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Abstract

In an increasingly automated world, trust between humans and autonomous systems is critical for successful integration of these systems into our daily lives. In particular, for autonomous systems to work cooperatively with humans, they must be able to sense and respond to the trust of the human. This inherently requires a control-oriented model of dynamic human trust behavior. In this paper, we describe a gray-box modeling approach for a linear third-order model that captures the dynamic variations of human trust in an obstacle detection sensor. The model is parameterized based on data collected from 581 human subjects, and the goodness of fit is approximately 80% for a general population. We also discuss the effect of demographics, such as national culture and gender, on trust behavior by re-parameterizing our model for subpopulations of data. These demographic-based models can be used to help autonomous systems further predict variations in human trust dynamics.
Dynamic Modeling of Trust in Human-Machine Interactions
Kumar Akash, Wan-Lin Hu, Tahira Reid, and Neera Jain
Abstract In an increasingly automated world, trust between
humans and autonomous systems is critical for successful
integration of these systems into our daily lives. In particular,
for autonomous systems to work cooperatively with humans,
they must be able to sense and respond to the trust of the
human. This inherently requires a control-oriented model of
dynamic human trust behavior. In this paper, we describe a
gray-box modeling approach for a linear third-order model
that captures the dynamic variations of human trust in an
obstacle detection sensor. The model is parameterized based
on data collected from 581 human subjects, and the goodness
of fit is approximately 80% for a general population. We also
discuss the effect of demographics, such as national culture and
gender, on trust behavior by re-parameterizing our model for
subpopulations of data. These demographic-based models can
be used to help autonomous systems further predict variations
in human trust dynamics.
I. INTRODUCTION
Motivation and Problem Definition: The prevalence of
autonomous systems facilitates process efficiency in both
complex systems (e.g., aircraft) and devices in daily life (e.g.,
automated teller machines). Among various strategies studied
to optimize automated processes, improving collaboration
between humans and these systems is of great importance.
This is because the benefits of automation may be lost
when a human overrides an automated decision due to a
fundamental lack of trust in a machine [1], [2]. Moreover,
accidents may occur due to mistrust [3]. We aim to design
autonomous systems that sense and respond to the trust levels
of the humans they interact with, thereby resulting in a more
productive relationship between the human and autonomous
system. In order to achieve this goal, we need a model of
dynamic human trust behavior that could be integrated into a
feedback control system for improving the system’s response
to human trust.
The trust between humans is not necessarily the same as
the trust of humans in autonomous systems. Scientists have
adapted elements characterizing trust in social psychology
and have investigated trust in human-machine interactions
(HMI) and human-computer interactions (HCI) [1], [4], [5].
Most research has been focused on examining the signifi-
cance of a specific factor (like gender) between different trust
behaviors [6], [7]. However, defining statistically significant
factors itself is insufficient for incorporating the factors into
*This material is based upon work supported by the National Science
Foundation under Award No. 1548616. Any opinions, findings, and con-
clusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the National Science
Foundation.
School of Mechanical Engineering, Purdue University, West Lafayette,
IN 47906 USA kakash@purdue.edu, hu188@purdue.edu,
tahira@purdue.edu, neerajain@purdue.edu
a control system. Furthermore, to develop a control system
for general HMI usage, there is a need to model human
trust based on human subject study data. The model should
elicit the trust dynamics in all classes of human-machine
collaborations.
Gaps in Literature: In order to derive a dynamic model
of human trust behavior that is suitable for HMI and HCI
contexts, an appropriate experimental design, modeling, and
verification is necessary. There is no experimentally verified
model for describing the comprehensive dynamics of human
trust level in HMI contexts. Existing trust models are either
nonlinear or do not capture the human behavior that is
not based on rationale [8]. They also ignore the influence
of the cumulative effect of past interactions on the present
trust level. Finally, humans have different behaviors that are
influenced by their surroundings and experiences. These are
in turn strongly influenced by demographics of the particular
human. With increasing globalization, autonomous systems
will be deployed in different societies. Therefore, the ability
to model human behavior for different demographics is a
necessity for autonomous systems. There does not exist a
generalized model structure in the present literature that can
be adapted to these variations in human trust behavior.
