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Running head: SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Simulating Conversations: A Markov chain model of a central speaker’s mnemonic
influence over a group of communicating listeners
Elif Ece Sozer1
Jeremy K. Yamashiro2
William Hirst1
1The New School for Social Research, Department of Psychology
2University of California, Santa Cruz, Department of Psychology
Word Count: 8323, excluding references and the title page and the abstract
Authors’ Note
Elif Ece Sozer https://orcid.org/0000-0001-5121-2685
Jeremy K. Yamashiro https://orcid.org/0000-0001-5378-1953
William Hirst https://orcid.org/0000-0002-8506-6492
Data and code are publicly available on the OSF site: osf.io/9cwy4/. We would like to
thank Hananiel Suradji, Cole Baisch, and Evelyn Perez-Amparan for their research assistance, as
well as the UCSC Institute for Social Transformation for Building Belonging fellowships to JY.
We acknowledge the support of NSF grant #1827182 to WH. ES and JY share co-first
authorship.
Correspondence concerning this paper should be sent to: Elif Ece Sozer, Department of
Psychology, New School for Social Research, 80 Fifth Avenue, New York, NY 10011, Email:
sozee287@newschool.edu, or to Jeremy K. Yamashiro, Department of Psychology, University of
California Santa Cruz, 1157 High St., Santa Cruz, CA 95060, Email: yamashiro@ucsc.edu
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Abstract
Through their selective rehearsal, Central Speakers can reshape collective memory in a
group of listeners, both by increasing accessibility for mentioned items (shared practice effects)
and decreasing relative accessibility for related but unmentioned items (socially shared retrieval
induced forgetting, i.e. SSRIF). Subsequent networked communication in the group can further
modify these mnemonic influences. Extant empirical work has tended to examine such
downstream influences on a Central Speaker’s mnemonic influence following a relatively limited
number of interactions – often only two or three conversations. We develop a set of Markov
chain simulations to model the long-term dynamics of such conversational remembering across a
variety of group types, based on reported empirical data. These models indicate that some
previously reported effects will stabilize in the long-term collective memory following repeated
rounds of conversation. Notably, both shared practice effects and SSRIF persist into future
steady states. However, other projected future states differ from those described so far in the
empirical literature, specifically: the amplification of shared practice effects in communicational
versus solo remembering non-conversational groups, the relatively transient impact of social
(dis)identification with a Central Speaker, and the sensitivity of communicating networks to
much smaller mnemonic biases introduced by the Central Speaker than groups of individual
rememberers. Together, these simulations contribute insights into the long-term temporal
dynamics of collective memory by addressing questions difficult to tackle using extant
laboratory methods and provide concrete suggestions for future empirical work.
Keywords: social aspects of memory, collective memory, Markov chains, socially shared
retrieval induced forgetting, shared practice effects
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Simulating Conversations: A Markov chain model of a central speaker’s mnemonic
influence over a group of communicating listeners
A burgeoning literature on psychological approaches to collective memory has explored
the socio-cognitive mechanisms through which communicating people can converge onto shared
representations of the past (Hirst & Echterhoff, 2012; Hirst et al., 2018; Roediger et al. 2009).
Although this empirical work has typically focused its analytical eye on one-off conversational
interactions, the effects of communication on mnemonic convergence have at times been
examined in broader contexts, for instance, across social networks and across time (Coman et al.
2016; Momennejad et al. 2019; Momennejad, 2021; Vlasceanu et al., 2018). As methodological
limitations often constrain the extent to which researchers can examine such extended dynamics
experimentally, simulations have become a critical tool in the collective memory researcher’s
arsenal (e.g. Coman et al., 2012; Luhmann & Rajaram, 2015). Here, we develop a Markov chain
model to explore the long-term dynamics of conversational influences on remembering
following selective rehearsal by a Central Speaker. In doing so, we make predictions about how
collective memories are likely to stabilize across members of a group under a variety of different
social conditions, and more precisely, when a Central Speaker’s influence is likely to persist – or
not persist – into that stabilized collective memory.
To create our model, we drew upon Yamashiro and Hirst’s (2020) empirical work on
group-wide mnemonic convergence when a Central Speaker addresses an audience who
subsequently talks among themselves. Such a sequence of conversational interactions is
common. For instance, following a breaking news story with broad exposure, a politician may
address the public, selectively rehearsing some elements of the news story while leaving others
unmentioned. Alternatively, students in a class may read a chapter of their textbook, then attend
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a lecture in which the professor focuses on some aspects from the chapter but neglects other
material. In both instances, the group – be it the public or the students – may talk to one another
after the Central Speaker’s selective rehearsal. The Central Speaker Scenario, then, involves two
junctures at which memories can be reshaped. At the initial point of influence, Central Speakers
can reshape their listeners’ memories via direct mnemonic influence, for instance, through
socially shared reinforcement, induced forgetting, or social contagion of memory (Cuc et al.
2007; Meade & Roediger, 2002; Roediger et al, 2009). These direct mnemonic influences have
been well studied (for a review, see Hirst & Echterhoff, 2012). Yamashiro and Hirst (2020) were
chiefly interested in the less studied and poorly understood downstream effects of subsequent
conversations. How is a Central Speaker’s mnemonic influence impacted by subsequent
conversation in a social network? Would these subsequent conversations amplify, mitigate, or
have no effect on the Central Speaker’s initial influence? Would the group slowly converge on
the Central Speaker's selective rendering of the original material, or would his influence wash
out?
