# A Study of Three Influencer Archetypes for the Control of
Opinion Spread in Time-Varying Social Networks

Michael DeBuse and Sean Warnick† †Michael DeBuse and Sean Warnick are with the
Information and Decision Algorithms Laboratories (IDeA Labs), Department of
Computer Science, Brigham Young University, Provo, UT 84602, USA
<EMAIL_ADDRESS>and<EMAIL_ADDRESS>
###### Abstract

In this work we consider the impact of information spread in time-varying
social networks, where agents request to follow other agents with aligned
opinions while dropping ties to neighbors whose posts are too dissimilar to
their own views. Opinion control and rhetorical influence has a very long
history, employing various methods including education, persuasion,
propaganda, marketing, and manipulation through mis-, dis-, and mal-
information. The automation of opinion controllers, however, has only recently
become easily deployable at a wide scale, with the advent of large language
models (LLMs) and generative AI that can translate the quantified commands
from opinion controllers into actual content with the appropriate nuance.
Automated agents in social networks can be deployed for various purposes, such
as breaking up echo chambers, bridging valuable new connections between
agents, or shaping the opinions of a target population—and all of these raise
important ethical concerns that deserve serious attention and thoughtful
discussion and debate. This paper attempts to contribute to this discussion by
considering three archetypal influencing styles observed by human drivers in
these settings, comparing and contrasting the impact of these different
control methods on the opinions of agents in the network. We will demonstrate
the efficacy of current generative AI for generating nuanced content
consistent with the command signal from automatic opinion controllers like
these, and we will report on frameworks for approaching the relevant ethical
considerations.

##  I INTRODUCTION

Social media is a rich platform to share ideas and opinions, debate, argue,
and influence others. The use of automated agents, or bots, in such
environments, however, raises important ethical issues related to the morality
of persuasion.

The study of social interactions and rhetoric has a long history, dating at
least as far as the ancient Greeks [1]. In the twentieth century, quantified
methods for describing social relations were developed with the advent of
sociometry [2], leading to the concept of a social network, Social Network
Analysis (SNA) [3, 4], and network science [5], while an emphasis on dynamics
and control for these systems began with Weiner’s Cybernetics and its
specialization as sociocybernetics [6, 7]. Nevertheless, according to [8, 9],
“The realm of social systems has remained almost untouched by modern control
theory in spite of the tremendous progress in control of complex large-scale
systems.”

Since 2017, when this observation was made, significant advancements have been
made. Leveraging diffusion and epidemic models [10, 11, 12, 13, 14], controls
researchers have modeled the spread of opinions [15, 16]. Meanwhile, other
researchers have focused on foundational models of opinion formation over
static networks [8, 17, 18, 19], eventually leading to models of opinion
dynamics over state-dependent graphs or other time-varying network models [9,
20, 21]. Convergence and stability proofs have borrowed heavily from the
consensus, flocking, and multi-agent systems literature [22, 23, 24, 25, 26],
and changes in these properties in the presence of certain types of agents,
such as stubborn agents [27, 28, 29, 30, 31], has lead to explicit work on
network control [32].

Figure 1: The feedback control of Social Networks using Automated Agents
driven by Opinion Controllers coupled with Large Language Models and other
Generative AI.

This paper builds on the results of these works, as well as many cited by
these and other papers. The contributions of this work include (see Figure 1):

  1. 1.

Section II: Introduction of a novel nonlinear, stochastic Social Network model
for the co-evolution of opinion and graph-topology dynamics,

  2. 2.

Section III: Novel models of archtypical classes of influencer dynamics
observed in social networks as Opinion Controllers (see Figure 3),

  3. 3.

Section IV: Simulation studies of the archtypical controllers from Section III
(see Figures 4, and 5),

  4. 4.

Section V: Demonstration of the use of generative AI technologies for both a)
Opinion Inference, quantifying the opinion reflected by content with respect
to a list of topics and including results from associated validation studies
(see Figure 6), and b) Content Generation, converting the numerical control
signal from the opinion controller into corresponding content that the
Automated Agent can post, using video, images, and/or text—all making the
realization and practical implementation of opinion controllers as Automated
Agents in social networks very easy (see Table I and Figure 7),

  5. 5.

Section VI: A discussion of the ethical issues surrounding social control
theory, including ethical frameworks from related areas for consideration.