Contribution: In this paper we propose an experiment
which captures the dynamic changes in human trust, specif-
ically in a HMI context. We establish a generalized linear
time-invariant (LTI) model structure for human trust that is
grounded in existing psychology literature. The simplicity
of the proposed model makes it suitable for integration
with feedback control systems. This will enable autonomous
systems to respond to human trust variations accordingly.
Supported by a large set of human behavioral data, we use
gray-box system identification techniques to estimate the pa-
rameters of the trust model. We further systematically incor-
porate individual demographic factors by re-parameterizing
our generalized model based on national culture and gender.
Outline: This paper is organized as follows. Section II
provides background on trust modeling. The experimental
procedure and behavioral response acquisition from human
subjects are described in Section III. The generalized model
description and methodology for model parameter estimation
are presented in Section IV. Results and discussions are
presented in Section V, followed by concluding statements
in Section VI.
II. BACKGROU ND
Trust in HMI and HCI contexts has been studied ex-
tensively [9], [10]. Broadly speaking, trust in autonomous
systems depends on a number of human, environmental,
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and robot/machine characteristics [11]. Trust itself can be
classified into three categories: dispositional, situational, and
learned [10]. Dispositional trust is based on characteristics
of the human such as culture, gender, age, and personality.
Situational trust consists of those factors that are external to
the human (e.g., task difficulty) and those that are internal to
the human (e.g., domain knowledge) [10]. Learned trust is
based on the accumulation of experiences with autonomous
systems and influences the initial mindset of the human.
During a new dynamic interaction with an autonomous
system, new experiences will be learned that will either
reinforce the prior experiences or update them with new ones.
In this paper, we will establish a human trust model that can
capture learned and dispositional trust characteristics.
A. Studies on Human Trust Modeling
Researchers have modeled human trust based on the
human’s past experiences, which forms an integral part of
learned trust. Jonker and Treur introduced two types of trust
dynamics: trust evolution functions and trust update func-
tions [5]. Trust evolution functions map a sequence of trust
related events (experiences) to a current trust level, while
trust update functions generate the next trust representation
based on a current trust level and a current experience. In
order to verify the proposed trust dynamics, Jonker et al.
conducted follow-up human subject experiments. The results
suggested that the temporal dynamics of trust depend on
positive or negative experiences. However, limited by the
number of trials (10 trials), these studies only induced a
single transition in trust level, making the comprehensive
understanding of trust dynamics inconclusive. Additional
limitations include the fact that this experiment only con-
sidered learned trust factors and the influence of a person’s
trust in an organization or object.
Other researchers have modeled human trust in the context
of HMI. Lee and Moray used a simulated semi-automatic
juice plant environment to characterize the users’ changes
in trust level [4]. The authors observed that performance,
trust, and faults affected the level of trust, and used an
ARMAV (Auto Regressive Moving Average Vector) analysis
to model the input-output relationship of the system. Their
follow-up study further showed automation is used when
trust exceeds self-confidence [12]. These pioneering efforts
demonstrated the effect of situational and learned trust on
the interactions between humans and autonomous systems;
however, the generality of their model was limited due to
a small sample size (i.e., four to five participants in each
group), and the standard deviation of the data used in their
regression model was considerably large.
More recently, researchers have incorporated elements
that are not based on rationale in the human trust model.
Hoogendoorn et al. introduced ‘bias’ into their model to
account for this [8]. They formulated models with biased
experience and/or trust and then validated these models via a
geographical areas classification task. Their result suggested
that biased model is capable of estimating trust more ac-
curately than models without an explicit bias incorporated.
However, their model was nonlinear in trust and experience,
making it less desirable for use in control design.
B. Factors that Influence Trust
Apart from experiences, human trust behavior is also
influenced by demographics including culture and gender.