Answers to these questions are critical for anyone interested in collective representations
because they speak to the extent to which a Central Speaker, such as a politician or educator, can
reshape a public’s collective memory. Yamashiro and Hirst (2020) found that Central Speakers
can indeed influence those listening to them by reinforcing some memories and inducing
forgetting for others. More critical to their concerns, subsequent conversations among a group of
listeners amplified the Central Speaker’s mnemonic influence. That is, subsequent conversations
increased the extent to which the Central Speaker's audiences converged onto the Central
Speaker's selective rendering of the original material. They did so by enhancing the mnemonic
accessibility for what the Central Speaker selectively remembered, which Yamashiro and Hirst
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attributed to shared practice effects. Subsequent conversation also enhanced forgetting for
information that went unmentioned by the Central Speaker, but which was related to what the
Central Speaker had selectively rehearsed. Yamashiro and Hirst attributed this selective
forgetting to retrieval-induced forgetting (RIF). Inasmuch as RIF was occurring as a result of
conversational interaction, the enhancement no doubt involved both within-individual retrieval
induced forgetting (WIRIF, which involves the overt recall of a speaker; Anderson, Bjork &
Bjork, 1994) and socially shared retrieval-induced forgetting (SSRIF; which involves covert
retrieval on the part of a listener, Cuc et al, 2007). Interestingly, RIF was more pronounced when
Speakers and Listeners belong to the same social group. This result is consistent with other
studies showing enhanced SSRIF across ingroup members (e.g., Barber & Mather, 2012; Coman
& Hirst, 2015; Stone et al., 2013, 2022; see also Mao et al, 2011; Coman et al., 2014). We refer
to the shared practice and RIF effects Yamashiro and Hirst observed as the Central Speaker’s
mnemonic influences.
Limitations of the Laboratory and the Need for Modeling
The laboratory setting utilized by Yamashiro and Hirst (2020) does not, of course, fully
capture the complexity of real-world Central Speaker situations. Several limitations are readily
apparent. First, they examined groups of four listeners at a time and only allowed them to speak
to each other twice. In the real world, social networks can be considerably larger. Additionally,
people will often have many more than two conversations after listening to a Central Speaker.
For many public events, people will continue to discuss the issue at hand extensively. In the
current studies, we simulate this long-term effect of repeated conversation in a network. Will
conversations among members of the public continue to enhance the Central Speaker’s
mnemonic influence as conversations proceed? Or is there a point at which additional
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conversations have little additional effect or even reverse effects that might have been observed
early on? Will the effect of multiple conversations differ for shared practice effects and induced
forgetting? And how will the initial dyadic influence between a Central Speaker and a listener
interact with subsequent rehearsal by the listener, in either social or non-social contexts?
It is far from clear what the answer to these questions might be. As conversations
continue, people may increasingly recall items that the Central Speaker had failed to mention, for
instance, through opportunities for cross-cueing. Over the long run, such a tendency could
diminish signs of the Central Speaker’s mnemonic influence on an emergent collective memor.
Of course, it is also possible that the dynamics that led to enhancement of the Central Speaker’s
influence in Yamashiro and Hirst’s (2020) data could propagate through multiple conversations,
with the group eventually converging around a Central Speaker’s selective rendering.
There are at least two methodological paths for addressing the above questions. The first
would be to attempt to examine these long-term dynamics “in the wild.” Such naturalistic studies
often come with a loss in experimental control (however, see Yamashiro & Hirst, 2014, and
Stone et al., 2022, for naturalistic attempts to examine mnemonic convergence in real groups; for
a review of well-controlled laboratory studies using larger, but still relatively moderately sized
groups, as well as limited rounds of communications, see Momennejad, 2021).
Alternatively, one could construct computational models. Convergence onto collective
representations have been successfully modeled in several instances, including the impact of
social network structure on mnemonic convergence and the effects of collaborative remembering
(e.g. Coman et al., 2012; Luhmann & Rajaram, 2015), how community members’ expectations
hinder the collective discovery of counter-intuitive virtual technologies (Thompson & Griffiths,
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
2019) and how biases in memory shape serial reproduction (Xu & Griffiths, 2008). None yet
have addressed the complexities of the Central Speaker scenario.
In what follows, we will: (1) describe the Central Speaker experimental paradigm in more
detail, inasmuch as it serves as the basis for the model, (2) outline the model, (3) apply the model
to the data presented in Yamashiro and Hirst to determine likely long-term dynamics of their
temporally constrained empirical data, (4) undertake a parametric investigation of how different
degrees of Central Speaker influence might interact with different types of subsequent rehearsal
by the group of listeners.
The Central Speaker Paradigm
In Yamashiro and Hirst (2020), groups of four participants individually read nine short
stories. Participants then attended to a Central Speaker (a confederate) selectively rehearse half
of the propositions from one third of the stories. This selective rehearsal categorized story
propositions into three Central Speaker (CS) retrieval categories: rehearsed propositions (CS-
RP+), unrehearsed propositions related to what was rehearsed (CS-RP-), and propositions from
entirely unrehearsed stories (CS-Nrp.) As Yamashiro and Hirst used the term, two propositions
are related if they are part of the same story. Participants were instructed to monitor the Central
Speaker’s accuracy. Following this selective practice phase, participants were assigned to either
a non-conversational group or conversational group condition. In the non-conversational group
condition, each participant verbally recalled all the story details they could remember alone in a
separate room, then were given the titles of the stories and wrote down as many details as they
could remember, thereby producing both a verbal and written recall. After a short break, they
repeated these verbal and written recall procedures. In the conversational group, participants
were taken into a separate room two at a time. One participant verbally recalled story details
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while the other participant monitored them for accuracy. After this verbal recall, the first
participant was given the story titles and individually wrote as much as they could remember for
each story. The second participant then served as speaker for the third participant, and so on,
such that Participant A recalled while B attended, B recalled while C attended, C recalled as D
attended, and D recalled as A attended. This serial transmission chain was looped twice.