##  II Network Model

The social network is represented as graph, $G=(V,E)$ with a set of $n$
vertices, $V$, that represent agents (users on the network) and a set, $E$, of
ordered pairs of vertices representing directed edges, $E=\\{(v_{i},v_{j})|$
$v_{i},v_{j}\in V$}. This structure can be effectively represented by an
adjacency matrix $A$, where entry $a_{ij}=1$ if $(v_{j},v_{i})\in E$ and
$a_{ij}=0$ otherwise.

We will consider time-varying networks, with a fixed number of vertices,
representing agents or users of the social media platform, but where edges may
appear or disappear as represented by $A_{[k]}$, $k=0,1,2,...$. Moreover, we
will assume $A_{[k]}$ is symmetric for all $k$, suggesting that if one agent
“follows” another on the social media platform, then the second agent will
reciprocate by also following the first; edges thus denote a “connection”
between vertices. Because of this symmetry, $G$ will always be undirected, as
in Figure 4.

Associated with each agent (i.e. vertex) is a vector of opinions on $m$
distinct topics, represented by an opinion matrix
$X_{[k]}\in\mathbb{R}^{n\times m}$ with entries $0\leq x_{ij[k]}\leq 1$
indicating the degree of support agent $i$ feels towards topic $j$ at time
$k$. The $i^{th}$ row of $X_{[k]}$ is indicated by $x_{i[k]}^{\top}$, where
$x_{i[k]}\in\mathbb{R}^{m}$, and the $j^{th}$ column of $X_{[k]}$ is indicated
by $x_{j[k]}\in\mathbb{R}^{n}$.

To model opinion dynamics on the network, we will use a variation of the
state-dependent French-DeGroot model [8, 9] given by:

$X_{[k+1]}=W(X_{[k]},A_{[k]})X_{[k]}$ (1)

where $W(X_{[k]},A_{[k]})\in\mathbb{R}^{n\times m}$ is a row-stochastic
weighting matrix that depends on both the evolving network opinions,
$X_{[k]}$, and the evolving topology of the social network, $A_{[k]}$.

The novelty of this model comes from the way $W$ is calculated and the way the
graph topology, $A_{[k]}$ co-evolves with agent opinions, $X_{[k]}$. We will
first describe the calculation of $W$, and then give the update equation for
$A_{[k+1]}$.

###### Definition 1

Let $\epsilon>0$ be a vanishingly small number; diag($v$) be a square,
diagonal matrix with the entries of the vector $v$ on the diagonal; and
$\mathbb{1}$ be the (appropriately sized) vector of ones. Then the row-
normalization operator of a matrix $M$, ${\cal R}(M)$, is given by:

${\cal R}(M):={\rm diag}(M{\mathbb{1}}+\epsilon{\mathbb{1}}))^{-1}M$

###### Definition 2

The row-wise difference matrix of a matrix $M$ is a square, symmetric, non-
negative, hollow, row-stochastic matrix $D_{N}$ characterized by:

$D_{N}(M):={\cal R}(D(M)),$

where $D(M)$ is a matrix with entries given by:

$d_{ij}(M)=\|m_{i}^{\top}-m_{j}^{\top}\|_{1}.$

###### Definition 3

With $\mathbb{1}$ and $I$ being the appropriately sized matrix of ones and
identity matrix, respectively, the row-wise similarity matrix of a matrix $M$
is a square, symmetric, non-negative, hollow, row-stochastic matrix $S_{N}$
characterized by:

$S_{N}(M):={\cal R}({\mathbb{1}}-(I+D_{N}(M)))$

With these definitions, and noting that here $\mathbb{1}$ and $I$ are the
appropriately sized vector of ones and identity matrix, respectively, and
$M_{1}\circ M_{2}$ is the element-wise, or Hadamard, multiplication of two
appropriately sized matrices, $W$ can now be characterized:

$W(X_{[k]},A_{[k]}):=S_{N}(X_{[k]})\circ A_{[k]}+\left(I-{\rm
diag}([S_{N}(X_{[k]})\circ A_{[k]}]{\mathbb{1}})\right).$ (2)

This expression can be understood as zeroing out the entries in the similarity
matrix $S_{N}(X_{[k]})$ by element-wise multiplication with $A_{[k]}$, and
then adding the appropriate value to the diagonal (the new vector of row-sums
is now given by $[S_{N}(X_{[k]})\circ A_{[k]}]{\mathbb{1}})$, so the result
becomes row-stochastic.