National culture consists of the values, behaviors, and cus-
toms that exist within the population of a country. One
of the most comprehensive studies of national culture is
Hofstede’s six cultural dimensions which include Uncertainty
Avoidance Index (UAI) [13], [14]. National culture affects
the cognitive processes of building trust, so people from
different cultures are likely to use different mechanisms to
form trust [15] and show particular trust behavioral inten-
tions [16]. Although national culture has a significant effect
on human trust behaviors, little research examines its effects
on trust in automation. Huerta et al. found that Americans
were less likely to trust autonomous (decision-aid) systems
than Mexicans in a fraud investigation scenario [17]. In
one study, Americans’ tendency to trust less in automated
systems was observed in their attitudes towards “auto-pilots”
while compared with Indians [18]. Gender differences in
trust have been studied, particularly in economic contexts [6],
[19], [20]. Although the gender effect on trust in automation
has not been studied as thoroughly as it has been in economic
studies, some studies showed gender differences in HCI and
human-robot interaction (HRI) contexts [7], [21], [22].
In summary, published literature lacks comprehensive
modeling of human trust dynamics. Existing experiments do
not induce continuous and multiple transitions in trust level
over time. Moreover, the influences of demographic factors
on trust behavior have only been discussed in literature, but
not modeled. The effects of different trust factors on dynamic
behavior of human trust remain unexplored. We will address
these key gaps in the following sections.
III. HUMAN SUB JEC T STUDY
The focus of our experimental design is to capture how
autonomous system performance as well as the humans’
demographic background influence trust dynamics in HMI
contexts.
A. Stimuli and Procedures
In this study, participants interacted with a computer-
based simulation in which they were told that they would
be driving a car equipped with an image based obstacle
detection sensor. The sensor would detect obstacles on the
road in front of the car, and the participant would need
to repeatedly evaluate the algorithm report and choose to
either trust or distrust the report based on their experience
with the algorithm. The instructions specifically informed the
participant that the image processing algorithm used in the
sensor was in beta testing.
There were two equally probable stimuli: ‘obstacle de-
tected’ and ‘clear road’. Participants could choose ‘trust’
or ‘distrust’ after which they received feedback of ‘correct’
or ‘incorrect’. The trials were divided into two classes:
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reliable and faulty. In reliable trials, the algorithm accurately
identified the road condition, which was in fact the stimuli.
For the participant, this meant that selecting ‘trust’ would
be marked as ‘correct’ and selecting ‘distrust’ would be
marked as ‘incorrect’. For the faulty trials, there was a 50%
probability that the algorithm incorrectly identified the road
condition. Fig. 1 shows the sequence of events in a single
trial.
Each participant completed four initial practice trials fol-
lowed by 100 trials. The trials were divided into three phases,
called ‘databases’ in the study as shown in Fig. 2. Before
the start of each database, participants took a break of
30 seconds. In database 3, the accuracy of the algorithm
was switched between reliable and faculty according to a
pseudo-random binary sequence (PRBS) in order to excite
all possible dynamics of the participant’s trust responses. The
order of reliable and faulty trials was counterbalanced on a
between group basis in groups 1 and 2 (see Fig. 2).
B. Participants
Five hundred eighty-one participants (340 males, 235
females, and 6 unknown) recruited using Amazon Mechan-
ical Turk [23], ranging in age from 2073 (mean 35.32
and standard deviation 10.84) participated in our study.
The compensation was $0.50 for their participation, and
each participant electronically provided their consent. The
Institutional Review Board at Purdue University approved the
study. We collected participants’ demographic information
via a post-study survey which included information about
their gender along with the country in which they grew up.
The latter is defined as national culture in this study.
IV. MODELING
In this section we discuss how the discrete responses
of human participants were processed. We also present the
generalized trust model that we will later parameterize using
the human participant data.
A. Data Processing
We identified outliers and removed them from the data set
according to the interquartile range (IQR) rule (the 1.5×IQR
rule) [24]. We calculated the first quartile (Q1) and the third
quartile (Q3) for three categories of data: the number of trust
responses, distrust responses, and no responses. As a result,
63 outliers were removed from the dataset out of a total of
581 participants.
