# Measurement of $\pi^{0}$ and $\gamma$ in d+Au collisions at $\sqrt{s_{NN}}=$
200 GeV by PHENIX experiment

Ondřej Chválaa for the PHENIX collaboration  a University of California –
Riverside, 900 University Ave, Riverside CA 92521, USA

###### Abstract

Previous results indicated that high $p_{T}$ particle suppression in Au+Au
interactions is a final state effect, since RdA ratios were compatible with
unity, albeit within large experimental errors. It is important to test this
conclusion to higher precision since the modification of structure functions
may be involved. Recent d+Au data taken in 2008 improve the integrated
luminosity by about a factor of thirty compared to the 2003 data. A more
precise measurement of both $\pi^{0}$ and $\gamma$ at higher $p_{T}$ will shed
new light on whether the initial state in the heavy nuclei is modified.

††journal: Nuclear Physics A

##  1 Introduction

The PHENIX experiment at RHIC is designed for high rate measurement of
electromagnetic probes, specifically direct photons $\gamma$ and neutral pions
$\pi^{0}$ at mid-rapidity ($|\eta|<$ 0.35). The high event rate allows unique
access to rare probes, such as particles produced at very high transverse
momentum ($p_{T}$).

Early results for the nuclear modification factors RAA, the spectrum in Au+Au
collisions over the spectrum in p+p interactions scaled by the respective
nucleon overlap integrals, showed suppression of $\pi^{0}$ and charged hadron
production at high-$p_{T}$ ($p_{T}\gtrsim$ 6 GeV/c) [1, 2, 3]. This result,
combined with the apparent lack of suppression for high-$p_{T}$ direct
$\gamma$ production [4] has been interpreted as an indication of the formation
of a dense strongly interacting medium, the sQGP, in heavy ion collisions.

Furthermore, the preliminary analysis of the high statistics 2004 Au+Au run
showed a possible decrease of direct photon RAA above 14 GeV/c of transverse
momentum [5]. Possible explanations for this observation include the isospin
effect (the difference of partonic content between protons and neutrons), the
EMC effect (modifications of the distribution of partons in the heavy nuclei),
and the suppression of the direct photons originating from fragmenting partons
which are quenched by the medium.

RHIC measurements of particle production in d+Au collisions from 2003 show no
suppression of produced particles within large experimental error bars [6, 7],
indicating little or no modification of the initial state in gold nuclei. This
result confirmed the attribution of the large suppression observed in central
Au+Au interactions to final state effects in the sQGP medium.

The final analysis of the 2003 data set revealed some suppression of $\pi^{0}$
production at the highest $p_{T}$ in the most central d+Au interactions [8],
however the experimental uncertainties are too large to estimate cold nuclear
matter effects quantitatively [9, 10].

##  2 RHIC year 2008 data set

The RHIC run in year 2008 improved the total integrated luminosity of the d+Au
sample by a factor of $\approx$30 compared to the 2003 run: 1.65$\times$109
minimum bias (MB) events, and 3.68$\times$109 events from a high-$p_{T}$
photon (ERT) trigger were recorded. There were also 0.53$\times$109 MB
triggered and 1.17$\times$109 ERT triggered p+p collisions taken in 2008. The
uncorrected $\pi^{0}$ yields are shown in Fig. 1.

The improvement in total d+Au integrated luminosity can be appreciated from
the relative statistical errors in the $\pi^{0}$ measurement using PHENIX PbSc
EMCal. The error at $p_{T}=$ 15 GeV/c is 32 % using the 2003 sample, and is
reduced to 3.5 % in the recent high statistics run.

Figure 1: Raw mid-rapidity yields per event of $\pi^{0}$ production from the
2008 data sets: p+p minbias, d+Au minbias, and three centrality bins in d+Au
collisions using PHENIX PbSc EMCal. The spectra from ERT triggered runs (red)
are scaled to match MB yields (blue) in 6–13 GeV/c region of $p_{T}$. Only
statistical errors are shown.

##  3 Conclusions

Previous results from data taken in year 2003 indicate that the high $p_{T}$
suppression observed in Au+Au interactions is a final state effect since the
RdA ratios are consistent with unity, albeit within large experimental errors.
It is important to test this conclusion to higher precision. Recent d+Au data
taken in 2008 improve the integrated luminosity by about a factor of thirty
compared to the 2003 run. The 2008 PHENIX measurement will shed more light on
the origin of cold nuclear matter effects.

## References

  * [1] K. Adcox et al. [PHENIX Collaboration], Phys. Rev. Lett. 88, 022301 (2002) [arXiv:nucl-ex/0109003].
  * [2] K. Adcox et al. [PHENIX Collaboration], Phys. Lett. B 561, 82 (2003) [arXiv:nucl-ex/0207009].
  * [3] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. 91, 072301 (2003) [arXiv:nucl-ex/0304022].
  * [4] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. 94, 232301 (2005) [arXiv:nucl-ex/0503003].
  * [5] K. Reygers [PHENIX Collaboration], J. Phys. G 35, 104045 (2008) [arXiv:0804.4562 [nucl-ex]].
  * [6] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. 91, 072303 (2003) [arXiv:nucl-ex/0306021].
  * [7] D. Peressounko [PHENIX Collaboration], Nucl. Phys. A 783, 577 (2007) [arXiv:hep-ex/0609037].
  * [8] S. S. Adler et al. [PHENIX Collaboration], Phys. Rev. Lett. 98, 172302 (2007) [arXiv:nucl-ex/0610036].
  * [9] G. G. Barnafoldi, G. Fai, P. Levai, B. A. Cole and G. Papp, [arXiv:0805.3360 [hep-ph]].
  * [10] B. W. Zhang and I. Vitev, arXiv:0810.3194 [nucl-th].