Thus, in both group types, all participants engaged in two verbal recalls interleaved with
two written recalls. The only difference between the two group types was the presence or
absence of social communication during verbal recall. In the analysis of the two sets of written
protocols, for both groups, it was apparent that the Central Speaker had elicited in his listeners
both shared practice effects (CS-Rp+ > CS-Nrp; Abel & Roediger, 2018) and socially shared
retrieval-induced forgetting (CS-Rp- < CS-Nrp; Cuc et al., 2007). As a result of these influences,
participants' memories converged around the Central Speaker’s selective rendering. Moreover,
subsequent networked communication impacted the strength of this influence. The relative
inaccessibility of CS-Rp- items vis-à-vis CS-Nrp items increased in the conversational groups
but not in the non-conversational (solo remembering) groups. As already noted, inasmuch as
each participant in the transmission chain both recalled the information themselves and listened
to another person recall the information, there was opportunity for both WIRIF and SSRIF, that
is, RIF on the part of a speaker and on the part of a listener. Networked communication had
amplified the Central Speaker’s mnemonic influence across the Speaker's audience, at least as
regards RIF. This downstream modification to memory may have arisen because changes in
relative accessibility induced by the Central Speaker shaped how the listeners talked to each
other, with subsequent distributed communication reproducing the Central Speaker’s pattern of
mentions and silences, thus reinforcing and amplifying his influence.
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A second experiment manipulated relational motives toward the Central Speaker. It was
found, as indicated above, that when a Central Speaker was perceived as an outgroup member,
his initial mnemonic influence was relatively weak and was not enhanced as a result of the
looped serial transmission chain. When perceived as an ingroup member, initial influence was
stronger and further amplified during subsequent communicational remembering.
As we have noted, our interest here is simulating a longer series of conversations and
exploring whether this leads to different results from those obtained by Yamashiro and Hirst’s
(2020) two rounds of communication. Our interest will not only be in the pattern of results after
multiple conversations, but whether it is the case that the effects of conversational interactions
eventually stabilize, and if they do, what kind of collective memory might emerge. We choose to
build our model and test it around the Yamashiro & Hirst (2020) study because they focused on a
situation that was both ecologically valid and tapped into our interest in the formation of
collective memories in social networks. They assessed both practice effects and SS-RIF as
memories were discuss across a serial transmission chain. Moreover, they compared the effects
of participating in serial transmission with solo remembering, a necessary comparison if one is to
study the advantages and disadvantages of serial transmission. Finally, they examined the role of
group membership, which allowed one to assess the effects of serial transmission in different
social contexts. With samples larger than required for power at the .80 level with a moderate
effect size (N = 100 for Study 1, N = 80 for Study 2), we felt confident enough using their data
as a basis for our simulation.
The Model: Simulating Conversations with Markov Chains
Markov chain simulations, which have been widely employed in psychology (e.g., Miller,
1952; Visser et al, 2017), allow one to project future states of a system based on its current state
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and known transition probabilities. They are characterized by three components: a state space, an
initial state, and a transition matrix. The state space is the full set of states a system may occupy.
In our model, we assume that during a given conversation n (or act of remembering n) items
from a given class C may become more accessible in memory (+), may be unchanged in
accessibility (0), or may become less accessible (-) as a result of the conversation, with such
mnemonic accessibility implicating the likelihood with which the item will be mentioned in the
subsequent conversation. This state of affairs can be expressed as a state vector for items in a
given class at a given iteration of the system, i.e., SC,n = {p+, p0, p-}. Class C refers to item type
as categorized by the Central Speaker’s selective rehearsal. That is, C may take the value of CS-
Rp+ (items rehearsed by the Central Speaker), CS-Rp- (items related but unrehearsed by the
Central Speaker), or CS-Nrp (items unrehearsed and unrelated). n refers to the nth time the
listeners recall the initial material, either by themselves (in non-conversational groups) or in a
looped chain of communication (in conversational groups).
As to the initial state, So, in our model, this represents the memory participants form of the
original material prior to listening to either the Central Speaker or other participants. The initial
state can be viewed as a three-element vector that captures the probability that an item is more
likely, equally likely, or less likely to be remembered again. In our model, initial states are
randomly distributed across the state space, reflecting participants’ idiosyncratic processing
during initial learning.
The final component of the model is the transition matrix, which defines how one iteration
of recall (non-conversational or conversational) can reshape the subsequent state vector, which
represents mnemonic accessibility. Given that the state vector has three possible states, the
transition matrix is a 3x3 matrix, with each row representing a state at time n, and each column
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representing a state at time n+1 (See Figure 1). Each cell of the matrix represents the probability
with which items in a given state at time n will transition into each available state at time n+1. In
the example matrix given in Figure 1, if an item were mentioned in the last conversation (thus
increasing its accessibility), the probability it will be mentioned again in the next conversation
(increasing accessibility again) is adjusted by, for example, a factor of .69. The state vector at
cycle n+1, then, is the product of the state vector at time n and the transition matrix. It
represents an updating of mnemonic accessibility due to the act of solo recall (in non-
conversational groups) or conversational recall (in conversational groups).
One interest here is the point at which the system’s state stabilizes. That is, is there a point
at which the group converges onto a stable collective memory, characterized by reliable
accessibility for some details of the event and reliable inaccessibility for other details, or do
event details continue to oscillate between different levels of accessibility? Based on the three
components described above – the state space, the state, and the transition matrix – the model
will allow us to estimate whether a steady state of mnemonic accessibility is likely to emerge
after repeated cycles of conversations (or isolated recall) and if so, how and for which items.
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Figure 1
Example transition matrix. During one conversation or act of solo recall, mnemonic accessibility
for items in a given class may increase (+), remain the same (0), or decrease (-). From each
possible state at time n (rows), the transition matrix gives the probability items will transition
into each available state in the subsequent conversation (columns). The diagram to the left
represents the transition matrix in graphical form.
As described above, to run the model, the transition matrix is applied to a state vector at
time n to generate a new state vector at time n+1. For example, the state vector for items in
Central Speaker retrieval category C at tn might be SC,n = (.16, .68, .16), indicating a 16% chance
that C has increased in accessibility, a 68% chance that it has remained neutral, and a 16%
chance that it has decreasing in accessibility. Given the example transition matrix in Figure 1, the
updated state vector at tn+1 will be the product of the state vector at tn and the transition matrix.
That is, the value of the first element of the vector (i.e. p+) for time tn+1 would be .16*.69
+ .68*.69 + .16*0 = .58. The bias toward remembering items the Central Speaker practiced thus
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increases the probability of recalling those items in the next conversation from 16% to 58%.
Continuing this matrix algebra, we find that SCS-Rp+, n+1 = (.58, .18, .24).