We calculated the probability of trust response for each
trial across all subjects in groups 1 and 2. The probabilities
varied from approximately 0.5to 1with 0.5representing
low trust and 1representing high trust. These probabilities
of trust, that varied with the evolution of the scenario,
could be interpreted as the level of trust for the sample
population and hereafter will be referred to as trust level
T(n), where n[1,100] is the trial order. Similarly, We
calculated the probability of reliable performance for each
trial across all subjects in groups 1 and 2. The probabilities
varied from approximately 0.5to 1with 0.5representing
TABLE I
P-VALUE S OBTAI NED FRO M A PAIRE D T-T EST BE TWEE N THE DATASE T OF
AL L PART ICIPA NTS AN D EACH D EM OG RA PH IC B IN
Dataset All US India Female Male
All - 0.0000* 0.0000* 0.0001* 0.0063*
US - 0.0000* 0.3178*0.0000*
India - 0.0000* 0.0000*
Female - 0.0007*
Male -
*p < 0.05; pairs are significantly different
negative experience and 1representing positive experience
and hereafter will be referred to as experience E(n). Thus
we obtain the dynamic variation of trust level T(n)with
experience E(n)for all participants. In order to reduce noise
from the dynamically varying signal, T(n), we used the
Savitzky-Golay filter with order 3 and window of size 5 [25].
The variation of trust level and experience as a function of
trial number is shown in Fig. 3.
We divided the responses of the participants into bins
based on their demographics: two bins based on national
culture (United States (US) versus India) and two bins
based on their gender (male versus female). In order to
determine the differences between the dataset of all par-
ticipants and each of the demographic-specific datasets, or
bins, we conducted paired t-tests between all five datasets.
The results (see Table I) show that the dataset consisting
of all participants is significantly different from each of the
individual demographic bins. This indicates the necessity of
tuning parameters on the basis of demographics. Moreover,
the t-test results indicate a potential coupling effect between
US and female.
In order to decouple the effect of one demographic on
another, e.g., effect of country on gender, the number of
participants from both sections of the former demographic
were equalized for the later demographic. This was done
by randomly choosing a smaller set from the demographic
with a larger sample population. For example, for the female
bin, the number of Indian females and US females were
equalized by selecting a random smaller set of US females
as the number of US females were larger than number of
Indian females in the sample population.
B. Trust Model Description
Most of the previously developed human trust models
observed trust to be directly related to experience. A well-
known model presented in [5] described the change in
trust to be proportional to the difference of experience and
trust. However, in addition to experience, we recognized
the significance of the cumulative perception of trust and
the human’s expectations of the autonomous system in our
pilot studies. Therefore, we adapted Jonker’s model and
introduced two additional states—Cumulative Trust (CT) and
Expectation Bias (BX)—to accommodate the bias in human
behavior due to human’s perception of past trust and their
expectations as shown in (1). The proposed model is a three–
state model as compared to a single–state model in Jonker et
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Your Choice?
(Respond)
TRUST /
DISTRUST
4.0 s
(Feedback)
CORRECT /
INCORRECT
1.3 s
OBSTACLE
DETECTED /
CLEAR ROAD
(Blank Screen)
The Outcome
is...
Detecting
Obstacle (Blank Screen)
1.0 s
0.5 s1.3 s1.0 s0.8 s
1.0 s
Fig. 1. Sequence of events in a single trial. The time length marked on the bottom right corner indicates the time interval that the information appeared
on the screen.
Algorithm Evaluation
Database 1
A (20 trials)
Database 3
A-B-A-B (15-12-15-18 trials)
Database 2
B (20 trials)
Group
1
Group
2
A: reliable trials
B: faulty trials
Database 1
B (20 trials)
Database 3
B-A-B-A (15-12-15-18 trials)
Database 2
A (20 trials)
Fig. 2. Participants were randomly assigned to one of the two groups.
The ordering of the three experimental sections (databases), composed of
reliable and faulty trials, were counterbalanced across groups.
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
(a) Variation of trust level as a function of trial number.
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Experience
(Probability of
reliable performance)
(b) Variation of experience as a function of trial number.
Fig. 3. The trust level and the experience for all participants. Faulty trials
are highlighted in gray, and black lines mark the breaks. Participants showed
trust in reliable trials and distrust in faulty trials.
al. All of the variables and parameters in the model belong
to [0,1] with E(n)as the input and T(n+ 1) as the output
of the model.