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# What is Escalation? Measuring Crisis Dynamics in International Relations
with Human and LLM Generated Event Data

Rex W. Douglass

University of California, San Diego

&Erik Gartzke

University of California, San Diego

&Jon R. Lindsay

Georgia Institute of Technology

&J. Andrés Gannon

Vanderbilt University

&Thomas Leo Scherer

University of California, San Diego

(2024-01-17)

###### Abstract

When a dangerous international crisis begins, leaders need to know whether
their next move is going to resolve the dispute or amplify it out of control.
Theories of conflict have mainly served to deepen the confusion, revealing
fighting, bargaining, and signaling to be high-dimensional and subtle
equilibrium behaviors with deeply contextual consequences. Should a leader
communicate resolve through aggressive acts, avoid spirals through
accommodation, or focus on ensuring the possibility of a bargain? We offer a
data-driven empirical solution to this logjam in the form of a new large-scale
analysis of actions taken within 475 crises. We combine two complimentary
measurement projects, the human-coded International Crisis Behavior Events
(ICBe) dataset and the new machine-coded ICBeLLM. We model directly whether an
action tends to shorten or extend the length of a crisis. The result is a
directly interpretable measure of the latent escalatory/deescalatory nature of
each action leaders have chosen over the last century.

1 University of California, San Diego
2 Georgia Institute of Technology
3 Vanderbilt University

##  1 Introduction

What does it mean that an international crisis is escalating, and what actions
within a crisis are escalatory? This question haunts recent and ongoing crises
such as missile tests on the Korean Peninsula, Russian incursions in Ukraine,
partial state death in Syria, and Chinese claims of sovereignty in the South
and East China Seas. In these situations, leaders face a shared fundamental
question about how to navigate a dangerous situation without accidentally
sliding over the line into a larger-than-desired conflict (Snyder and Diesing
1977; Slantchev 2005). Often leaders must make decisions with limited time and
inadequate information (Jervis 1976, p. 95). What guidance can we offer to
help maintain peace and stability? Can we predict how states will react to
specific events during crises? Can we recommend policies or actions that are
most likely to lead to success without being destabilizing? In short, what
empirical evidence can we bring to bear on the practical questions of crisis
management?111See Gannon (2022) for a recent review in the context of cross-
domain deterrence and escalation.

The international relations field offers two foundational perspectives on
crisis dynamics, classically described by Robert Jervis (1976) as the
deterrence model and the spiral model. The former blames escalation on the
failure to credibly communicate threats (Rovner 2020) or misperceptions about
capability or resolve (Morrow 2019). The latter views escalation as a
retaliation to provocation where a tit-for-tat response fails to end the
crisis (O’Neill 1991). These models offer contradictory policy prescriptions:
on one hand, policymakers should use bold words and actions to discourage
aggression; on the other, they should mitigate security dilemmas through
compromise and accommodation. Historical studies typically provide more
nuance, but the additional context needed to make sense of specific crises
just highlights the fact that both models are underspecified. Neither model,
moreover, is well integrated with more recent thinking about the underlying
bargaining dynamics of military contests (Fearon 1995). Previous empirical
research designed to validate or reject competing theoretical explanations for
escalation has faced daunting challenges given that the basis for comparison
and/or the logical discrepancies between alternative theories have not been
resolved (Glaser 1992; Kydd 1997; Zagare and Kilgour 1998) and the ability to
empirically assess such efforts is complicated by the structural indeterminacy
of uncertainty (Gartzke 1999; Chen, et al. 2022). These efforts have yet to
establish a consensus pecking order between canonical alternatives (c.f.,
Wright 1965; Carlson 1995; Kinsella and Russett 2002).

Recognizing the enormous efforts of previous theoretical and empirical
scholarship, we adopt an abductive approach designed to explore the correlates
of escalation/de-escalation in a novel data source constructed by the authors
and others (Douglass, et al. 2022; Douglass, et al. forthcoming). Our approach
capitalizes on a new dataset, the International Crisis Behavior Events (ICBe)
dataset, augmented by machine-coded data ICBeLLM. To our knowledge, these are
the first international conflict data to code the full sequence of statements
and actions by actors necessary to capture escalation as a process. These data
allow us to track the actions and reactions of every relevant actor in the 475
interstate crises available from the canonical ICB dataset; who did what to
whom, when, where, and how. Doing so allows us to identify various factors
most likely to lead to escalation or de-escalation in crises. Using these
triggers, we can develop a model that estimates (predicts) both the path and
duration of international crises and that indicates likely precursors and
their effects. We find support for neither the deterrence nor spiral model, in
their classic forms, suggesting the need for a more nuanced theory that can
accommodate the historical contingency and complexity of crisis processes.

This analysis is organized as follows. Section 2 briefly formalizes the
concept of an international crisis and the concept of escalation within a
crisis. It then draws prior beliefs from existing theories of escalation,
particularly deterrence and spiral models of conflict. Section 3 introduces
the data, turn-by-turn event data collected for 475 individual crises
(Douglass, et al. 2023). This section also presents our estimand—the
unobserved latent quality of an action being escalatory or de-escalatory at a
specific point in a crisis—and our measurement strategy, which involves
observing the empirical increase or decrease in the remaining duration of a
crisis as a function of the observed actions. Section 4 describes our modeling
strategy and presents empirical results. Section 5 provides a qualitative deep
dive with a few choice case studies (Tavory and Timmermans 2014; Heckman and
Singer 2017). Section 6 offers concluding remarks and implications of our
findings.