In order to discover the steady state into which a system is likely to settle, this same
process can be iterated until the system reaches a stable distribution in which the probability
distributions for the three states cease changing across iterations. This stable state is the system’s
ergodic distribution. In our model, the ergodic distribution represents the likelihood that items in
a particular class will become part of the group’s stable collective memory, either by being
reliably remembered or reliably forgotten. To illustrate this point using an extreme edge case, an
ergodic distribution of SCS-Rp+, ergodic = (1, 0, 0) would indicate that, following extensive
conversations in the group, items a Central Speaker mentioned would have a 100% chance of
retaining high mnemonic accessibility, making it certain that those items would become part of
the group’s collective memory. Conversely, an ergodic distribution of SCS-Rp+, ergodic = (0, 0, 1)
would indicate 100% of items a Central Speaker mentioned would settle into a state of low
accessibility, being reliably forgotten and becoming a “blank spot” in the group’s collective
memory (Wertsch, 2008). An ergodic distribution of SCS-Rp+, ergodic = (.33,.33, .33) would suggest
that the Central Speaker’s mnemonic influence had not survived multiple rounds of subsequent
conversational or solo recall. Propositions mentioned by the Central Speaker would have an
essentially random likelihood of increasing, remaining neutral, or decreasing in mnemonic
accessibility. As a result, we would expect no mnemonic convergence across the group, at least
in reference to the Central Speaker’s selective rendering, either in terms of collective
remembering or collective forgetting. By generating ergodic distributions based on transition
probabilities derived from established empirical data, we can forecast the extent to which a
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collective memory reflecting what the Central Speaker said will survive multiple conversations
or multiple acts of solo remembering.
The Effect of Multiple Conversations
Conversational Remembering vs. Solo (Non-Conversational Group) Remembering
The first set of simulations built on data from Yamashiro and Hirst’s (2020) Experiment
1, which contrasted the influence of solo remembering (non-conversational group condition) vs.
networked conversational remembering (conversational group condition) following a Central
Speaker’s mnemonic influence. As described above, in conversational groups, participants
recalled to one another along a looped serial transmission chain, whereas in non-conversational
groups, the same number of participants underwent the same number of recall attempts, but by
themselves. The simulations explored the projected long-term dynamics of collective memory
using this Central Speaker paradigm.
In what follows, we first describe how we constructed transition matrices using published
data from Yamashiro and Hirst (2020). We then turn to the effects of multiple conversations,
specifically, whether a stable pattern of mnemonic accessibility or inaccessibility emerges and if
so, what this projected pattern says about the collective memory likely to be formed by the group
in the long run. Simulations utilized the R “markovchain” package (Spedicato, 2017). Code for
all simulations is available on the Open Science Framework at https://osf.io/9cwy4/. As noted
above, Yamashiro and Hirst offer good vehicle for studying collective memory over the long-
term because it examines the effects of social transmission and do so with a robust sample, with
ample power.
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Constructing the transition matrices
The first step in building the model was to construct transition matrices based on the
empirical recall protocols in the two different group types (conversational and non-
conversational). Yamashiro and Hirst (2020) had collected two written memory protocols for each
participant, representing, respectively, the Central Speaker’s initial influence and the influence of
subsequent conversational exchanges. From these two protocols, transition probabilities were
calculated for items in each Central Speaker retrieval category. For instance, at tn, a proposition
could either be recalled or not recalled. If a proposition were recalled at tn, there were two
possibilities for tn+1, again, either being recalled or not recalled. Based on recall across the two
time points, a proposition would be scored as increasing in accessibility (due to retrieval),
remaining neutral (neither practiced nor suppressed, if, for instance, the entire story was
unpracticed), or decreasing (due to socially shared retrieval induced forgetting). See Table 1. If an
item was recalled at Time tn+1, it received a score of +1. If it was recalled at Time tn, but not at
Time tn+1, it received a score of -1. If an item were forgotten both times and no other propositions
from the story were mentioned, it was assigned a 0.
Table 1
Calculating transition matrices
Time tn+1
Time tn
Recalled
Not recalled
Recalled
+1
-1
Not recalled
+1
0
We calculated the proportion of propositions that received scores of +1, 0, or -1, separately
for items from each Central-Speaker retrieval category (CS-Rp+, CS-Rp-, and CS-Nrp), across
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all participants. For illustration purposes, let us focus on items from stories totally unmentioned
by the Central Speaker (i.e., CS-Nrp items). Participants mentioned some of these items in the
first memory protocol and did not mention others. Of CS-Nrp items that participants mentioned
in the first protocol, an average proportion of .48 might have received a score of +1,
demonstrating an increase in accessibility across the two protocols for 48% of the propositions,
while an average proportion of .07 received a score of 0, indicating 7% of items did not change
in accessibility as a category, and an average proportion of .45 items receiving a score of -1, thus
45% of such items decreased in accessibility across the two protocols. These three probabilities
represent the top row of the 3x3 transition matrix.
The same procedure was followed to fill in the next two rows, this time beginning from the
subset of propositions that were not recalled in the first protocol, which were either from stories
totally unmentioned in the first protocol (row 2) or which were related to recalled items, but
which were not themselves recalled (row 3). In this manner, we created a 3x3 transition matrix
for each of the three Central Speaker retrieval categories, in the two group type conditions, for a
total of six matrices (see OSF repository). Note, in our model an item can only transition into
adjacent accessibility states, i.e., transitions directly between the high accessibility (+) state and
low accessibility state (-) are not permitted; an item must transition through the neutral (0) state
first. See Figure 2 for an example transition matrix.
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Figure 2
Example transition matrix established using the coding scheme capture in Table 1 and the data
collected in Yamashiro and Hirst for CS-Nrp propositions in the conversational condition.
The emergence of stability: Ergodic distributions and their interpretation
Having created transition matrices based on empirical transition probabilities, we next
generated an ergodic distribution for each matrix, forecasting the likely probability distributions
for different levels of mnemonic accessibility following repeated rounds of recall (see Table 2).