With $W$ defined, the meaning of the dynamics in (1) can be better understood.
The $i^{th}$ agent’s new opinion on topic $j$ is the convex combination of
agent $i$’s neighbors’ opinions on the topic, and its own, where more weight
is given to neighbors with opinions that align better with those of agent $i$
over all topics. That is to say, in this model, agents are more receptive to
the opinions of those who’s overall opinion profile mirrors their own,
reinforcing each other’s point of view. Also, agents with lots of connections
will tend to be more influenced by their (many) friends, while those with
fewer connections will put more stock in their own ideas.

Natural Formation of Echo Chambers

Figure 2: The nonlinear, stochastic Social Network Model in (1) and (4)
results in strong homophily, where agents congregate with those of similar
opinions and reject differing opinions.

Besides the dynamics in (1), which describe the evolution of a vector of
opinions associated with each vertex, or agent, in the social network, our
network model also considers the co-evolution of edges, or connections, among
agents in the social network graph. Like other bounded confidence models [8,
9], we describe a situation where agents are insensitive to the opinions of
other agents with sufficiently different opinion profiles. While other models
explicitly define a threshold characterizing the degree to which opinions
between agents can differ while remaining connected, our notion is stochastic,
where connections are randomly sampled from an evolving probability
distribution.

In particular, we consider the matrix:

$\hat{S}_{[k]}:={\cal R}(S_{N}^{\circ\theta}(X_{[k]}))$ (3)

where $\theta\in\mathbb{Z}^{+}$ is a positive integer modeling parameter, and
the notation $M^{\circ\theta}$ describes the operation of raising each element
of a matrix $M$ to the $\theta^{th}$ power (or Hadamard multiplying the matix
M $\theta$ times, $M\circ M\circ\dots\circ M$). Raising the entries in a
stochastic matrix to a positive power $\theta$ and then renormalizing has the
effect of driving the larger entries closer to $1$ and zeroing out the smaller
entries, making the distinctions between values more extreme. $A$ then evolves
as:

$a_{ij[k+1]}=a_{ji[k+1]}=\begin{cases}1,&\text{if }\gamma\sim
U_{\\{0,1\\}}<\text{max}(\hat{s}_{ij[k]},\epsilon)\\\ &\text{and }i\neq j\\\
0,&\text{otherwise}\end{cases}$ (4)

where $\gamma$ is a sample from $U_{\\{0,1\\}}$, the uniform distribution on
the unit interval, and $\epsilon<<1$ is a modeling parameter establishing the
minimum probability for edge formation. Note that because $\hat{S}_{[k]}$ is a
stochastic matrix, its entries are non-negative and bounded by $1$, so edge
formation occurs by randomly sampling the uniform distribution and checking to
see if the sample is less than the associated entry in $\hat{S}_{[k]}$—or
$\epsilon$ (in case the associated entry in $\hat{S}_{[k]}$ has become very
small or zero, $\epsilon$ ensures that there is always some chance of edge
formation, as occasionally agents may form connections in spite of strong
differences of opinion). The dynamics in (1) and (4) thus describe our
nonlinear, stochastic model of opinion formation and connection co-evolution,
respectively.

Figure 3: Tree showing the relationships between the three controller
archetypes: Popular, Stubborn, and Strategic. The Hadamard power value,
$\rho$, creates a spectrum of behaviors for the popular and strategic agent
archetypes.

##  III Three Controller Archetypes

The model illustrated in Section II provides a network composed of one
specific type of a user on social media (i.e. the standard agent), one who
desires to connect with those agents who are most similar. To better
understand how influential bodies drive opinions in social networks, we
present three controller archetypes modeled off inluencer behaviors seen in
real life social networks that attempt to drive opinions of the network agents
in different ways:

  * •

Stubborn Agent: Attempts to move the distribution of opinions towards its own
opinion value by refusing to alter its opinion.

  * •

Popular Agent: Attempts to shape the distribution of opinions, choosing what
opinions should become popular.

  * •

Strategic Agent: Attempts to move the distribution of opinions towards a goal
opinion by persuading those furthest from the goal towards the goal.