##  2 Crises, Escalation, and the State of the Art

The scientific state of the art on crisis escalation is too large and
amorphous of a topic to fully summarize, and so we draw attention to the
minimal necessary machinery for understanding the empirical argument made
here. Those components are the domain of the activity in question, the
definition of the outcome we seek to explain, theoretical priors about the
connection between different possible actions and that outcome, and empirical
attempts to measure the above.

###  2.1 Crisis and Stability

The status quo in international relations is almost always one of stability,
slow-changing bargains, and relative cooperation. War and conflict are the
exceptions (Vasquez and Valeriano 2010). Formally, consider a set of
autonomous political actors or players, $p\in P$, consisting of states,
international organizations, and subnational organizations. At each moment in
time, $t$, they engage in behaviors, $b\in B$, individually and towards each
other which they each then hold preferences over. Any player can transition to
a period of crisis when those behaviors swing toward “disruptive interaction
with a heightened probability of military hostilities that destabilizes
states’ relationships or challenges the structure of the international system”
(Brecher and Wilkenfeld 1982). The International Crisis Behavior project has
documented 496 such periods since 1918 (Brecher and Wilkenfeld 1997).
Formally, we can think of this as a simple Markov model with two discrete
latent states, stability $S$ and crisis $C$, $\Theta_{p,t}\in[S,C]$. This
latent state is in turn partially observed in the current and historical
behavior of the players.

The measurement strategy for the unobserved latent state is to use observables
like behaviors as proxies, $b_{p^{-}1,t}=F(\Theta_{p,t})$. When other players
are behaving badly, we think a player is strictly more likely to be in a state
of crisis. However, the policy-relevant question we want to answer concerns
the causal impact of a behavior on the continuation or resolution of a crisis,
$\Omega_{p,t}=F(b_{p^{-}1,t-1},b_{p,t-1})$. This reveals an immediate
conceptual difficulty. Behaviors appear on both sides of the regression
equation, first on the left hand side as a proxy measurement for the dependent
variable of state of crisis in time $t$ and then individually on the right
hand side as potential causes of crisis if observed in time $t-1$. This means
the definition and measurement of a discrete-time step within a crisis is
doing the majority of our conceptual work. This fact has created unending
confusion between measurement, explanation, prediction, and prescription in
the study of crises, and we tackle it directly below.

###  2.2 Defining Crisis

For now, imagine a stylized crisis with two discrete and clearly
distinguishable time steps, $t$ and $t-1$. In $t$, we want to know whether a
player is in a state of stability or crisis. We observe the behaviors of other
actors in time $t$, $b_{p^{-}1,t}$. International relations theory holds
strong beliefs about which behaviors are more crisis-like. For each behavior,
$b$, assign a weight $w=[w_{1},w_{2},...,w_{n}]$, representing the strength of
the signal it provides that a player is currently in a crisis state and the
discrete state is some function of the sum of each of these weighted observed
behaviors $\Theta_{p,t}=F(\sum^{n}_{i=1}w_{i}*b_{i})$.

We draw prior beliefs from international relations literature about the sign
and rank ordering of these weights across behaviors. Much of 20th-century
security studies was preoccupied with conventional warfare as the most extreme
behavior, e.g. the Correlates of War (COW) project. In the shadow of possible
nuclear war, scholars turned to measuring events that might be a precursor to
actual fighting, e.g. the threat, display, or use of military force short of
war recorded by the Militarized Interstate Disputes (MIDs) dataset (Maoz, et
al. 2019). Others recorded entire streams of events from news headlines
(McClelland 1978; Goldstein 1992; Azar 1993; Sherman 1994) and defined their
level of departure from stability by hand, e.g. Goldstein scores (Goldstein
1992), or through unsupervised dimensionality reduction, e.g. Item Response
Scores (Schrodt 2007). The ICB project took an even wider view, recording a
“trigger” for each crisis which could take one of 9 different forms (verbal
act, political act, economic act, external change, other non-violent act,
internal verbal or physical challenge to regime or elite, non-violent military
act, indirect violent act, or violent act).

The ICBe ontology divided crisis events into two conceptual categories across
armed actors vs unarmed actors and, given that, escalatory/uncooperative vs
de-escalatory/cooperative behavior, shown in Table 1 below. It further
recorded details related to scale and severity, like the number of troops
involved in an act, number of casualties, amount of territory exchanged, etc.
The labels of escalatory/de-escalatory were perhaps premature, and instead for
our purposes here we argue these are better thought of as indicators for and
against a state of crisis/stability within a single discrete time step.

###  2.3 Defining Escalation/De-escalation

We take exactly one time step back in our stylized crisis to $t-1$ and define
the relationship between a given behavior and crisis stability. For
simplicity, we assume the player is already in a state of crisis at $t-1$, and
so the only transition probabilities we are interested in are from crisis to
crisis, $P(C\rightarrow C)$, and from crisis to stability $P(C\rightarrow S)$.
Because the two outcomes are mutually exclusive, we can further consider just
a single transition, and so we choose $P(C\rightarrow C)$, the probability of
crisis being followed by more crisis. As before, we can think of all of the
same behaviors, $b_{p^{-}1,t}$, simply observed one time step earlier, and we
can assign another weight vector $\beta=1,2,..,n$, and specify some function
that maps the last period’s behaviors to the next period’s probability of
being in a state of crisis
$\Theta_{p,t}=F(\sum^{n}_{i=1}\beta_{i}*b_{t-1,i})$.

