#  Politicians’ Willingness to Agree:
Evidence from the interactions in Twitter of Chilean Deputies

Pablo A. Henríquez<EMAIL_ADDRESS>Jorge Sabat<EMAIL_ADDRESS>José Patricio Sullivan<EMAIL_ADDRESS>Faculty of Business and
Economics, Universidad Diego Portales  Washington University in St. Louis

###### Abstract

Measuring the number of “likes” in Twitter and the number of bills voted in
favor by the members of the Chilean Chambers of Deputies. We empirically study
how signals of agreement in Twitter translates into cross-cutting voting
during a high political polarization period of time. Our empirical analysis is
guided by a spatial voting model that can help us to understand Twitter as a
market of signals. Our model, which is standard for the public choice
literature, introduces authenticity, an intrinsic factor that distort
politicians’ willigness to agree [Trilling, 2009]. As our main contribution,
we document empirical evidence that ”likes” between opponents are positively
related to the number of bills voted by the same pair of politicians in
Congress, even when we control by politicians’ time-invariant characteristics,
coalition affiliation and following links in Twitter. Our results shed light
into several contingent topics, such as polarization and disagreement within
the public sphere.

###### keywords:

Disagreement; Polarization

##  1 Introduction

Since Poole and Rosenthal [1985] dozens of papers have tried to infer
politicians’ ideology using voting data. Similar analysis have also been
conducted using campaign contributions [Bonica, 2013], surveys and texts
[Laver, 2014]. Bølstad and Dinas [2017] suggest that these applications of the
spatial voting theory can successfully identify clusters of political actors
that can be associated to the same ideology (e.g. left and right-wing
coalitions).111The empirical analysis of these political networks follows a
revealed preference approach where politicians and voters’ preferences could
be characterised from their observed political behavior [Henry and Mourifié,
2013]. However, this methodology is mostly agnostic of the many endogenous
factors that determine the positions of political actors in the network, being
very effective on localizing political actors but not on offering explanations
for how and why they reached that position. In this paper we look into how
political communication, understood as a channel of agreement and
disagreement, can determine how politicians reach a given position within the
political spectrum.

We follow Barberá [2015], who complements the analysis of politicians behavior
using interactions in Twitter (e.g. “retweets” and “following” links) of U.S.
political actors.222A “retweet” is a re-posting of a Tweet (message) from
another user in Twitter. A “follower” is someone that decides to receive the
Tweets of another user. Our main contribution is to augment the analysis of
politicians’ behavior by combining their Twitter interactions with voting data
from Congress. Specifically, we exploit Twitter “likes”, a strong signal of
appreciation from one user to another, to measure instances of agreement in
the public political debate among politicians in Chile.333We understand the
public political debate in a Habermasian sense, this is, as a public sphere
where different actors try to advance their positions trough communicative
rationality. We use this empirical setting to test our main hypothesis,
communications dynamic in Twitter does not translate into voting agreement,
after controlling by by politicians’ time-invariant characteristics, coalition
affiliation and following links in Twitter.

Our main empirical result is that, after including the different controls, on
average, politicians that agree in Twitter agree less in Congress. This
empirically puzzling result is explained by a differential effect based on
coalition affiliation. We find that, at the same time, the number of “likes”
is negatively (positively) related to bills voted in Congress by coalition
mates (opponents).

Our results can be interpreted using a public choice model. In the model,
politicians use “likes” as signals for manipulating voters’ beliefs. The model
is standard in the sense that politicians decide based on electoral incentives
(popularity). However, we include a non-standard mechanism based on
authenticity. Following Trilling [2009], we argue that politicians weight
being consistent with their own ideology. We use authenticity as a factor that
generates a trade-off between popularity and ideological consistency. Under
the theoretical implications of our proposed public choice model, we suggest
that our analyzed interactions are consistent with a fraction of politicians
taking authenticity into account at the moment of deciding which “tweets” to
“like”. In addition, our model suggest that “likes” between opponents work as
costly signals of political agreement, while “likes” between coalition mates
would work as signals of group loyalty.