The stubborn agent is included as a standard controller for comparison due to
its use in many opinion spread studies. Our strategic and popular agents make
use of Hadamard powers in determining where to set their opinions each time-
step (see Sections III-B and III-C). The selection of the Hadamard power
value, $\rho$, creates a spectrum of behaviors for those two archetypes.
Figure 3 shows a tree representing the relationships between the three
controller archetypes. The following subsections provide detailed explanations
of each.

Within the subsections for each controller, we do not provide proofs of
stability or convergence. As A. Proskurnikov and R. Tempo explain in section
5.3 of [9] when talking about HK and DW models (of which ours can be seen as a
relative):

> “In spite of many numerical results and experimental observations, dealing
> with the behavior of the… model and its modifications over complex networks,
> the compound of randomness and nonlinear dynamics makes these models very
> hard for mathematical investigation.”

Proofs of this nature for networks and controllers like what we present in
this paper are often long and complex. Due to the limited space, we leave our
proofs of convergence and stability for subsequent work.

###  III-A Stubborn Agent

The goal of the stubborn agent is to move the opinions of the network towards
its own opinion. It does this by retaining its opinion each time-step. In this
way, whenever an edge is created between it and another agent, the stubborn
agent’s opinion becomes part of the convex combination that determines that
agent’s opinion in the next time-step. The stubborn agent, however, is not
influenced by that other agent. It acts as in immutable input signal into the
network.

The update steps for the stubborn agent differ slightly from the standard
agent. In Equation 2, we set its row in $W(X_{[k]},A_{[k]})$ to zeros and its
diagonal element to one. This results in its row in the weight matrix having
full weighting to itself and none to any other agent. Or in other words, when
we calculate $W_{[k+1]}$ in Equation 1,
$x_{stubborn[k+1]}^{\top}=x_{stubborn[k]}^{\top}$.

###  III-B Popular Agent

The popular agent does not have an opinion of its own but instead chooses
which opinions among its neighbors it should propagate. To do this, it bases
its opinion completely on its neighbors, weighted according to the similarity
of each neighbor’s opinion to every other neighbor’s opinion.

###### Definition 4

Let $i$ be the row index of the popular agent in the adjacency matrix, $A$.
The set of neighbor indices, $\mathcal{N}^{i}$, is given by:

$\mathcal{N}^{i}:=\\{j\in V\;|\;a_{ij}=1\\},a_{ij}\in A$

###### Definition 5

The $j^{th}$ element of the neighbor distance vector, $d^{i}_{[k]}$, for
agent, $i$, at time, $k$, and its corresponding neighbor weight vector,
$\mathbf{{\omega}}_{[k]}$, are given by:

$\begin{array}[]{rcl}d^{i}_{j[k]}:=\sum_{l\in\mathcal{N}^{i},l\neq
j}||x^{\top}_{l}-x^{\top}_{j}||,&{\rm and}&\mathbf{{\omega}}_{[k]}:={\cal
R}(d^{i\top}_{[k]}).\end{array}$

The resulting stochastic weight vector, $\mathbf{{\omega}}_{[k]}$, contains
weights for each neighbor of the popular agent based on the difference of
opinion of each neighbor from every other neighbor. The more similar to all
other neighbor opinions, the lower the weight value. The more different, the
larger the weight value.

###### Definition 6

The emphasized neighbor weight vector increases the popular agent’s emphasis
on the level of similarity of the opinions by taking the $\rho$th Hadamard
power of $\omega_{[k]}$ and re-normalizing:

${\hat{\omega}}_{[k]}:={\cal R}({\omega}^{\circ\rho}_{[k]})$ (5)

###### Definition 7

$X^{i}_{[k]}$ is the sub-matrix of $X_{[k]}$ that only contains rows
corresponding to popular agent, $i$.

With these definitions, the opinion update of the $i^{th}$ row of $X_{[k]}$
represented by the popular agent is given by:

$x_{i[k+1]}=\hat{\omega}_{[k]}X^{i}_{[k]}$ (6)

The resulting opinion of the popular agent will not necessarily be the average
of the neighboring opinions, but instead will be shifted either towards those
opinions that are most popular among its neighbors or those that are fringe
opinions among its neighbors, depending on the value of $\rho$ in the Hadamard
power of Equation 5.

###### Fact 1

As $\rho\rightarrow-\infty$, $x_{[k+1]}$, the opinion of the popular agent at
time-step $k+1$, will become the average of those agents with maximum opinion
similarity to all other neighboring agents at time $k$.