On average, ergodic distributions stabilized after 8.7 iterations (Conversational = 8.3, Non-
conversational = 10). Figure 3 below illustrates the dynamic emergence of stable probability
distributions across multiple iterations of the system. This time course is of note because the
number of iterations required for the system to stabilize exceeds considerably the number of
conversational interactions examined in most empirical work to date, which tend to be limited to
two or three interactions at most. It would be valuable if future empirical work could confirm
this time course to the stabilization of a collective memory in conversing groups.
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Table 2
Vectors for ergodic distributions* for CS-Rp+, CS-Rp- and CS-Nrp propositions in the
conversational and non-conversational groups
CS-Rp+
CS-Rp-
CS-Nrp
Conversational
S (.61, .28 .11)
S (.17. .31, .52)
S (.32, .35, .33)
Non-conversational
S (.43, .34, .23)
S (.16, .30, .54)
S (.20. .35, .45)
*S (+, 0, -)
Turning now to the specific retrieval types, first consider CS-Nrp propositions, that is,
items from stories that went totally unmentioned by the Central Speaker. As indicated in Table 2,
accessibility for CS-Nrp items remained largely unbiased, with items in this class approximately
equally likely to increase, decrease, or remain neutral, or, perhaps in solo remembering (non-
conversational groups), with some tendency toward being forgotten. There was no statistical
difference between ergodic distributions in conversational and non-conversational groups for
CS-Nrp items, X2(2) = 4.62, p = .099.
On the other hand, the Central Speaker’s mnemonic influence remained evident into the
stable state for items the Central Speaker had selectively rehearsed (CS-Rp+ items) and for
related but unmentioned items for which the Central Speaker had induced socially shared
retrieval induced forgetting (CS-RP- items). Conversational interactions, relative to non-
conversational group (solo remembering), amplified accessibility for items the Central Speaker
mentioned (i.e., CS-Rp+ items), X2(2) = 7.57, p = .023, but did not impact CS-RP- items, X2(2) =
0.08, p = .96. Items mentioned by the Central Speaker had a probability of .61 of stabilizing into
a state of high accessibility following conversation, relative to only .41 in solo-remembering,
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non-conversational groups. That is, the Central Speaker’s sustained influence was much weaker
when people remembered by themselves, even though participants in non-conversational groups
did engage in retrieval practice.
These results speak to the fate of CS-Rp+, CS-Rp-, and CS-Nrp items after multiple
conversations or multiple acts of solo remembering. They do not engage the question of whether
the pattern observed for these items is consistent with the presence of practice effects or RIF per
se. To explore this issue, we needed to determine whether CS-Rp+ > CS-Nrp, for a practice
effect, and CS-Rp- < CS-Nrp for RIF. Moreover, to investigate whether practice effects and RIF
were enhanced by conversational interactions, we need to compare the size of these differences
across the non-conversational and conversational conditions.
First, the Central Speaker’s shared practice effects (CS-Rp+ > CS-Nrp) persisted into the
ergodic distributions for both conversational groups, X2(2) = 20.82, p < .001, and non-
conversational groups, X2(2) = 15.53, p < .001. On the other hand, RIF (CS-Rp- < CS-Nrp)
persisted into the ergodic distributions only for conversational groups, X2(2) = 9.08, p = .01, and
not for non-conversational groups, X2(2) = 1.65, p = .44. These results are noteworthy because
they differ from the empirical findings reported after two recalls in Yamashiro and Hirst (2020),
who found both shared practice effects and RIF in both group types, albeit weaker RIF in the
non-conversational groups. These simulations suggest that in the long run, conversational
interaction is necessary for a Central Speaker’s RIF to persist, and that the effect, even if it
appears shortly after a Central Speaker’s selective rehearsal, is likely to disappear in the absence
of sustained conversational interaction.
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Figure 3
Sample diagrams demonstrating convergence onto the ergodic distribution for items from each
Central Speaker retrieval category (CS-Rp+, CS-Rp-, and CS-Nrp) for the two group types
(conversational and non-conversational). In the simulations, initial states, represented by the
starting iteration on the far left of each chart, were randomly generated.
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Conversational Remembering: Ingroup vs. Outgroup Central Speaker
A second set of simulations addresses the same issues as the just described simulation, but
now focused on Yamashiro and Hirst’s (2020) Experiment 2. Experiment 2 differed from
Experiment 1 in two ways. First, the Central Speaker’s selective rehearsal was televised rather
than presented in-person by a live Central Speaker, and, prior to conversational recall along
looped serial transmission chains, participants were led to think of the Central Speaker as either
an ingroup or an outgroup member. Yamashiro and Hirst found that conversations only enhance
the Central Speaker’s ability to induce forgetting when the Central Speaker and participants were
members of the same group.
In the present simulation, as before, six transition matrices were created following the
procedures described above, one for items in each of the Central Speaker’s selective retrieval
practice types (CS-Rp+, CS-Rp-, CS-Nrp), separately for the two group types (Ingroup vs.
Outgroup) (for transition matrices and sample ergodic convergence charts see the OSF
repository). We then generated ergodic distributions for each of the six matrices (see Table 3).
These emerged after 8 conversational loops for the Conversational-Ingroup Speaker condition
and 8.3 conversational loops for the Conversational-Outgroup Speaker condition.