Unlike before, the theoretical literature on crisis stability is far more
divided on what those weights should be (Brams and Kilgour 1987; Powell 1989).
As a gross simplification, one major vein of literature views the weights of
escalation to be highly correlated with the weights indicating a crisis
(Colaresi and Thompson 2002), while another views at least some of the weights
as flipped (Spaniel and Idrisoğlu 2023).

###  2.4 Perspectives on Escalation

One might assume that doing more aggressive and destructive things would be
followed by even more aggression and destruction. Yet those same aggressive
actions might intimidate others into backing down. In one case, aggression
begets aggression, and in the other, aggression encourages submission.
Security dilemma models following from pessimistic assumptions tend to focus
on the first case, and relatively more optimistic deterrence models on the
second. Scholars have explored subtle situations in which even two well-
meaning players might find themselves caught in a conflict that neither of
them intended. The so-called spiral model considers tough talk and a forward
military posture to be inflammatory, exacerbating security dilemmas and
heightening the risk of war (Herz 1950; Smoke 1977; Jervis 1978; Glaser 1997).
Threats alert an adversary, weakening defense and triggering anticipatory
reactions. A nation targeted by an adversary with threats of retaliation
should be less likely to back down if there are reputational costs (domestic,
international) or psychological burdens for failing to fight (Jervis, Lebow,
and Stein 1989; Lebow and Stein 1989). Indeed, such threats may trigger action
where none exists. In the model above, the weights of escalation and crisis
indicators are highly correlated.

Another vein of literature argues that at least some of the weights should be
flipped. If weakness or uncertainty invites conflict, then some of the most
crisis-like behaviors may in fact be needed to transition back to stability.
Deterrence theory fundamentally sees conflict onset, and by extension
escalation, as a cost-benefit analysis (Freeman 2004). Nations that find war
prohibitive, or that are unwilling to endure the risks of escalation, are
unlikely to fight (Morgan 1977). Deterrence is most effective when threats are
clear, plausible, and consequential—when words credibly signal contingent
actions (Powell 1990). Deterrence theory thus advocates the use of threats to
impose costs or risks on a potential adversary in the hopes that the prospect
of risk or harm will derail aggression and discourage escalation (Brodie 1959;
Wohlsletter 1959; Snyder 1961; Schelling 1966; Waltz 1990; Danilovic 2002).
The empirical challenge in identifying deterrence success given strategic
self-selection into disputes (Fearon 2002) has motivated others to
disaggregate this idea further, introducing distinctions between, for
instance, immediate deterrence, where a state or other actor is seeking to
prevent an actual attack from an adversary, and general deterrence, where the
effort to discourage an adversary from even considering force as an option
(Huth 1988). Many other such nuances have been employed, highlighting the
underappreciated role of historical context in determining the escalatory
dynamics of any given crisis (Kreps and Schneider 2019; Cunningham 2020; Lin-
Greenberg 2023).

Despite the better part of a century of speculation and debate, experts have
been unable to establish a consensus theoretical understanding of escalation,
its causes, or likely triggers (Kahn 1965; Kydd 1997; Smith 1999; Sechser and
Fuhrmann 2013). Fundamental disagreement persists about what words or actions
are escalatory and which are more likely to reduce tensions between actors.
Other research questions whether crisis actions such as threats and
mobilizations are even a primary driver of crisis dynamics or if
circumstantial factors, such as power and distance, are sufficient to account
for actions and outcomes (see Stam 1996, Schultz 1998, Smith 1998, Gelpi and
Griesdorf 2001, Kinsella & Russett 2002, and Gartzke & Hewitt 2010 on
interests, Huth 1988 and Mearsheimer 1983 on capabilities, Banks 1990,
Slantchev 2010, and Fey & Ramsay 2011 on information, Gartzke 1999 and Chen et
al. 2022 on uncertainty, and Huth, Gelpi, & Bennett 1993 on nuclear weapons).
Scholars have begun to make sense of various conflict processes, creating the
opportunity to develop tools capable of predicting and assisting in the
evaluation of policy options (e.g., Hegre et al. 2017). However, contemporary
theories fall short of providing clear, consensus perspectives on escalation
management (Altfeld 1983, Diehl 1985, Nalebuff 1986, Moul 1988, Fearon 1994,
Carlson 1995, Bueno de Mesquita, et al. 1997, Reed 2000, Huth and Allee 2002).
Ambiguity is rooted in the conflicting spiral and deterrence frameworks that
have developed to explain crisis dynamics.

Both the classical spiral and deterrence frameworks are rooted in earlier
intuitions about the nature of war. More recently scholars have come to
appreciate the centrality of bargaining in conflict processes (Fearon 1995).
In this view, actors are strictly better off coming to a mutually advantageous
deal rather than engaging in costly conflict, which destroys the bargaining
surplus, but they also have incentives to misrepresent their capabilities or
intentions to get a better deal without fighting. Yet, this means that there
is an important endogenous role for bargaining moves in a crisis that can
either resolve or exacerbate information problems (Gartzke 1999; Coletta and
Gartzke 2003).