Chile is an interesting setting to test our hypothesis. Our interest is
related to the different political cleavages that have shaped the political
landscape since its return to democracy in 1990 [Bonilla et al., 2011], as
well as, the evidence of “centrifugal forces” generated by the electoral
system early documented by Dow [1998]. After the return of democratic
governments, Chile set up for a fast-paced economic development, sustained on
free market-oriented policies and a stable political system, which transformed
Chile in one of the best performing countries in the region [Barro, 1999].
However, in October 2019, after almost three decades of sustained growth, the
country’s social stability crumbled under huge protests and popular
demonstrations against economic inequality. The political parties reacted by
proposing a referendum to reform Pinochet’s Constitution. In October 2020, a
referendum took place, with an overwhelming majority approving the rewriting
of the constitution trough a democratically-elected Constitutional Assembly.
Consequently, we argue that the current political situation in Chile offers a
unique setting to analyze how politicians can reach agreement in a highly
polarized political environment.

This paper intends to contribute to three strands of the literature. First, we
contribute to the empirical spatial voting literature pioneered by Poole and
Rosenthal [1985], which focuses on identifying coalitions and other political
associations using data on politicians’ voting behavior, campaign
contributions [Bonica, 2013], or surveys and text [Laver, 2014]. Second, we
contribute to the literature on disagreement, which acknowledges the
importance of rationality as a mechanism to reach agreement [Habermas, 1998,
Aumann, 1976]. This theoretical predictions based on rationality are
inconsistent with persistent disagreement observed in societies ($cite$). The
persistence of disagreement has been explained by behavioral theories of
homophily [Halberstam and Knight, 2016] or identity [Taylor and Bosworth,
2020]. Finally, our study has implications for research on polarization.
[Zhang et al., 2008] proposes modularity as a measure of polarization based on
network theory. On the other hand, social scientists have studied polarization
using a different approach, categorizing it as either ideological, affective
or perceived [Fiorina and Abrams, 2008, Iyengar et al., 2012, Hetherington et
al., 2016].

The paper proceeds as follows. In Section 2 we describe the institutional
framework. In Section 3 we review relevant related literature in spatial
voting theory, political disagreement and polarization, highlighting how they
connect with the present study. Section 4 provides a description of our three
data sets: the CEP survey, interactions of politicians in Twitter and the
bills voted in the Chilean Chamber of Deputies. Section 5 outlines our public
choice theoretical model. Section 6 we detail our empirical approach to test
our proposed hypothesis. In Section 7 we present our results. Finally, in
Section 8 we provide our main conclusions with some open ended discussion
questions for future research.

##  2 Institutional Framework

Chile returns to democracy in 1989 after Pinochet’s dictatorship. The
Constitution established that Congress is divided in two Chambers. The Chamber
of Deputies with 120 members, and the Senate with 38 members. The electoral
system that ruled the allocation of seats in both chambers was a variant of
the well studied D’Hondt electoral system, a system locally known as
“Binominal”. As has been analyzed by Dow [1998], the Chilean variant forced
the formation of two coalitions formed by multiple parties. This incentive is
set by mandating that each coalition presents two candidates by district. The
“Binominal” system awarded the first seat based on the largest number of votes
by coallition. However, if the combined number of votes is more than 2/3 of
the total votes in that district, the candidates of the same coalition win
both seats. Otherwise, one seat goes to each coalition. Authors have suggested
that proponents of the system believe that it maintained political stability,
at the same time that caused malapportioned [Riquelme et al., 2018]. Moreover,
Dow [1998] suggested that favor reward extremists and punish moderates.

In 2009, after 37 years without parliamentary representation, the Communist
Party returned to Congress, trough the election of 3 deputies. This electoral
victory was made possible by a deal with the left wing coalition, which
presented no candidate in some districts. Later, in 2013 the Communist Party
and other independents group joined the left wing coalition for the
Presidential and Congressional Elections. One of the main objectives of this
coalition was to reform the electoral system to increase the representation of
new groups that have been excluded from parliamentary representation.

In 2017 the Chilean electoral system was reformed for a traditional D’Hondt
system. This reform has coincided with the downfall for the traditional left,
and the increasing representation of the radical left and right wing groups
[Bunker, 2020]. Moreover, Fábrega et al. [2018] suggest that this electoral
reform is related to a latent political polarization that started in the
2000s.444Fábrega et al. [2018] suggest that the student protests of 2006 and
2011 are early signs of their measured political polarization.

In October 2019, after almost three decades of sustained growth, Chile
experienced a series of protests, an political unrest against economic
inequality. The political parties reacted by proposing a referendum to reform
Pinochet’s Constitution. In October 2020, a referendum took place, with an
overwhelming majority approving the rewriting of the constitution trough a
democratically-elected Constitutional Assembly.

During 2020 Chile has been affected by the COVID crisis, which in the context
of the 2019 social outbreak, has been a new source of disagreement for Chilean
politics [Oyarzún-Serrano, 2020].

