is a
meaningful feature of the input data. We expect this feature to be
related to positive emotions such as joy, pleasure, enthusiasm and
so on. About 15% of the neurons (n=100,...,130) are sensitive
to high arousal and high displeasure degrees, a region which may
be related to negative emotions such as distress, anger, anguish
and so on. We note that only these two groups of neurons
qualify as pointers to emotions within the requirement that an
emotion must be characterized by both high intensity and high
hedonicity (Cabanac, 2002). However, there are other mental
states, which may not qualify as emotions, but which describe
the subjects feelings when answering the choice questions. For
example, surprise and desire are mental states that can be very
intense but may be neutral regarding the degree of hedonicity.
In fact, about 10% of the neurons (n=70,...,90) seem to be
sensitive to this type of stimulus. There are two small groups of
neurons (n=140,...,160) and (n=190,...,200) which are
somewhat unusual as they respond to data characterized by
practically null arousal degrees but by high degrees of pleasure and
However, as suggested by Vesanto and Alhoniemi (2000), when
the number of SOM units is large, to facilitate quantitative analysis
of the map and the data, similar units need to be grouped,
i.e., clustered. Since our basic input data is two-dimensional we
choose to group the data points of Fig. 1 directly, rather than the
SOM neural representation of the data.
3.4. Emotion names
As pointed out in Section 2, 33 participants described the
emotions they felt at making a choice by a single emotion word.
They used a total of 77 different emotion words for the 330 choice
questions. (See Table 6 for a list of all emotion words used by the
participants.) In Table 4 we present the ten most frequently used
emotion words together with their frequencies. In addition, we
note that 35 emotion words were used only once, and 13 were used
twice. In Fontanari et al. (2011) we have lumped the 77 emotion
words together into 18 classes according to our common sense
intuition of the proximity between those words.
The first issue we need to address is whether the participants
used the 77 emotion words in a coherent way, i.e., whether
different participants used the same emotion word to describe
their emotions for the same choice question. To quantify this
expectation, we will calculate the probability that two randomly
selected participants describe their emotions by the same word
for a same choice question. The desired probability, which we
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J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64 61
Table 4
The ten more frequently used emotion names
together with their frequencies.
Emotion name Frequency
Indifference 48
Joy 25
Interest 22
Pleasure 16
Hope 13
Expectation 13
Desire 11
Anxiety 10
Fear 10
Surprise 9
Table 5
Probability Pithat one selects two participants at random and they
describe the emotions elicited by the choice question iby same
emotion word. The third column is a sample of the null model.
i PiNull model
1 0.0757 0.0445
2 0.0738 0.0568
3 0.0530 0.0321
4 0.0890 0.0246
5 0.0284 0.0587
6 0.1193 0.0321
7 0.0625 0.0662
8 0.0719 0.0416
9 0.0511 0.0454
10 0.0435 0.0340
denote by Pi, can be estimated by counting the number of pairs
of participants (there are 528 pairs in total) who choose the same
emotion word for each choice question i=1,...,10 and then
dividing the result by 528. Table 5 shows these probabilities for
the 10 items together with a realization of a hypothetical situation
in which the participants pick the 77 words with probability
proportional to their frequencies (see Table 4 for the frequencies
of the most used words). The abnormally high value of P6is due to
the fact that 11 participants used the word indifference to describe
their feelings at choosing between a violin and a piano sonata.
A better appreciation of the difference between the data and the
random null model is achieved by considering the probability that
two participants selected at random use the same word to describe
the emotion evoked by the same choice question, regardless of the
question. This probability is Pd=10
i=1Pi/10 =0.0668. For
the purpose of comparison, the same procedure applied to the
probabilities in the third column yields Pr=0.0437. The relevant
question here is whether the value of Pdcould be replicated by
some realization of the random null model. To investigate this
possibility we have generated 106realizations such as that shown
in the third column of Table 5 so as to calculate the mean and the
standard deviation of the probability distribution of Pr. The results
are Pr=0.0425 and σr=0.0025. Hence Pdis about 10 standard
deviations away from Pr, which means we can safely discard the
possibility that the assignment of the emotion words to the choice
questions were random.