Process matters, as historians have long understood, but the spiral and
deterrence models do not explicitly incorporate contingency. Process seems to
be more relevant in the spiral model, which implies a long history of tit-for-
tat interactions building up to an explosive crisis, yet even here, each event
is assumed to be positively correlated with a greater likelihood of war in the
future, so the temporal sequence is less relevant than it first appears. The
deterrence model, likewise, cannot explain why the same type of move, say the
mobilization of troops on a border or deployment of warships to a coast, is
followed by stability in one crisis yet instability in subsequent crises. The
string of crises leading up to World War I is only the most obvious example.
To use the terms of the illustrative model above, there is some other vector
of $X$ contextual conditions that determines whether escalatory weights are
correlated one way or the other. Classical theories are underdetermined
because they’ve just taken a coarse average over all of those conditions.

###  2.5 The Measurement Problem in Escalation Research

At least part of the difficulty with making sense of escalation empirically
lies in the limitations imposed by existing data. Conventional datasets in
international security either code outcomes or events, which means that the
conflict processes modeled above are aggregated into discrete data points.
However, escalation is a process, a series of relationships that both tie
events together across time and that are sequentially meaningful or
significant. Immediate deterrence implies a general deterrence failure
(perhaps). A spiral requires triggers and effects, each related to the other.
If researchers lack information about what might be called the “begats” of
international relations—what factors preceded and precipitated outcomes of
interest—then it will be difficult to decide whether deterrence or a spiral
even occurred, let alone how they work and why.

There are generally two types of datasets that code conflict behaviors in
international relations, conflict and events data. Conflict data provides
information about outcomes. Events of interest such as wars, disputes, or
other behaviors are recorded, with dates and other relevant and useful
information (actors, initiator/target, intensity, location, etc.) included to
aid researchers in conducting analysis. A prominent example of conflict data
is the Correlates of War dataset, especially the Militarized Interstate
Disputes (MIDs) dataset (Maoz, et al. 2019). While far from perfect, these
data have been utilized in hundreds of studies over decades. They are
considered fairly reliable. However, they do not specifically delineate why
outcomes of interest occurred. Indeed, this is generally the subject of
conjecture (hypothesizing) and testing using these data. It is especially
difficult to discern whether given outcomes are the product of other acts or
behaviors, such as is assumed to occur with escalation and other conflict
processes. A standard practice is actually to use statistical techniques
intended to eliminate any correlation between events in these data, due to
concerns about common priors (dependence) (Beck, et al. 1998; Carter and
Signorino 2010). Because of the structure and coding of conflict data, it is
thus extremely difficult to effectively assess claims about processes, such as
escalation, where values of given variables in the dataset are assessed to
discern whether they lead to other values.

A second, less common though important, and innovative form of conflict data
collection involves events datasets. Events data have a long history in
international relations (McClelland 1978; Goldstein 1992; Azar 1993; Sherman
1994), which has ebbed and flowed over time as new techniques have been
introduced and as theoretical and substantive interests evolved. In essence,
the promise of events data is the ability to capture precisely what conflict
data is missing, the “begets” in world affairs (Merritt, et al. 1993). By
collecting a large and, increasingly with the rise in computing power, vast
amounts of events the expectation was that the bonds between events would
become apparent also. Projects such as CAMEO (Schrodt 2012), ACLED (Raleigh
2010), and others have managed to hoover up enormous quantities of data. The
problem has been what to do with it, and how to make it make sense of the
world.

As it turns out, there may not be a direct connection between the amount of
information (number of events) collected and the ability to capture the
“begats” that are intrinsic to making sense of processes. We just do not know
in a large corpus of conflict events what prior events do to make subsequent
events more or less likely. Lacking clear theory or correlates, the tendency
has been to “bin” events, creating counts by type or intensity by time period
that begin to look much more like conflict data than was originally the intent
of events researchers. We propose a different, hybrid approach seeking to sort
out cause and effect in studying escalation, at least as an interim measure.

##  3 Data and Measurement Strategy

We employ narratives of 475 crises recorded by the ICB project version 12\. To
measure the actions that take place within those crises we employ the
International Crisis Behavior Events dataset (ICBe) (Douglass et al. 2022).
Human codings are provided by ICBe v1.1, which we subset to just expert-
trained coders (discarding additional novice student coders). Machine codings
are provided by ICBeLLM (Douglass et al. 2023), which uses a large language
model with engineered prompts to approximate the human application of the ICBe
ontology to crisis texts. To maximize precision, we keep only details that
were reported by at least two experts or by one expert and the LLM. The raw
unit of analysis is the crisis-sentence-actor set (n=15,487). An actor-set is
a unique combination of values for {think_actor_a, say_actor_a, say_actor_b,
do_actor_a, do_actor_b}. Each sentence can then be mapped to multiple events
as long as those events involve the same actors (e.g. an action by actor A
against actor B can be coded alongside a different action by actor B against
actor A, and a speech act can be coded in addition to a separate action,
etc.). The inclusion of ICBeLLM increases the number of observations from
9,358 expert human coder-only events to 15,487 events total, a 65% increase in
the sample size without compromising quality and without hiring and training
additional human coders.

###  3.1 Unit of Analysis

Our unit of analysis is the crisis-time step. We have 475 crises. Our stylized
example crisis had only two time steps, whereas we estimate between 2 and 68
time-steps (median 13) for our corpus of narratives. There are 7,126 crisis-
time steps in total. A time-step is defined as a sentence in a narrative that
generated any ICBe/ICBeLLM events. We aggregate all behaviors observed across
events within that time-step, e.g. a sentence describing a threat by one actor
and an attack by another are all assigned to that single time step.