Table 3
Ergodic distributions* for CS-Rp+, CS-Rp- and CS-Nrp propositions in the Ingroup and
Outgroup conditions
CS-Rp+
CS-Rp-
CS-Nrp
Ingroup
S (.44, .36, .20)
S (.11, .29, .60)
S (.27, .36, .37)
Outgroup
S (.39, .35, .26)
S (.20, .33, .47)
S (.24, .35, .41)
*S (+, 0, -)
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Bias toward remembering the Central Speaker’s rehearsed items persisted into the
stabilized distributions. Central Speaker identity did not impact the extent of this mnemonic
influence, X2(2) = 1.10, p = .58. Furthermore, in both conditions the mnemonic handicap for CS-
Rp- items persisted into the forecasted stable state. Moreover, numerically it appeared that a
steady state of low accessibility was more probable in the Ingroup CS condition. However, there
was no statistical difference between Central Speaker identity conditions in ergodic distributions
for CS-Rp- items, X2(2) = 4.45, p = .11. CS-Nrp ergodic vectors also did not differ between
ingroup and outgroup conditions, X2(2) = 0.40, p = .82
As to practice effects and RIF, as opposed to simply changes in CS-Rp+, CS-Rp-, and CS-
Nr-, the Central Speaker’s shared practice effects (CS-Rp+ > CS-Nrp) persisted into the ergodic
distributions for both ingroup, X2(2) = 9.14, p = .01, and outgroup condition, X2(2) = 6.93, p
= .03. On the other hand, RIF (CS-Rp- > CS-Nrp) persisted into the ergodic distribution only in
the ingroup condition, X2(2) = 12.94, p = .002, but not in the outgroup condition, X2(2) = 0.83, p
= .66. Thus, unlike Yamashiro and Hirst (2020), which did show an initial, though weaker, RIF
effect for an outgroup Central Speaker after only two rounds of conversations, the present
simulation suggests that the RIF induced by an outgroup Central Speaker may be quite transient
relative to the more robust effect exerted by an ingroup Central Speaker.
Discussion of Simulations Based on the Empirical Data
The simulations highlight how multiple conversations can produce mnemonic outcomes
not observed in empirical studies that examine only two or three interactions. The simulations
clearly show that a Central Speaker’s mnemonic influence can persist into the dynamically stable
form of a collective memory. This persisting influence appeared as both a strong bias towards
high accessibility for items the Central Speaker mentioned, and by relatively strong biases
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
towards low accessibility states for related but unmentioned items that had presumably been
subject to the Central Speaker’s socially shared retrieval induced forgetting. There was no clear
bias in accessibility for Central-Speaker’s unmentioned but unrelated items.
Where the simulations differ from the empirical work, which was confined to two-
interaction, is in establishing when a Central Speaker’s mnemonic influence is likely to
disappear, even if such influence is initially detectable. Continued conversation heightened
convergence around the Central Speaker’s rehearsed items and maintained the Central Speaker’s
SSRIF. Conversation did not maintain a Central Speaker’s SSRIF, however, if that Central
Speaker had been perceived as an outgroup member, or if audience members did not
communicate with each other while remembering. Under these conditions, even if a Central
Speaker were able to exert mnemonic influence initially, such influence was likely to be both
weak and fleeting.
The present simulations do not allow us to determine why more than two – typically
eight, but ten for the non-conversational condition – rounds of conversation were necessary for
the group’s collective memory to reach dynamic stabilization. They also do not explain why the
Central Speaker’s initially present SSRIF disappears in non-conversational groups’ steady state
and, in conversational groups when a Central Speaker is perceived as an outgroup member. One
possibility is that the amount of the Central Speaker’s initial mnemonic influence matters.
Relatively weak initial SSRIF, as may be the case for the outgroup Central Speaker (Coman &
Hirst, 2015) may not survive repeated conversational buffeting, whereas initially strong SSRIF,
associated with the ingroup Central Speaker, may experience conversational reinforcement. The
nuanced details of the pathway to stabilization vs. attenuation of SSRIF across multiple rounds
of conversation merits future empirical work. In any case, the simulations do establish that a
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Central Speaker’s mnemonic influence over a group of listeners changes as the number of
conversations among listeners increases.
Parametric Manipulation of Mnemonic Influence
In the final set of simulations, we aimed to gain a more systematic understanding of the
conditions under which a given group type would converge around a Central Speaker’s selective
rehearsal. To do so we parametrically adjusted the degree of bias immanent in the transition
matrices, again with the matrices derived from the empirical data as a reference point. Doing so
allowed us to gain a more precise understanding for how conversational groups differ from non-
conversational groups in their sensitivity to a Central Speaker’s mnemonic influence, as well as
how they differ in the potential maximum degree of influence maintained in the stable state.
Constructing hypothetical transition matrices
We generated hypothetical transition matrices representing progressively stronger and
weaker degrees of influence relative to each of the 12 transition matrices derived for the
simulations discussed in preceding sections. We will refer to these previous 12 matrices as the
empirical transition matrices, given that they reflect transition probabilities drawn from
previously reported data. We generated our hypothetical transition matrices, which captured
progressively weaker or stronger mnemonic influences, relative to the deviation of the empirical
matrix from an unbiased random matrix, in increments of 10%. That is, a given hypothetical
transition matrix was multiplied by .10 and the result was added or subtracted from a given
matrix to obtain a new hypothetical transition matrix. The first .10-step-up or step-down will be
labeled Parametric Step +.10 or -.10. We generated ten hypothetical transition matrices in each
direction, weaker and stronger, each in incremental steps of 10% change. Thus, we ended up
25
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
with 20 hypothetical transition matrices for each of our empirically derived transition matrices.
Parametric Step 0 identified the empirically derived transition matrix from the first simulation.
Inasmuch as we used as our starting or baseline point the empirically derived transition matrices,
we ended up with 20 hypothetical transition matrices for each of the 12 empirically derived
transition matrices [ie., 3 (Central Speaker retrieval categories: CS-Rp+, CS-Rp- and CS-Nrp) x
4 (subsequent remembering group types: non-conversational, conversational, conversational
ingroup, conversational outgroup)]. The limit in the weaker direction (Parametric Step -1) was a
matrix suggesting minimal Central Speaker influence. This “random” matrix yields a neutral
ergodic distribution of SRandom, Ergodic = (.285, .43, .285).
Interpreting distributions of ergodic states derived from hypothetical transition matrices
We generated an ergodic distribution for each hypothetical transition matrix, yielding a
total of 240 ergodic distributions. See Figure 4 for the results based on the transition matrices
associated with the comparison of conversational and non-conversational group conditions.
Graphs for parametric manipulations of mnemonic influence between conversational groups with
ingroup and outgroup Central Speakers are provided in the supplemental online materials and are
not discussed in the current paper.