###### Fact 2

As $\rho\rightarrow 0$, $x_{[k+1]}$, the opinion of the popular agent at time-
step $k+1$, will become the average opinion of all neighboring agents at time
$k$.

###### Fact 3

As $\rho\rightarrow\infty$, $x_{[k+1]}$, the opinion of the popular agent at
time-step $k+1$, will become the average of those agents with minimum opinion
similarity to all other neighboring agents at time $k$.

The proofs of Facts 1–3 are trivial and stem directly from the behaviors of
renormalized Hadamard powers of stochastic matrices explained just before
Equation 4. These three facts mean that by selecting values for $\rho$, we can
determine how the popular agent views the collective opinions of its
neighbors. By having a large, positive $\rho$, the popular agent attempts to
drive the collective opinions of its neighbors towards the fringe opinions, or
in other words it tries to make those fringe opinions more popular, giving it
the title, “Popularizer.” By making $\rho$ large and negative, the popular
agent attempts to drive opinions to strengthen the collectively most popular
opinion, giving it the title, “People Pleaser.” At zero, the popular agent
tries to drive opinions towards the average of its neighbors, giving it the
title, “Conciliator.”

###  III-C Strategic Agent

The purpose of the strategic agent is to direct the network towards some goal
opinion by basing its opinion off its neighbors and coaxing them towards the
goal.

###### Definition 8

Let $i$ be the row index of the strategic agent and $g^{i}$ be the goal
opinion of the strategic agent. Using Definition 5 Section III-B to define a
neighbor set, the neighbor distance vector for the strategic agent at time,
$k$, is given by:

$d_{j[k]}:=||x^{i\top}_{j[k]}-g^{i}||\text{ for }j\in\mathcal{N}^{i}$ (7)

where $x^{\top}_{j[k]}$ denotes the $j^{th}$ row of $X_{[k]}$.

Since we do not know what the resulting distances will be at any time-step, we
cannot arbitrarily choose a set weighting for the goal opinion for the convex
combination. Instead, we append to the bottom of $d$ the minimum value of $d$,
meaning that the weighting of the goal opinion will be the same as the closest
of the neighbors to it after normalization. We can now use second half of
Definition 5 to normalize by the vector sum to get the weight vector,
$\mathbf{\omega}_{[k]}$.

Using Equation 5 from Section III-B, we can increase $\rho$ to further weight
towards the most distant opinion and away from the goal opinion whose weight
matches the minimal element of $\mathbf{\omega}_{[k]}$. We once again defin
$X^{i}_{[k]}$ as the sub-matrix of $X_{[k]}$ according to Definition 7. We
transpose and append the goal opinion, $g^{i}$, at the bottom row of
$X^{i}_{[k]}$ so that the matrix dimensions for both $X^{i}_{[k]}$ and
$\mathbf{\hat{\omega}}_{[k]}$ are compatible in Equation 6. We can now use
that same opinion matrix update function to update the opinions of the
strategic agents in $X_{[k+1]}$. So long as $\rho\neq\infty$, each convex
combination will include influence from $g^{i}$, nudging standard agents
towards the goal opinion.

Initial Network

(a) Colored Opinions

(b) Node Degree

Figure 4: Initial random network of 50 standard agents used for controller
archetype experiments. Each agent has 3 opinions, and $\theta=7$ in Equation 3
for edge connectivity. Average opinions once stable are $[0.48,0.44,0.52]$.

Results of Controller Archetype Simulations

(a) Resulting average RGB opinion values for different numbers of “people
pleasers” and “popularizers.”

(b) Effects of different Hadamard powers for the strategic agent with goal
opinion of $[0,0,0]$.

(c) The comparison between strategic and stubborn agents with target opinion
of $[0,0,0]$ given different minimum edge probabilities.

Figure 5: Overview of simulations demonstrating the influence of various
agents in opinion dynamics. Each figure represents a unique setup and outcome,
illustrating the complex interplay between different agent strategies and
their effects on opinion distribution within a network. The results of Figure
5(a) are explained in Section IV-A, Section IV-B for Figure 5(b), and Section
IV-C for Figure 5(c).