###  3.2 Measuring Crisis – ICB Universe of Crises

We rely on the human judgments of the ICB project to define the start and stop
of a crisis. We imagine the qualitative coding process as dragging a
convolutional filter across a sequence of behaviors and then firing once the
perceived departure from the norm reaches sufficient strength. When the ICB
narrative stopped describing events for that crisis we consider that a
transition from crisis to stability.

###  3.3 Measuring Escalation/De-escalation – Time Until Crisis End

Our outcome of interest is the number of time steps remaining until a given
crisis ends, $Y_{c,t}\in[0,...,max(t_{c})]$. Our stylized example crisis
consisted of only two time steps and a single transition. Our full crises
consist of multiple steps, any one of which could have transitioned to
stability. The number of steps remaining provides more information than a
single yes/no transition, and it has a nice intuitive interpretation. ‘Time
until crises end’ is a directly interpretable proxy measure of escalation/de-
escalation. A behavior that greatly increases the expected length of the
crisis is escalatory and one that shortens the length is de-escalatory. This
definition does not rely on pre-decided judgments of behaviors, and it allows
for theories that argue even more aggressive/violent behaviors might actually
shorten or deter a crisis altogether.

##  4 Modeling Strategy

Our ultimate goal is to be able to give policy decision-makers evidence-based
recommendations about what kinds of actions they can take to de-escalate a
crisis and restore a stable international environment. Unfortunately, we lack
the leverage to establish the necessary counterfactuals to make such strong
causal claims. However, with a large and increasingly detailed historical
repository of international events, we can achieve a related goal of giving
policymakers the analytical ability to see how an unfolding crisis compares
with other crises, especially those that are objectively “most similar” within
a given period of history. For any currently unfolding crisis, we should be
able to say that given events up until a certain point in time $t$ are the
most valid historical analogies with similar histories. Although history never
repeats itself exactly, knowing the distribution of outcomes among an event’s
nearest rhymes or whether an ongoing crisis has no near historical analogs is
itself useful for policymakers.

###  4.1 When Behaviors Appear in Crises

To illustrate the idea, we begin first with a simple descriptive exercise
arranging the types of behaviors we observe empirically in crises by when
(i.e. the time point) that they tend to occur within a crisis. Our unit of
analysis is the crisis-sentence-behavior. We calculate each behavior’s
relative position within a crisis by counting the number of behaviors
occurring before it and dividing this number by the total number of events,
$Y∈[0,1]$. The mean location within narratives across the entire corpus is
shown in Figure 1 below.

We find that behaviors align in time in a way that largely mirrors our prior
beliefs about what constitutes escalatory/non-cooperative versus de-
escalatory/cooperative behaviors. The ICBe ontology explicitly binned actions
into escalator/non-cooperative (red)—which we find here appear earlier in
crises—and de-escalatory/cooperative (green)—which we find appear later in
crises. The two groups are so strongly correlated with time within crises that
they are nearly linearly separable. Thought behaviors were not pre-divided
into types, but they similarly align over time with motivations for conflict
appearing early (start of crisis, territory aims, regime change aims,
preemptive aims, discovering or becoming convinced of a fact, etc.) and
thoughts ending late (perceptions of defeat, perception of end of a crisis).
Likewise, speech acts that appear early on in crises include accusations,
demands, ultimatums, and threats, while speech acts that tend to be associated
with the ending of crises include promises, offers, and acceptances. The
details of actions tend to appear earlier in crises, e.g. how many troops,
while the consequences, e.g. changes in territory, tend to come toward the
end.

###  4.2 Predicting Time Until Crisis Resolution

We can now move to analyzing variation within crises. Our unit of analysis
shifts to the crisis-time step, where each sentence of the crisis narrative
with coded ICBe events represents a single step. This measure (number of time
steps remaining until the termination of a given crisis) roughly represents
our earlier discussion of crisis resolution versus extension. When a crisis
begins at $t=0$, participants do not know whether it is going to last a long
time or end quickly. Once we’ve seen a few behaviors, we want to update our
beliefs and ask whether it is more likely that participants are getting closer
to, or conversely further away from a resolution of the crisis. Importantly,
we want to understand which behaviors signal the likely impending termination
of a crisis.

We want to predict the time it will take to resolve a crisis as a function of
the history of behaviors until time $t$, $Y_{c,t}=F(X_{t})$. We encode the
history of crisis behaviors as features of the crisis in the following way.
For each of the 140 possible behaviors/details, we calculate the number of
time steps since it was last observed (0 in cases where it appeared in the
current time step, 1 for one time step ago, etc.). For behaviors/details not
observed at all, we set them at an extreme value of 100, allowing our tree-
based estimator to intelligently bin events that never appeared with those
that appeared a very long time ago, or alternatively to split them off
entirely as a different category of behaviors altogether. We further add a
single control variable of the crisis number coarsened into five blocks of
~100, to account for the ICB crisis project trending toward writing longer
narratives for more recent years.

Our cross-validation strategy takes into account the nested-panel structure of
our data. We divide the $C=475$ crises into 10 test folds. For each test fold
($c=48$), we fit a model dividing the remaining crises, $c=427$, into a
training set of crises, $c=405$, and a validation data set, $c=23$. The same
crisis will therefore never appear in both training and test, or training and
validation, etc. Because we fit 10 different models predicting out-of-sample
for each of the 10 test folds, we are able to present results below that cover
the entire dataset and are based only on out of sample predictions.