We highlight two landmarks of theoretical interest captured on the distribution of ergodic
states in Figure 4. First is the point at which the bias introduced by the Central Speaker’s
selective rehearsal appears, that is, the point at which the probability of a high or low state of
accessibility (p+ or p-) exceeds the probability of no change (p0). We may conceive of this
landmark as the minimal degree of influence required for a Central Speaker’s influence to persist
into the steady state. As an illustration, in Figure 4, top left panel, this point is around Parametric
Step -.40, that is, at about 40% of the degree of bias found in the empirical data.
26
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Figure 4
Ergodic states for different hypothetical transition matrices, of different parametric steps.
The second landmark concerns the degree to which the Central Speaker influences the
accessibility of an item. A stronger influence is indicated as the relative distance between p0 and
p+ (or p-) increases. That is, a wider wedge-shaped relation between p0 and p+ (or p-) indicates a
more sensitive response to a Central Speaker’s influence across multiple conversations.
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Effect of different strengths of conversational influence on recall
With respect to the first landmark, the degree of influence at which signs of a Central
Speaker’s selective rehearsal begin to appear in the stabilized group memory, for items the
Central Speaker mentioned (CS-Rp+), there is a clear advantage in the conversational group. In
Figure 4, the crossover of curves associated with p+ and p0 occurs at Parametric Step -.70 for the
conversational condition and Parametric Step -.40 for the non-conversational condition. That is,
much weaker Central Speaker influences can persist into stable group memory for
communicating groups than for non-conversational groups of individuals recalling by
themselves. Interestingly, the same is not true for the CS-Rp- items. Whether participants
interacted with each other or not, the crossover point of p- and p0 occurred at Parametric Step
-.60. Finally, for CS-Nrp items, the non-conversational group had a crossover point at Parametric
Step -.40. Conversational groups, on the other hand, demonstrate the expected lack of relation
between degree of Central Speaker influence and mnemonic accessibility for items from totally
unpracticed categories.
A parallel story emerged when examining the second landmark, again representing a
projected doubling of the empirically observed degree of influence. For CS-Rp+ items, the
conversational group showed a much more dramatic increase in accessibility as a function of
increasing influence than the non-conversational group. This enhancement of the Central
Speaker’s influence through conversational interaction, as documented by Yamashiro and Hirst
(2020) and the simulation above, clearly grew as a function of the strength of the mnemonic
influence in the present simulation. For CS-Rp- items, accessibility declined with increasing
influence, but as we observed with respect to the cross-over point, there appears to be little
difference between the non-conversational and conversational condition. On the other hand, the
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
presence of conversational interaction seems to limit any increase in accessibility for CS-Nrp
items. The curves associated with increasing, unchanging, or declining accessibility are flat and
overlapping. There is neither an increase or decrease in accessibility, no matter what the strength
of the mnemonic influence. As we speculated in the Introduction, this may be the case because
there is cross-cueing in the conversational condition. As a result, there may be a "tug-of-war"
between the tendency to forget what went unmentioned by the Central Speaker and a tendency
for one person in a conversation to trigger another person’s memory.
Practice and RIF effects
The above analyses only consider the effects of changing degrees of influence on
accessibility for items within a particular class C. To examine changes in the size of the shared
practice effects or RIF, we need to compare the changes in accessibility for CS-Rp+ with the
changes of accessibility of CS-Nrp (for shared practice effects), as well as the changes in
accessibility of CS-Rp- with changes in accessibility of CS-Nrp (for retrieval induced
forgetting). To examine retrieval induced forgetting, we selected only p- curves for each
Parametric step across CS-Nrp and CS-Rp- rehearsal categories and the two group types. This
relation of increasing RIF as Central Speaker influence increases is depicted in Figure 5.
Comparably, to examine shared practice effects we selected only p+ curves for each Parametric
step across CS-Nrp and CS-Rp+ rehearsal categories and the two group types, in Figure 6.
29
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Figure 5
Retrieval-induced forgetting (CS-Nrp versus CS-Rp-)as a function of parametric step and group
type
Figure 6
Practice Effects (CS-Nrp versus CS-Rp+) as a function of parametric step and group type
As can be seen, both practice effects and RIF can be observed in the conversational
group, but not to the same extent in the non-conversational group condition. Interestingly, these
effects for the conversational group, especially when considering RIF, grow out of, to a large
degree, the flat curve associated with CS-Nrp items. We accounted above for this flatness by
considering the dynamics of cross-cueing. But why would the same dynamics not apply to the
30
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
conversational interactions and the way they might trigger memories for CS-Rp- items? Indeed,
one might expect that they would be more likely to serve as a trigger for CS-Rp- items than CS-
Nrp items in that the former are related to the well-remembered CS-Rp+ items. For us, the
explanation rests with the most widely accepted explanation of RIF, that the act of remembering
CS-Rp+ items inhibits the related CS-Rp- items, making them difficult to remember, even when
cued by someone else in the conversation. This explanation could apply to both recognizing an
item remembered by another conversational participant or recalling a memory on the basis of
what another conversational participant said, inasmuch as RIF can be found when memory is
accessed by either a recall or recognition test (Hicks & Starns, 2004).
General Discussion
Understanding the long-term dynamics by which communicating networks of humans
either converge or fail to converge onto shared cognitive representations remains a primary
challenge in the scientific study of collective memory. The topic is complex, in that it requires
the integration of insights at multiple levels of analysis, from memory processes in individual
cognition, to conversational influences on memory, to the propagation of information across
different social network structures and temporal dynamics (Momennejad, 2021; Vlasceanu et al.,
2018). Methodological and analytical challenges arise in attempting to capture these complex
dynamics in traditional laboratory settings. In the current set of empirically informed
computational models, we offered some insight into the likely long-term dynamics of the Central
Speaker Scenario, beyond the capacity of extant laboratory work. In our simulations, we
examined these long-term stabilization patterns along two axes: first, by extending the
empirically observed effects into future states of the system, and second, by parametrically
31
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
modulating the strength of a Central Speaker’s initial influence across different group types to
examine the wider space of likely long-term stabilization patterns.