##  IV Experiments and Results

Figure 4 shows the initial 50 agent network used for all proceeding
experiments. We set $m=3$ (three opinions) so that we can visualize opinions
by assigning each opinion to a respective RGB value. For edge connectivity, we
set $\theta=7$ in Equation 3 so that as time progresses, agents isolate from
each other into groups of similar opinions (echo chambers). The average RGB
opinions of this network once stability is reached are $[0.48,0.44,0.52]$. The
most common opinions of this network are a high-blue and low-green. The
following experiments and tests are to see how each controller archetype
changes the resulting final average opinion values of the network.

###  IV-A Popular Agent Spectrum

We envision popular agents as any number of influencer accounts that standard
agents may choose to follow. The popular agents then base their opinions on
their followers and act as independent input signals into the system (no edges
to each other). We conduct three experiment sets. First, we run until network
stabilization without popular agent influence as a control comparison. Next,
we set the Hadamard power, $\rho=-10$, in Equation 5 of Section III-B to
propagate the dominant opinions of the network (“people pleaser”). Lastly, we
set $\rho=10$ to increase the influence of the fringe opinions of the network
(“popularizer”). For the second and third experiment sets, we run simulations
for 180 time-steps using 1, 2, 5, 10, and 50 popular agents with the same
$\rho$ value.

Figure 5(a) shows the resulting average RGB opinion values. As expected, the
“people pleasers” increase the blue opinion while decreasing the green opinion
and eventually the red, although the influence of the people pleasers is
minimal when there are few of them. The “popularizers,” however, show a
stronger influence on the opinions of the network even when only one popular
agent is present. With only five popularizers, the formerly unpopular opinion
of a high-green becomes dominant over a high-blue opinion. However, once
enough popularizers are present, the high-blue opinion eventually becomes
fringe enough that some of them take that stance and propagate it through the
network, which is why we see an increase in blue opinion at fifty
popularizers.

###  IV-B Strategic Agent Spectrum

To explore the impact of the strategic agent spectrum on network opinions, we
set a strategic agent’s goal to $[0,0,0]$ and conducted eleven experiments
with Hadamard power values from $-100$ (heavy-handed) to $100$ (gentle
approach), as depicted in Figure 5(b). A heavy-handed strategy aligns the
strategic agent’s opinion closely with its goal, impacting connectivity with
distant standard agents by increasing the likelihood of losing connections.
Conversely, a gentle approach aligns the strategic agent’s opinion more
closely with distant agents, diminishing the goal’s influence. These
experiments, after 180 iterations, reveal that a heavy-handed approach lowers
RGB values, moving them closer to zero, but at $\rho=2$ and $\rho=5$, the blue
opinion significantly drops. The gentle approach balance at $\rho=2$ and $5$
enables the strategic agent to maintain connections effectively while exerting
enough influence towards the goal opinion.

###  IV-C Strategic Agent Versus Stubborn Agent

Both strategic and stubborn agents move the network’s opinion distribution
toward a target opinion—stubborn agents aim for their own opinion, while
strategic agents target a predefined goal without directly adopting it. Given
the network’s dynamic nature, an edge from a standard agent to a strategic or
stubborn agent is not always present. The strategic agent’s tactic of
adjusting its opinion based on acquired neighbors is crucial for influencing
the network’s opinions through enhancing the likelihood of maintaining
connections once established. To compare these two agents, we test various
edge creation probabilities, $\epsilon$, in Equation 4, over 3500 time-steps
with either a stubborn or strategic agent in the network, both targeting
$[0,0,0]$. The strategic agent’s $\rho$ is set to 2, following outcomes from
Section IV-B.

Figure 5(c) shows the resulting average RGB opinion values for both stubborn
and strategic agents with minimum edge probabilities of zero, 0.001, and 0.01.
At zero, the opinion of $[0,0,0]$ eventually becomes the furthest from any
regular agent, and after applying the Hadamard power and normalizing before
Equation 2, the weight of influence becomes effectively zero. When a minimum
edge probability of 0.001 is used, the strategic agent can gain followers,
adopt opinions similar to theirs, and retain edges, outperforming the stubborn
agent. The stubborn agent’s opinion remains starkly different and must rely
solely on the minimum edge probability to facilitate influence. At an edge
probability of 0.01, the stubborn agent is comparable to the strategic agent,
though still at a slight disadvantage. Overall, the strategic agent has an
advantage in moving the opinions of agents in the network towards its target
when the probability is low but not zero due to its ability to adopt opinions
similar to the standard agents in the network.