T(n+ 1) T(n) = αe[E(n)T(n)] (1a)
+αc[CT(n)T(n)] (1b)
+αb[BX(n)T(n)] (1c)
CT(n+ 1) = [1 γ]CT(n) + γT (n)(1d)
BX(n+ 1) = BX(n)(1e)
In the proposed model (1), change in trust T(n+ 1)
T(n)linearly depends on three terms: E(n)T(n)(1a),
CT(n)T(n)(1b), and BX(n)T(n)(1c), where each
term is bounded between -1 and 1. The difference between
experience E(n)and present trust level T(n),E(n)T(n)
(1a), updates the predicted trust level T(n+ 1), so that
it approaches E(n). If the present experience is less than
present trust level, then E(n)T(n)<0, thereby decreasing
the predicted trust level and vice-versa.
We defined cumulative trust CTas an exponentially
weighted moving average of past trust level as shown in (1d).
Cumulative trust incorporates the learned trust in the model
using a weighted history of past trust levels. A higher value
of the parameter γdiscounts older trust levels faster, and thus
γcan be called the trust discounting factor. The difference
between present cumulative trust CT(n)and present trust
level T(n),CT(n)T(n)(1b), updates the predicted trust
level T(n+ 1), so that it approaches CT(n).
Expectation bias BXaccounts for a human’s expectation
of a particular interaction with an autonomous system. This
is meant to be constant during an interaction, as shown in
(1e), but could change between different interactions. The
difference between expectation bias BX(n)and present trust
level T(n),[BX(n)T(n)] (1c), accounts for the discrep-
ancy between the expectation bias and the actual trust level
of the human; it updates the predicted trust level T(n+ 1)
so that it approaches BX(n). The parameters αe,αc, and αb
determine the weights given to each of the difference terms
in the rate of change of the trust level. We call αe,αc, and αb
the experience rate factor,cumulative rate factor, and bias
rate factor, respectively, as they control the rate by which
each individual difference affects the predicted trust level.
Since the model (1) is linear, it can be represented in state
space form as shown in (2). The state space representation
makes the proposed trust model amenable to design, synthe-
sis, and implementation of simple control architectures.
x(n+ 1) =
(1 α)αcαb
γ(1 γ) 0
0 0 1
x(n) +
αe
0
0
u(n)
y(n) = 100x(n)
(2)
where
x=
T
CT
BX
, u =E, α =αe+αc+αb.
C. Parameter Estimation
In order to identify the optimal parameter set, we imple-
mented nonlinear least squares estimation using the function
nlgreyest in the System Identification Toolbox (version 9.4)
from MATLAB 2016a. We estimated parameters using 1) the
data of all participants and 2) the data in each of the four
demographic bins. Each dataset consisted of data from each
of the three ‘databases’ in both group 1 (in which participants
were initially faced with reliable trials) and group 2 (in which
participants were initially faced with faulty trials). Parameter
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estimation was conducted on multi-batch data by treating
each ‘database’ as a batch because participants were given
short breaks between databases during the experiment.
Finally, it is worth noting that the quality of any data-based
parameter estimation is only as good as the data itself. In the
context of human subject data, no number of samples can
fully represent the human population. In order to calculate
the possible error in parameter estimation caused by the
variation in sample selection, we iterated the estimation 1000
times, with each iteration using a new randomly selected
subset of data representing 90% of the total dataset for all
participants and each demographic bin. The errors caused
by the variation in sample selection for a 95% confidence
interval were less than 2% for all of the parameters (Table
II). Thus, the obtained parameters are robust to variations in
the sample selection.
V. RES ULTS AND DISCUSSIONS
We verified our experimental design and the prediction
model of human trust dynamics by fitting the model structure
for a general population, which included all 581 valid par-
ticipants in our experiment. Fig. 4 shows the experimentally
obtained trust level and the predicted values using the trust
model. The goodness of fit between the data and the model
was calculated using the NRMSE (normalized root mean
square error), and was 83.77% and 76.17% for group 1 and
2, respectively.