The association of emotion words to items of the questionnaires
offers us an opportunity to investigate the underlying organization
of the emotion name categories, a line of research that has
been extremely influential on the quantitative characterization
of emotions in the 1980s (Russell,1980,1989;Shaver, Schwartz,
Kirson, & O’Connor, 1987;Watson & Tellegen, 1985). See,
however, Russell and Feldman Barrett (1999) for a reappraisal of
the conclusions drawn from those studies. An important outcome
of this research avenue was the finding that emotion words are
highly interconnected and so saying that someone is anxious is
not independent of saying that person is happy or sad (Russell,
Table 6
The partition of the 77 emotion names into 8 clusters according to the Wards
minimum variance hierarchical clustering algorithm.
Category Emotion names
I Joy, pleasure, delight, satisfaction, enthusiasm, excitement,
elation, greed, waiting, relaxation, relief, thinking, frustration,
despair, challenge, commitment, curiosity.
II Uneasiness, puzzling, irritation, anxiety, distress, sadness,
indignation, hesitation, disgust, solidarity.
III Fun, indifference, anticipation, rejection, comfort, patience,
nervousness, difficulty, disdain.
IV Displeasure, purpose, wrath, fatalism, weariness, stress, unbelief,
V Well-being, luck, desire, impatience, surprise, hope, nostalgia,
courage, expectation.
VI Discomfort, embarrassment, guilt, anguish, interest, incertitude,
motivation, serenity, safety, concern, fear, doh!, indecision,
swindle, anger, contempt, boredom.
VII Disarray, furor, exasperation.
VIII Uncertainty, disappointment, perplexity, repulsion.
1989). A complementary approach to the structural models of
emotion names categories, such as the Circumplex model, is
the exploration of the hierarchical structure of those categories
(Shaver et al., 1987).
The central element in those studies of emotion names
categories is a distance matrix produced by asking individuals
to rate the similarity between a given set of distinct emotion
words using a fixed discrete scale. See Petrov, Fontanari, and
Perlovsky (2011) for an alternative approach where the distance
is derived from the contexts in which the emotion names are used
in web retrieved texts. Here we take advantage of our experimental
setup described in Section 2to obtain an indirect measure of
the distances between the emotion names used to describe the
participants’ feelings when answering the questionnaires items.
More specifically, for each emotion word we associate a unique
coordinate in the two dimensional space spanned by the arousal
and pleasantness dimensions. In the (typical) case where there are
Kpoints Ek,Hk,k=1,...,Kassociated to the same emotion
word, we associate that word to the mean coordinate K
kHk/K. Hence the distance between any two emotion words
becomes simply the Euclidean distance between points in a plane.
The variance or spread of a set of points (i.e., the sum of
the squared distances from the center) is the key element of
many clustering algorithms (Murtagh & Heck, 1997). In Ward’s
minimum variance method (Ward, 1963) we agglomerate two
distinct clusters into a single cluster such that the within-class
variance of the partition thereby obtained is minimal. Hence the
method proceeds from an initial partition where all objects (77
emotion names, in our case) are isolated clusters and then begin
merging the clusters so as to minimize the variance criterion.
Table 6 shows the resulting partition of the emotion names
into 8 clusters. We note that although these classifications are
overall reasonable there are a few dissonant groupings such as the
lumping together of the words interest and boredom into category
VI. However, as we will argue below the appearance of antagonistic
words in this particular category is somewhat expected since it
describes indecision. As each emotion word in Table 6 corresponds
to a point in the (E,H)plane, it is natural to think of the location
of the abstract categories in that plane as the position of the center
of mass of the component words, which are presented in Table 7.
3.5. Discussion
To conclude our analysis we partition the 340 points in the
scatter plot of Fig. 1 into 8 clusters using Ward’s minimum variance
hierarchical clustering algorithm. Note that, except for the emotion
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62 J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64
Table 7
The center of mass of each emotion name category in the
arousal–pleasantness plane.