Experimental Results for Opinion Inference

Figure 6: Rankings by human annotators (Orange) and GPT-4 (Blue) of 25 social
media posts about Religion, Science, and Sports on a scale from zero (oppose)
to one (support). Variance is low when ranking opinions with strong language
supporting a topic, but both humans and GPT-4 have some difficulty with
negative language due to some posts with sarcasm, which were included in the
study. Posts with neutral opinions or without reference to a topic were nearly
universally identifiable by both humans and GPT-4.

##  V Generative AI Makes Implementation of Opinion Controllers Easy

In this section, we investigate how an automated agent can drive opinions in
social networks, not as a how-to demonstration but to emphasize that now is
the time to think of the ethics and real-life implications of opinion and
social control research in control theory. We begin by first showing than an
LLM can act as an opinion inference engine for social media posts, and then we
show that generative AI can create content based on a provided opinion vector.
The feedback control relationship can be seen in Figure 1.

###  V-A Opinion Inference Engine

For the first experiment, we gathered from Facebook, Twitter, and Reddit 25
social media posts on three topics of religion, science, and sports, and
included posts that were not on any of those topics as a control. We had
twelve human volunteers annotate the opinion vectors for each individual
opinion topic. We then had six independent instances of GPT-4 [33] output its
inference on the opinion vectors in $\mathbb{R}^{3}$. Figure 6 shows the
variance for the human annotators (orange) and GPT-4 (blue). We see a general
correlation between opinion assessments, but where the variance is low in
posts with strong supportive language on a topic, there is some disagreement
in strong negative language due to sarcasm (some sarcastic posts were included
in the data). Neutral stances on topics and posts that were not on any of the
three topics were nearly universally identifiable by both humans and GPT-4.
After averaging the opinion rankings for the human and GPT-4 assessments, we
find that the difference in opinions on average was 0.023 for religion, 0.177
for science, and 0.11 for sports. These results show that the ability of GPT-4
to assess opinion vectors of social media posts is fairly similar to human
assessments, though not equal. The capability of GPT-4 to take in image data
means these results may extend to interpretation of image content as well. For
example, GPT-4 properly identified the opinion values of the images in Figure
7.

Memes on Taking Action Against Climate Change

(a) Opinion Value 1.0 (Support)

(b) Opinion Value 0.1 (Oppose)

Figure 7: Memes generated by Dalle-3 (left) and Midjourney V6 (right). Notice slight errors in the text spelling and spacing, but, nevertheless, these demonstrate that there are multiple tools available to automate effective meme generation responding to a numerical scale on an issue. TABLE I: Chat-GPT Generated Media Post Given Controller-Generated Opinion Value Opinion Value |  Social Media Bot Posts About Taking Action on Climate Change
---|---
1.0 (Support) |  I simply cannot fathom why anyone would oppose the fact that climate change is real. Ignoring this issue is not an option. We need to come together as a global community to address this challenge head-on by reducing our carbon footprint, investing in renewable energy, and advocating for policies that protect our planet for future generations.
0.7 |  We have a responsibility to take care of our planet and ensure that it remains habitable for future generations. Despite the challenges we face, I’m optimistic about the steps we can take to address climate change. Renewable energy sources like wind and solar power are becoming more affordable and accessible every day, and innovative technologies are helping us to reduce our carbon footprint and conserve resources.
0.5 (Neutral) |  Climate change is a complex and often controversial issue, with arguments for and against its existence and significance. On the one hand, there is a wealth of scientific evidence that suggests that human activities are a major contributing factor. There are those who dispute these findings and contend that efforts to address climate change may be too costly or difficult to implement, and that more research is needed before we can take action.
0.3 |  I also think that some of the proposed solutions to address climate change may be unrealistic or unfeasible, particularly for those who live in developing countries or who rely on certain industries for their livelihoods. While I believe in taking care of our planet, I think we need to balance this with practical considerations and not make hasty decisions that could have unintended consequences.
0.1 (Oppose) |  I simply cannot stand the constant fearmongering and doom-and-gloom surrounding the topic of climate change. I think that the push for climate change solutions often overlooks the economic and social costs of these policies. It’s not as simple as just “going green” — there are real trade-offs and sacrifices that would need to be made, and I don’t think it’s fair to expect everyday people to bear the brunt of these changes.