We employ a gradient-boosted trees estimator, specifically LightGBM (Ke, et
al. 2017). We choose this estimator because of its speed, flexibility, and
predictive performance. It is nonparametric, allowing us to easily distinguish
differential effects of a behavior happening recently from long ago, and to
automatically search for interactions among behavior types. We optimize an L1
regression loss, mean absolute error, rather than mean squared error, which is
less sensitive to outlier very long crisis narratives, and empirically had
better out-of-sample performance.

Our estimand is the degree to which previous behaviors lengthen or shorten a
crisis, the degree to which a behavior is escalatory, the weights $\beta$
introduced earlier. We approximate that estimand using the out of sample
feature contributions of each behavior - time since observed. Our measure of
feature contributions is SHAP values which is a local approximate
decomposition of each feature’s contribution to the final prediction produced
by the full black box model.

The results are shown in Figure 2 below. The outcome is predicted time until
the end of the crisis (defined as no more events coded from the narrative).
Along the Y-axis each row lists the behaviors with the greatest contribution
to the model’s predictions. Along the X-axis, each column lists the number of
time steps in the past that behavior was last observed, with 0 being
concurrently to a given time $t$. The cells are shaded with the observed SHAP
value for that behavior last observed that many time steps ago, with bright
red reflecting a strong increase in the expected number of steps until the end
of the crisis and deep blue representing a strong expected decrease in the
number of steps until the end of a crisis. Behaviors are arranged in
descending order, from the largest expected increase in time until crisis end
to the largest expected decrease (sum each row’s total SHAP contribution,
dividing each cell’s value by the time since it was observed to place greater
weight on more recent acts).

We start by describing the easiest-to-understand behavior, “end of crisis,”
which is something that was explicitly mentioned in each crisis narrative and
coded by ICBe as a thought behavior. Once the narrative mentions that one of
the actors has decided that the crisis has ended, the model expects the whole
narrative to wrap up shortly and stop producing coded events. The effect also
grows stronger in time; the longer in the past that an end to the crisis is
mentioned, the more likely it is that the narrative really will be wrapping up
soon, until at some point the sign flips and it becomes more likely that the
crisis ended for only a subset of actors and the rest continued on their own
path. On the opposite end of the spectrum, forming a military alliance is most
indicative that the crisis is going to extend longer and as before the
strength is greatest the more recent the behavior was observed.

Zooming out, several general trends are immediately apparent. First, there was
a strong signal for only some behaviors with many having little or no
contribution to the model’s predictions (we show 123 of 140 here). This is a
function of the actual data-generating process (some behaviors are orthogonal
or redundant to crisis duration), to measurement (some behaviors are measured
or reported more noisily than others), and to the sample size (a larger corpus
would likely tease out the role of more behaviors). Second, the effect of a
behavior generally decays in time, with more recent events being more
informative than those that are more distant in time. Third, there is
variation in the degree of decay across behaviors. Figure 2 depicts a
triangle-shaped surface, with behaviors toward the middle still being
informative but only if they have occurred relatively recently (the shape is
an intentional artifact of the ordering).

Moving to a substantive interpretation, the types of behaviors that extend
versus those that reduce the length of a crisis lend support to some theories
of international relations more than others. We find the biggest winners to be
bargaining models of war (Fearon 1995; Wagner 2000, 2007) that see large
violent shocks as stability-inducing because they provide information to both
sides about who is likely to win should the contest continue (Shirkey 2016,
Weisinger 2013). Behaviors that indicate a crisis is coming to an end include
a perception of victory or defeat, a surrender or withdrawal from an area or a
retreat, a large gain in territory, and to a lesser degree even
battles/clashes and attacks. Meanwhile behaviors that indicate a lengthening
of the crisis are large changes in the international system that might
increase uncertainty, like the formation of a new military alliance (Benson
2012; Benson and Smith 2022), a political succession, a declaration of war, a
third party entering a way (Shirkey 2012), or a change in institutions change.

In terms of diplomacy, aggressive speech that might signal resolve like making
an ultimatum or breaking off negotiations, are more likely followed longer
crisis periods. Meanwhile engaging in mediation, making an offer without
conditions, even expressing disapproval, rejection, or acceptance, all
indicate the crisis is shifting to speech and away from actions and likely to
end sooner.222These could be associated with the end of a crisis because the
structure of the narratives describes mediation efforts at the conclusion of
the crisis summary. Later analyses could identify the time period when
mediation efforts occurred relative to the observed end of the crisis to see
if different patterns emerge. Mentions of grievances and specific topics are
also indicators of more time until resolution, such as threats or accusations,
fears or desires, territorial or policy aims, becoming convinced of a policy
fact, human rights violations, etc.

We stress that this is a purely observational research design that cannot
distinguish causes of crisis resolution from coincident indicators of a crisis
winding down. For example, mediation may not actually cause a crisis to end.
Rather, mediation may be associated with the end of a conflict process that’s
already begun to terminate for other reasons. That said, we do find unexpected
correlates in behaviors we considered escalatory/un-cooperative being
associated with a crisis ending sooner and others that we have considered de-
escalatory/cooperative being associated with a crisis persisting for longer
periods of time. In particular, the ones that flipped appear to be consistent
with a bargaining model view of international conflict, with cooperative acts
that signal major realignments—and thus create additional
uncertainty—extending crises, while escalator/uncooperative acts that kill and
destroy but provide information being more often associated with bringing a
crisis to a close.