Category E H
I 0.57 ±0.08 0.27 ±0.09
II 0.67 ±0.09 0.19 ±0.05
III 0.10 ±0.05 0.01 ±0.1
IV 0.21 ±0.06 0.39 ±0.08
V 0.39 ±0.05 0.16 ±0.03
VI 0.42 ±0.09 0.04 ±0.07
VII 0.78 ±0.05 0.44 ±0.03
VIII 0.50 ±0.06 0.35 ±0.05
Fig. 5. Partition of the 340 arousal–pleasantness coordinate points into 8 clusters
using Ward’s minimum variance hierarchical clustering algorithm. Points belonging
to different clusters are represented by different symbols. The orthogonal straight
lines are the first and second principal components. The Roman numerals indicate
the location of the emotion name categories described in Table 6.
words used only once and so represented by a single point in
the scatter graph, this partition is different from the clustering of
the 77 words into the 8 categories summarized in Table 6. The
resulting partition together with the location of the emotion name
categories given in Table 7 are exhibited in Fig. 5. That figure
together with Table 6 allow us to offer an interpretation for the
8 emotion name categories, namely, I (pleasure), II (uneasiness),
III (indifference), IV (displeasure), V (desire), VI (indecision), VII
(furor), and VIII (disappointment). Of course, although there is
a considerable degree of arbitrariness in the naming of these
categories we have chosen names that are representative of the
majority of the member words of a category.
A few words are in order about Fig. 5 which summarizes the
main results of our analysis of the participants’ answers to the
items of the questionnaires presented in the Appendix A. Category
VI is located at the center of the (E,H)plane and so correspond
to answers which are inconsiderable from both the arousal and
the pleasantness dimensions. In addition, the list of emotion words
used to describe those answers comprehends pairs of antagonistic
words such as discomfort and serenity, and interest and boredom.
Overall there is a well-balanced mixture of positive and negative
emotion words which cancel out and in the average one get neutral
words such as incertitude and indecision which we think provide
a very good description for category VI: it is not associated to
any particular emotion name. This is a most interesting situation
because one of the predictions of the Circumplex model of affect is
exactly an empty region in the center of the (E,H)plane (Russell,
1980,1989). Another interesting point, is that classes I (pleasure)
and IV (displeasure) are diametrically opposed, though not along
the Haxis as one would expect.
As pointed out in Section 3.2, our finding that the measures
Eand Hare correlated, in spite of the experimental effort to
minimize their influences on each other, prompts us to look
for a set of uncorrelated variables to describe the experimental
points of the scatter plot shown in Fig. 1. This is easily achieved
using principal component analysis (PCA) and the results are
exhibited by the orthogonal straight lines in Fig. 5. The first
principal component has the slope 0.876 and the second has the
slope 1.141, so they are really orthogonal; they look distorted
because the figure is not a square. Most interestingly, the principal
component corresponds to the effective dimension of pleasantness
since categories I and IV are roughly located at its opposite
extremes. The interpretation of the second principal component
is more difficult. Categories VII (furor) and II (uneasiness) fall
very close to that axis which seems to represent a decrease in
arousal (furor is more intense than uneasiness) but the lack of
points in the other extreme of this axis prevents a more assertive
In summary, given the PCA reorientation of the axis and the
interpretation of category VI as a ‘non-emotion’ class we found that
our characterization of cognitive dissonance emotions is consistent
with the Circumplex model of affect.
4. Conclusion
Decision-making in situations of conflicting motivations (cog-
nitive dissonance) is a source of emotion, usually described as
a feeling of discomfort that results from holding two conflicting
thoughts simultaneously in the mind. These decisions appear to be
made in the hedonic dimension of consciousness; the hedonic ex-
perience taking place as an actual or an expected reward. In this
paper we made a step toward exploring a new type of emotions,
aesthetic emotions related to knowledge or more specifically, emo-
tions of cognitive dissonance related to contradictions between
two pieces of knowledge. These emotions could in principle be dif-
ferent from basic emotions. Whereas specific words exist to name
basic emotions, there are no specific words for most emotions of
cognitive dissonance. This fact might be a reason that these emo-
tions have not been systematically studied in the psychological
Although the expression ‘cognitive dissonance’ has been used
for a long time (Brehm,1956;Festinger,1957,1964), emotions
of cognitive dissonance have not been recognized as a special
type of emotions different in principle from basic emotions. By
presenting to participants questions as alternative mental choices,
our paper presents the first steps to address the intricate issue
of distinguishing experimentally between aesthetic and basic
On the one hand, it can be argued that there is a fundamental
theoretical difference between basic and aesthetic emotions. Fol-
lowing Grossberg and Levine (1987), basic emotions can be consid-
ered as feelings and mental states related to neural signals, which
indicate to various brain regions satisfaction or dissatisfaction of
fundamental organism needs. Mechanisms measuring these needs
we call instincts. Hence basic emotions are mostly related to bod-
ily needs, whereas aesthetic emotions are related to the need for
knowledge. In addition, Perlovsky (2010) argues that emotions
of cognitive dissonance could be in some way similar to musical
On the other hand, the experimental study reported here failed
to uncover any distinction between basic and cognitive dissonance
emotions; rather we found that the latter can be described
remarkably well by the Circumplex model, which is a structural
model proposed to describe basic emotions (Russell,1980,1989).