Several patterns reported in the empirical literature, which looks at best at two or three
repeated conversations, seem likely to remain stable over long runs of repeated conversation.
Both a bias toward high mnemonic accessibility for items a Central Speaker mentions (shared
practice effects) and towards low accessibility for related but unmentioned items (retrieval
induced forgetting) persisted into the steady state, but only under certain conditions. Shared
practice effects persisted in both conversational and non-conversational groups, as well as in
conversational groups with both ingroup and outgroup speakers. On the other hand, RIF only
persisted in conversational groups – and even there not when a Central Speaker was perceived as
an outgroup member. Even if a Central Speaker exerts mnemonic influence in the short run, in
the long run, certain other conditions are necessary for that influence to stabilize into a collective
memory.
Critically, in addition to the persistence of initial mnemonic influence into future states, the
simulations indicate that mnemonic influence can appear after a long run of the system even
though it was not initially apparent and, further, can appear initially but disappear after a long
run. These results underscore the advantage of using modeling. As an example of a mnemonic
effect that was not initially apparent but appeared after a long run, items mentioned by the
Central Speaker were more likely to settle into a high accessibility state following multiply
repeated conversation than following only multiply repeated isolated recall. This difference was
not apparent in the two-round empirical data. Regarding effects that appear initially but which
disappear in the long run, we can point to the disappearance of RIF unless supported by
conversation, an ingroup Central Speaker, or a strong mnemonic influence. The transitory nature
32
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
of RIF in non-communicating individuals and conversational networks with outgroup Central
Speakers or with weak mnemonic influence by the Central Speaker is in line with, but goes
beyond, previous empirical work demonstrating that outgroup speakers either tend not to induce
SSRIF (Coman & Hirst, 2015), or to induce weaker SSRIF (Yamashiro & Hirst, 2020).
It would appear, then, that RIF may only stabilize in a group’s collective memory over the
long run if the initial, direct influence of a Central Speaker is both relatively strong and is
repeatedly reinforced in conversation. Strength of the initial influence and subsequent
conversational reinforcement are likely related. Under conditions where people perceive the
Central Speaker to be an ingroup member toward whom an audience presumably feels relational
motives to create a shared reality (Echterhoff et al., 2009), items mentioned by a Central Speaker
may achieve a special social relevance (Shteynberg et al., 2020), prioritizing them as topics of
conversation and in the process, reinforcing SSRIF for related but unmentioned items. Both the
emergence of initially non-apparent influences and the disappearance over the long run of
influences that had originally appeared drive home a more general point that the temporal
dynamics of conversational mnemonic influences ought to receive greater empirical attention
(for a similar argument, see Momennejad et al., 2019) and, in doing so, underscores the
developmental dynamic of convergence onto a collective memory.
We were also able in the current set of simulations to go beyond projected future states
immanent in existing empirical data to explore parametrically a range of degrees of mnemonic
influence across different group types. The primary novel finding here was that conversational
networks are much more sensitive to Central Speaker influence than groups in which only solo
remembering takes place. In communicating networks, proportionally weaker mnemonic
influences were required for a Central Speaker’s bias to become detectable in the stabilized
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SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
collective memory, particularly for shared practice effects. Additionally, the maximal potential
impact for a Central Speaker’s shared practice effects was also dramatically stronger in
conversational groups, suggesting that people in communicating networks have much higher
potential to converge around a Central Speaker’s selective rendering than individuals
remembering by themselves. This sensitivity indicates that it is not solely the dyadic, direct
influence of a Central Speaker that predicts the likelihood of their mnemonic influence taking
hold in a group, but that downstream conversational practices in the affected community (or lack
thereof) interact with this initial influence to stabilize an emergent collective memory.
Future Directions
In highlighting the amplification of shared practice effects in conversational networks
relative to solo remembering, the relatively short-lived nature of SSRIF in the absence of
conversation or as exerted by outgroup speakers, and the increased sensitivity of communicating
networks to Central Speaker induced mnemonic bias, our simulations project developmental
trajectories for collective memories that would not have been apparent in the simple pre- to post-
conversation measurements typical in extant empirical research. The simulations, however,
engaged just two mnemonic conversational influences: practice effects and RIF. Moreover, they
focused on only two social and/or cognitive factors: the strength of influence of the Central
Speaker and the Central Speaker’s group membership. Finally, they examined a relatively
straightforward social network: a looped serial transmission chain. Future research could use the
same modeling techniques to explore a wider range of possible mnemonic influences, e.g., the
presence of social cognition across a social network and the factors affecting the placement of
misinformation into a collective memory. It could also expand upon the factors shaping
transmission beyond the two explored herein. For instance, in their model of belief systems,
34
SIMULATING CONVERSATIONS WITH MARKOV PROCESSES
Friedkin et al. (2016) explored the extent to which factors such as the relatedness of different
beliefs, the extent to which members of a social network are wedded to their initial beliefs, and
the extent to which social influences can override the logical structural relations among beliefs.
All three of these factors would be relevant in the formation of collective memories and could be
examined using techniques similar to those employed herein.
Finally, as the extensive work on social network theory (see, for instance, Barabási, 2016;
Chrystakis & Fowler, 2008; Friedkin, 2011; Watts, 2003), as well as empirical work on the
formation of collective memories in complex social networks (Momennejad, 2021) underscore,
the topology of a social network matters. In the present work, we focused on the Central Speaker
paradigm, a reasonable choice given the extent to which Central Speakers, such as politicians,
play a role in shaping collective memories. However, as the work on belief systems and other
studies of connectedness underscore, beliefs – and memories – can spread across a network
without there being a Central Speaker to start the process. The social network can be much more
complex than the serial transmission chain explored here. Clearly, future work would address
this limitation of the present work.
As we have emphasized, what the present work does is underscore how modelling can
allow researchers to examine the dynamics underlying the formation of collective memory in
ways that might prove impossible in the laboratory. Whereas much more needs to be done, the
present study underscores that unexpected findings might emerge from such modeling efforts.
35
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