###  V-B AI Generation from Opinion Vectors

To show that generative AI can create posts based on opinion vectors, we
provided GPT-4 with the topic of “taking action on climate change” and had it
create short posts following opinion values from 0.1 to 1.0. Table I shows the
posts generated by Chat-GPT, revealing the subtle nuances in stances toward
climate change action even between similar opinion values. Although current
image generation AI do not have the full capability of simply taking in an
opinion vector and topic, interpret it, and then generate a resulting image
following that opinion, we can use LLMs like GPT-4 to generate an image prompt
for image AI like Dalle-3 and Mdjourney V6. Figure 7 shows two examples of
memes generate by Dalle-3 (left) for support and Midjourney V6 (right) for
opposition against climate change action. With the vast improvements in video
generation as seen in OpenAI’s Sora [34], it will not be long before video
content can be generated in the same manner.

##  VI  Ethical Considerations

Although previous work on opinion control may have considered the idea in the
abstract, this paper demonstrates how easy it now is to implement such
controllers on real social media networks using current generative AI
technologies. This widespread access to systematic methods for mass
manipulation highlights the urgent need for discussions on the morality of
applying control methods to people and the development of corresponding
ethical principles.

Certainly there are many uses for automated agents in social media networks
that would seem to contribute to the common good, such as compensating for
levels of homophily that may appear to be unhealthy, or making introductions
between agents with common interests. Nevertheless, the same control methods
that enable these capabilities can just as easily contribute to real social
harm [35, 36, 37].

This isn’t the first time the scientific community has conducted research or
developed technologies with the potential for real social harm, however, so
there are frameworks we can use for considering the ethical implications. For
example, the Belmont Report [38] offered critical guidance for biomedical
research in 1978, and the Menlo Report [39] offered similar principles for
research on information and communications technologies in 2012:

  1. 1.

Respect for Persons, including Informed Consent,

  2. 2.

Beneficience,

  3. 3.

Justice, and

  4. 4.

Respect for Law and Public Interest, including Transparency

Kevin Macnish and Jeroen van der Ham have more recently modified the Menlo
Report [40], with a special focus on cybersecurity research that includes a
section looking beyond research activities to explore the ethics of
cybersecurity development in industrial contexts. This application closely
parallels questions surrounding the ethics of publishing effective opinion or
social control techniques since such techniques are both research and, as
demonstrated here, nearly immediately deployable in practice using widely
available generative AI.

The Association for Computing Machinery (ACM), however, developed a framework
in 2022 even more applicable to social control than cybersecurity in their
“Statement on Principles for Responsible Algorithmic Systems” [41]:

  1. 1.

Legitimacy and Competency,

  2. 2.

Minimizing Harm,

  3. 3.

Security and Privacy,

  4. 4.

Transparency,

  5. 5.

Interpretability and Explainability,

  6. 6.

Maintainability,

  7. 7.

Contestability and Auditability,

  8. 8.

Accountability and Responsibility,

  9. 9.

Limiting Environmental Impacts

These principles correspond strongly to those from [39] and refined in [40],
but add new refinements such as interpretability/explainability and
contestability/auditability.

Since then, various organizations have worked on further refinements in the
context of ethical AI systems, resulting in guidelines for Trustworthy and
Responsible AI from the National Institute of Standards and Technology (NIST)
[42], that added fairness to its list of principles for ethical systems, and
various other guidelines, of which the list from Intel is typical [43]. These
criteria, however, continue to evolve and could benefit from input from the
controls community.

##  VII Conclusion

Automatic methods designed to change people’s minds have reached a new level
of expertise. This paper presented a new model of Social Media Networks along
with algorithms for three opinion controllers. Results from a simulation study
were then described, and details for using generative AI to deploy such
controllers were illustrated–including experimental results demonstrating the
efficacy of using Large Language Models for quantifying the opinion
characteristics of social media posts. Ethical concerns and frameworks from
related fields were then presented with an invitation for more work
understanding the morality of using automatic control methods for persuasion.

Organizations like the NSF and DARPA have long recognized the risks of
powerful techniques developed for feedback control, including jobs lost to
automation [44] and, specifically, the need for cognitive security to protect
populations from influence operations and mass manipulation [45]. Future work
could explore how to accomplish these goals.

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