It might well be that our experimental setup centered on the record
of the degrees of arousal Eand pleasantness Helicited by the choice
questions is not sensitive enough for the fine distinctions required
to differentiate details of aesthetic emotions. The measurement of
other emotion dimensions in addition to Eand Hmay be necessary
for achieving that fine distinction, if indeed it exists.
Author's personal copy
J.F. Fontanari et al. / Neural Networks 32 (2012) 57–64 63
To conclude, we note that understanding the underlying psy-
chological structure of emotions is germane for the development
of robotic systems capable of exhibiting as well as recogniz-
ing emotion-like responses (Cañamero,2005;Khashman,2010;
Levine,2007;Taylor, Scherer, & Cowie, 2005). In fact, according to
our results and, more generally, in conformity with the predictions
of the Circumplex model of affect (Russell,1980,1989), the com-
bination of two quantities – the degree of arousal Eand the de-
gree of pleasantness H– can explain a large part of the spectrum of
human emotional experience. Hence the design of artificial neural
networks with sensors and estimators for these two quantities may
be an efficient manner to mimic human-like emotion responses in
machines. The neural network models for decision making based
on positive or negative affect directed at objects or potential ac-
tions (Grossberg & Gutowski, 1987;Leven & Levine, 1996) can be
viewed as examples of work in this research direction.
The research at São Carlos was supported by The Southern
Office of Aerospace Research and Development (SOARD), grant
FA9550-10-1-0006, and Conselho Nacional de Desenvolvimento
Científico e Tecnológico (CNPq).
The 10 items of Questionnaire E aiming at measuring the
degree of arousal of the evoked emotion are presented below.
We note that the questions were formulated in French (the
participants were native French speakers), so the following items
are a nonliteral translation of the original items.
1 Focus on what you feel when you are asked to make
the following choice: Do you prefer red or white wine to
accompany duck with orange? Do you feel an emotion at the
idea of this choice? Indicate its intensity on the line below.
0 _________________________ Max
2 Focus on what you feel when you are asked to make the
following choice: Do you prefer cinema or theater? Do you feel
an emotion at the idea of this choice? Indicate its intensity on
the line below.
0 _________________________ Max
3 Focus on what you feel when you are asked to make the
following choice: Do you prefer the sea or the mountain for
the holiday season? Do you feel an emotion at the idea of this
choice? Indicate its intensity on the line below.
0 _________________________ Max
4 Focus on what you feel when you are asked to make the
following choice: Do you prefer to receive a large amount of
money in a single parcel or the same amount in small parcels?
Do you feel an emotion at the idea of this choice? Indicate its
intensity on the line below.
0 _________________________ Max
5 Focus on what you feel when you are asked to make the
following choice: Do you prefer a secure but relatively poorly
paid job or a very well-paid job but at risk of loss of
employment? Do you feel an emotion at the idea of this choice?
Indicate its intensity on the line below.
0 _________________________ Max
6 Focus on what you feel when you are asked to make the
following choice: Do you prefer to hear a violin or a piano
sonata? Do you feel an emotion at the idea of this choice?
Indicate its intensity on the line below.
0 _________________________ Max
7 Focus on what you feel when you are asked to make the
following choice: If your employer requires you to learn
a Scandinavian language, which one would you prefer,
Norwegian or Swedish? Do you feel an emotion at the idea of
this choice? Indicate its intensity on the line below.