From the perspective of the debate between deterrence and the spiral model,
these results are much less supportive. Preparing to fight a war and actually
declaring it are closely related, and so mobilizing forces, events involving
tens of thousands of troops, conducting a weapons test, and other similar
events that potentially transmit information about resolve (signaling) all
tend to indicate that the crisis is just warming up. Likewise, intensive
fighting and to a lesser degree just fighting in general tend to indicate a
crisis is coming to an end. As a mental model, this corpus of crises can be
thought of as long lead-ups in grievances and disputes ending either in
diplomacy or exploding in the use of decisive violence. To the degree that
decisive violence is self-perpetuating, it is more likely to be evidenced in
the creation of new crises between the same actors over years as they regroup
and find a new approach/vector to attack one another.

##  5 Case Examples

In this section, we detail three case study examples that help to illustrate
how behaviors impact expectations over the course of a crisis. Additional
details of each case are depicted in Figure 3. The Y-axis in Figure 3 reports
the predicted number of steps estimated to remain in the crisis. The X-axis
details the step T in the crisis (note that the length of each crisis
differs). We annotate each point with the behavior that most strongly
contributed to a given prediction (colored by the strength and direction of
that particular contribution).

For example, at the first time-step of the Cuban Missile Crisis, the model
estimates that there are likely to be 10 more steps, which is driven primarily
by the global average and partly by the only information seen so far in the
behaviors of just that first step. The behavior in that first step that most
contributed to the prediction was that the United States discovered a fact,
leading the model to increase the expected length of the crisis. The next step
contained little information keeping the number of expected steps at 10
despite advancing 1\. In the third step, the model lowers its expected length
because of a rejection combined with the mobilization last observed only 2
steps prior. In this way, the model proceeds downward and to the right,
updating its expectation given the full history observed thus far. A series of
back-to-back promising signs, colored in blue, reduce the predicted length of
the crisis (e.g. withdraw from an area, mediation, mediation, withdraw), until
the shootdown of the U-2 spy plane which sparks an increase in the expected
length of the conflict. It does not begin to decline again until the signing a
formal agreement, a withdrawl from an area, and then an explicit end of crisis
craters the expectation to only 4 steps remaining. At some steps, the
behaviors of the top feature provide no clear signal, with small SHAP values
(gray color).

The three example cases vary in their overall temporal signature. The Cuban
Missile Crisis is U-shaped with a high level of intensity early on with a
reversion right toward the end. The Gulf War has three distinct phases,
starting first with the invasion of Kuwait, which is followed by furious
negotiating and brinkmanship, which the model predicts will end the crisis. In
the second phase, the coalition makes an ultimatum to invade and there is
another round of negotiation. A final third phase signals the start of the
war. Finally, the Crimea-Donbas crisis began with intensity but then stair
stepped down once mediation between the two sides began.

To see how representative these temporal trends are we next cluster the
predicted number of remaining steps at each time point for every crises, shown
in Figure 4 below. We find several general patterns similar to the case
studies above, across 6 clusters: crises that resolve almost immediately,
crises that begin to resolve but then revert to a high unsatisfying level of
hostility, crises that stair step down in escalation, and finally crises that
stair step upward over time. We interpret this as evidence of intermittent
rounds of fighting and bargaining within crises. This demonstrates the
importance of scale in measurement. Some of these crises have episodes and
breaks within them. Earlier we noted that beyond a certain scale of conflict,
events are likely broken down across separate crises over years. How we
interpret the consequences of a particular behavior turns on our beliefs about
the importance of the short-, medium-, and long-term consequences of a
statement, action, or outcome. Future work will need to pay close attention to
the endogenous nature of how combatants define the start and end of a crisis,
and how social scientists in turn choose to group events and periods into
large constructs when conducting their analyses.

##  6 Discussion

The research design here is purely observational and will require additional
strong priors to make causal determinations from otherwise correlational
findings. That said, we provide two different views on empirical regularities
in crisis events that allow us to begin the process of a more intensive, and
detailed, disentangling of causal claims. The first view lays out a large
number of behaviors (140) on an intensity scale from most to least escalatory
as represented by whether they tend to appear early in a blooming crisis (more
escalatory) or later when a crisis is winding down to its conclusion (less
escalatory). That proxy view very closely approximated our prior beliefs used
in building the original ICBe ontology and distinguishing
escalatory/uncooperative events from de-escalatory/cooperative events. The
second view we provide complicates the picture more and asks what kinds of
events are most indicative that a crisis is likely to end soon. We find
suggestive evidence that there may be certain types of events that can shock a
crisis into a quick conclusion - such as military contests that result in
territorial shifts, surrenders, or major realignments through coups or a
third-party joining in a war. Likewise, we found suggestive evidence that
certain kinds of behaviors are associated with causing or extending a crisis,
like changes in international millitary alignment or shifts in internal
institutions.

Much remains to be done to untangle relationships and to clarify cause and
effect. The relationships we identify are correlations, not causations. But
this may be sufficient if the goal is simply to delineate factors that are
associated with de-escalation, rather than making specific causal claims. Much
of our findings suggest that the classical dialectic between deterrence and
the spiral model is at best broadly descriptive and has little predictive
value. Deterrence may be influencing behavior earlier on before a crisis
manifests (i.e., general deterrence). Consistent with other findings
(Beardsley, et al. 2024), we find little evidence in our analysis to support
claims that immediate deterrence works as predicted in theory; actors are not
de-escalating because an adversary escalated. At least, it is far from clear
that this dynamic is in any way modal. Instead, it appears more usual for
states to mirror image one another, escalating when the other does so, and
vice versa.

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