A. General Trust Behavior Observations
The study elicited the variation of trust level as expected:
participants showed high trust level (i.e., probability of trust
response) in reliable trials and low trust level in faulty
trials. This was achieved without training participants or
providing them with specific information (e.g., a game rule or
background stories). The dynamics were modeled based on
past behavioral responses and the experience of the human,
and the prediction capability of the model was consistent
irrespective of the initial condition of the system perfor-
mance. In other words, the prediction capability of the model
was consistent for both groups 1 and 2. This implies that
the collaboration between the human and machine was the
most significant factor in temporal variations in trust level.
Therefore, the developed study is effective for modeling
dynamic human trust behavior in HMI contexts.
The proposed study design induced trust dynamics by ma-
nipulating multiple transitions between positive and negative
experiences. We observed that it took approximately eight to
ten trials for participants to establish a new trust level (i.e.,
approach steady state). The trust level still mildly increased
or decreased near the steady state in both reliable and faulty
trials. This finding was contrary to Jonker et al. [26] who
asserted that “after a negative experience an agent will trust
less or the same amount, but never more”. Jonker’s study
was composed of only two sets of five trials, each with one
transition in between, which we found to be less than the
required number of trials to reach a steady state trust level.
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(a) Group 1; Goodness of fit= 83.77%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(b) Group 2; Goodness of fit= 76.17%
Fig. 4. Participants’ trust level (blue dots) and the prediction (red curve)
based on past behavioral responses and the experience of all participants.
Faulty trials are highlighted in gray, and black lines mark the breaks between
databases.
B. Effects of National Culture and Gender
As expected based on the statistical analysis presented
in Table I, different demographic groups show significantly
different trust behavior from one another (p= 0.00 for US vs
India and p= 0.00 for female vs male). We also observe that
demographics such as national culture (Fig. 5) and gender
(Fig. 6) had an effect on the participants’ trust level towards
the obstacle detection sensor in terms of rise time and steady
state value.
Participants from the US trusted the autonomous system
less when they could not determine whether the system was
faulty or reliable in database 3 (see Fig. 5(a) and 5(c)).
This is consistent with the findings that Americans trust
autonomous systems less than Mexicans and Indians [17],
[18]. Furthermore, the rate of change of trust was faster
for Indian participants than US participants, and Indian
participants also reached a higher trust level as compared
to US participants. This agrees with the smaller Uncertainty
Avoidance Index of Indian culture as compared to that of
US culture (40 vs. 46) [27], which indicates that Indians are
more tolerant of imperfection. Considering variations based
on gender, males trusted more than females, especially when
the system did not perform well (see Fig. 6(b) and 6(d)). This
has also been discovered in several studies (e.g., [19], [20]).
On the other hand, females changed their trust level more
rapidly than males.
Based on the differences discussed above, the autonomous
system would be able to interact with humans more ap-
propriately based on customized models tuned to individual
demographics. Table II shows the optimal parameter values
for all participants and each demographic bin. The last two
columns of Table II show the goodness of fit for each
model with their corresponding group 1 and group 2 data.
The goodness of fit for ‘all participants’ was more superior
than that of individual demographic bins. This is due to
the smaller sample size for individual demographics which
resulted in more variations in probabilities.
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1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(a) US Group 1; Goodness of fit= 78.02%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(b) India Group 1; Goodness of fit= 68.99%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(c) US Group 2; Goodness of fit= 64.77%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(d) India Group 2; Goodness of fit= 68.46%
Fig. 5. Participants are grouped by the country where they grew up. Blue
dots are the reported trust level while the red curve is the prediction from
model. Faulty trials are highlighted in gray and black lines mark the breaks
between databases.
Our modeling approach enables us to quantify this dif-
ference using two kinds of parameters—the rate factors
and the discounting factor. Table II summarizes the iden-
tified parameters of the models. While comparing between
countries, the net rate factor α(αe+αc+αb) for Indian
participants is 27.8% larger than that of US participants.
This implies that Indian participants’ trust level increases
or decreases faster than US participants’ trust level after the
system performance changes. Moreover, the trust discounting
factor γis 14.5% larger for US participants, indicating that
US participants value their recent experience and information
more as compared to Indian participants.