0 _________________________ Max
8 Focus on what you feel when you are asked to make the
following choice: In order to treat a serious illness would you
opt for a quick surgery or for a life-long therapy? Do you feel
an emotion at the idea of this choice? Indicate its intensity on
the line below.
0 _________________________ Max
9 Focus on what you feel when you are asked to make the
following choice: Do you prefer a comprehensive but very
expensive insurance or a cheaper one but with many gaps?
Do you feel an emotion at the idea of this choice? Indicate its
intensity on the line below.
0 _________________________ Max
10 Focus on what you feel when you are asked to make the
following choice: Would you vote for a right wing party, which
guarantees citizen’s security, or for a left wing party, which
promotes an egalitarian society? Do you feel an emotion at the
idea of this choice? Indicate its intensity on the line below.
0 _________________________ Max
In order to measure the degree of pleasantness felt by the
participants in making those choices, they were presented the
same ten-questions questionnaire and after reading each item they
were asked to rate their pleasure by penciling a small vertical mark
on the straight line
____________0_____________ +.
Here the - sign indicates a most unpleasant choice and the +
sign a most pleasant one, and the distance from zero is the analog
magnitude rating of hedonicity. This set of questions comprises
Questionnaire H as described in Section 2.
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A mathematical model of perceptual symbol system is developed. This development requires new mathematical methods of dynamic logic (DL), which have overcome limitations of classical artificial intelligence and connectionist approaches. The paper discusses these past limitations, relates them to combinatorial complexity (exponential explosion) of algorithms in the past, and relates it further to the static nature of classical logic. DL is a process-logic; its salient property is evolution of vague representations into crisp. We first consider one aspect of PSS: situation learning from object perceptions. Next DL is related to PSS mechanisms of concepts, simulators, grounding, embodiment, productive-ity, binding, recursion, and to the mechanisms relating embodied-grounded and amodal symbols. We discuss DL capability for modeling cognition on multiple levels of abstraction. PSS is extended toward interaction between cognition and language. Experimental predictions of the theory are discussed. They might influence experimental psychology and impact future theoretical developments in cognitive science, including knowledge representation, and mechanisms of interaction between perception, cognition, and language. All mathematical equations are also discussed conceptually, so mathematical understanding is not required. Experimental evidence for DL and PSS in brain imaging is discussed as well as future research directions.
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This Research examines the relationship between emotion and two musical features, RMS (root mean square) amplitude and average frequency, based on the assumption that there are certain, underlying rules guiding this relationship. I obtained the RMS amplitude of nine different musical recording using a purchased, student version of MATLAB and the average frequencies of those recordings using MATLAB and Wavesurfer. For MATLAB, I wrote and tested several different versions of programs, the final ones being included in this paper. The musical recordings and emotional "ratings" of those recordings were provided by the NIMH Center for the Study of Emotion and Attention at the University of Florida, Gainesville, FL. I then compared the ratings for the "valence", "arousal", and "dominance" dimensions of the recordings to the RMS amplitudes and the average frequency of the recordings as determined by MATLAB and Wavesurfer. After adding trend lines to the charts, it becomes clear that RMS amplitude has some effect on the valence and dominance dimensions; a high value for RMS typically correlated with a higher mean rating for both dimensions. The charts comparing average frequencies from both MATLAB and Wavesurfer showed very few identifiable trends.
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A theoretical structure for multiattribute decision making is presented, based on a dynamical system for interactions in a neural network incorporating affective and rational variables. This enables modeling of problems that elude two prevailing economic decision theories: subjective expected utility theory and prospect theory. The network is unlike some that fit economic data by choosing optimal weights or coefficients within a predetermined mathematical framework. Rather, the framework itself is based on principles used elsewhere to model many other cognitive and behavioral data, in a manner approximating how humans perform behavioral functions. Different, interconnected modules within the network encode 1.(a) attributes of objects among which choices are made,2.(b) object categories,3.(c) and goals of the decision maker. An example is utilized to simulate the actual consumer choice between old and new versions of Coca-Cola. Potential applications are also discussed to market decisions involving negotiations between participants, such as international petroleum traders.