Similarly while comparing between genders, the net rate
factor α(αe+αc+αb) for female participants is slightly
larger (4.4%) than that of male participants, resulting in a
slightly faster rate of change of trust for female participants.
Additionally, the trust discounting factor γis larger for
male participants, indicating that male participants value their
recent experience and trust more as compared to female
participants. This finding partially agrees with Haselhuhn et
al. who suggested that women are more likely to restore
trust after a trust violation [28]. However, Haselhuhn et al.
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(a) Female Group 1; Goodness of fit= 69.98%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(b) Male Group 1; Goodness of fit= 73.95%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(c) Female Group 2; Goodness of fit= 65.80%
1 21 41 56 68 83 100
Trial number
0.4
0.6
0.8
1
Trust Level
(Probability of
trust response)
Data
Model
(d) Male Group 2; Goodness of fit= 68.48%
Fig. 6. Participants are grouped by their gender. Blue dots are the reported
trust level while the red curve is the prediction from model. Faulty trials
are highlighted in gray and black lines mark the breaks between databases.
found that womens’ trust decreases less than that of men
as they prefer to maintain interpersonal relationships. This
is contrary to our observations and is possibly due to their
experimental context being different from ours. These results
highlight that the dynamics of human trust behavior in HMI
contexts is different from their interpersonal trust behavior,
thus creating a need for human trust models in HMI contexts.
In summary, we derived a third-order linear model of
human trust dynamics based on an experiment that elicited
trust dynamics among more than 500 human subjects. Our
generalized human trust model can provide an autonomous
system with a mathematical characterization of a human’s
learned trust which is dynamically influenced by the sys-
tem’s performance. Moreover, by knowing the demographic
information of the human, a system can further identify
dispositional trust effects and facilitate the interaction ac-
cordingly. Although the number of input demographic factors
is limited to one in the current model, more demographics
can be incorporated by collecting more behavioral data for
each demographic, e.g., US males. This model can also be
implemented with an online system identification algorithm
in order to update the model in real-time for a given human.
1547
TABLE II
OPT IM AL PAR AM ET ER VAL UE S FO R AL L PART IC IPA NT S AN D EAC H DE MO GR A PH IC B IN
Bin Experience rate Cumulative rate Bias rate Trust discounting Fit percentage Fit percentage
factor αefactor αcfactor αbfactor γGroup 1 Group 2
All 0.1130 ±0.0003 0.1019 ±0.0009 0.1471 ±0.0005 0.1465 ±0.0009 83.80 ±0.04 76.16 ±0.06
US 0.1096 ±0.0004 0.0716 ±0.0005 0.1252 ±0.0008 0.1201 ±0.0009 77.90 ±0.07 64.78 ±0.13
India 0.1148 ±0.0008 0.1273 ±0.0028 0.1494 ±0.0015 0.1049 ±0.0013 68.86 ±0.17 68.43 ±0.12
Female 0.1185 ±0.0007 0.1014 ±0.0015 0.1348 ±0.0013 0.1197 ±0.0024 69.99 ±0.13 65.89 ±0.16
Male 0.1054 ±0.0004 0.0858 ±0.0007 0.1485 ±0.0009 0.1343 ±0.0015 73.94 ±0.12 68.55 ±0.08
VI. CONCLUSION
To attain synergistic interactions between humans and
autonomous systems, it is necessary for autonomous systems
to sense human trust level and respond accordingly. This
requires autonomous systems to be designed using dynamic
models of human trust that capture both learned and disposi-
tional trust factors. In this paper, we described an experiment
to elicit the dynamic change in human trust with respect
to HMI contexts. We established a third-order linear trust
model, grounded in existing psychology literature, which
we then parameterized using human subject data collected
from over 500 participants. In particular, we introduced two
important states, cumulative trust and expectation bias, to
more accurately capture human trust dynamics. The model
elegantly captured the complex dynamics of human trust
behavior and described differences in the trust behavior
among different demographics. In particular, while main-
taining a uniform model structure, we showed statistically
significant differences in the model parameterization for
different demographics.
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