##  3 Related literature

Our contribution to the literature is threefold. First, we contribute to the
empirical spatial voting literature that focus on recovering estimates of
politicians’ preferences (e.g. ideological positions) from their observed
voting behavior. A methodological approach pioneered by Poole and Rosenthal
[1985]. In more recent times, the same approach has included other types of
data sets, such as campaign contributions [Bonica, 2013], or surveys and texts
[Laver, 2014]. As Bølstad and Dinas [2017] suggest, applying this
methodological approach, several studies can successfully claim that they are
able to identify coalitions and other political associations. However, this
literature tend to be agnostic of the factors that can explain why two
politicians are voting in favor of the same law, other than the estimated
ideological closeness. In this paper, following Barberá [2015] we augment
voting data with interactions from Twitter. As opposed to Barberá [2015], who
analyzes ’retweets’, we focus on ’likes’ among deputies. A more direct signal
of appreciation that has been used to understand social networks in other
contexts [Wachs et al., 2017].

Second, we contribute to the literature that studies political disagreement.
Hinich and Munger [1996] propose that ideologies are a way to resolve
political disagreement with respect to three questions: what is good, who gets
what and who rules. In this interpretation, ideologies work as theorizations
of politicians’ own position in the political arena [Martin, 2015].555Martin
[2015] proposes that ideologies are not necessarily internally consistent.
However, ideologies would provide a representation of political alliances, and
more importantly, the nature of political opponents. In practice, political
disagreement would take the form of arguments.666Hinich and Munger [1996]
cites the case of the minimum wage debate analyzed by Friedman [1966].
Political disagreement in this case can be easily disentangled into values,
and different predictions over the effects on the poverty rate or the labor
market. In the “ideal speech situation” posed by Habermas [1979], if all
parties seek the truth and they do not behave strategically, this would lead
to the “best argument” to win, as has been argued by Habermas [1998].
Moreover, in theory, is well known since Aumann [1976] that, if it is common
knowledge that both parties are Bayesian rational, they cannot agree to
disagree on matters of fact. These theoretical results enter in contradiction
with the empirical evidence that suggests that disagreement is a very
persistent process. A finding that has also been associated with behavioral
theories of homophily [Halberstam and Knight, 2016] or identity [Taylor and
Bosworth, 2020]. At the same time, other authors argue that the internet have
exacerbated the emergence of echo chambers [Sunstein, 2008]. We contribute to
this literature combining new data from Twitter, that allows us to identify
instances of agreement between politicians, and matching it with bills voted
in favor in Congress. Trough a political economy model, we argue that our
analysis can shed light on the willingness to agree of politicians.

Third, we contribute to the broad literature on political polarization. Zhang
et al. [2008] proposes to study polarization using network theory, where the
network’s modularity is calculated using votes by U.S. Congress
members.777Intuitively, the modularity corresponds to an aggregated measure of
the intra-coallition versus inter-coallition interactions. For more details
see A. On the other hand, social scientists have studied polarization using a
multidisciplinary approach, understanding the phenomena either as ideological,
perceived or affective. Ideological polarization measures the differences
among policy choices and political positions. For example, Fiorina and Abrams
[2008] argued that there is no conclusive evidence of higher polarization of
citizens’ ideological positions in the U.S. Perceived polarization accounts
for how individuals perceive more polarization than actually exists. Thus
assuming that out-party members are farther away from them on the ideological
continuum than they actually are, according to measures of their survey
preferences [Enders and Armaly, 2019]. Affective polarization measures the
animosity between political opponents, heavily dividing the spectrum between
in-group and out-group. Iyengar et al. [2019] found that Democrats and
Republicans both say that the other party’s members are hypocritical, selfish,
and closed-minded, and they are unwilling to socialize across party
lines.888Westfall et al. [2015] provides evidence of higher perceived
polarization among individuals that identify more with the Republican or
Democratic parties in the U.S. Our paper intends to contribute to the
multidisciplinary literature on polarization trough the empirical analysis of
a polarized society (measured by modularity) during the 2019-2020 period. A
society that has experienced increasing levels of polarization in the last two
decades according to Fábrega et al. [2018]. In contrast to most of
polarization studies, we focus on the instances of depolarization, analyzing
cross-cutting votes and “likes”.

##  4 Data

###  4.1 Data sources

In this paper we combine different public data sources, from a public opinion
survey conducted by the Centro de Estudios Públicos (CEP), Twitter, and the
Chamber of Deputies of Chile.

####  4.1.1 CEP political opinion survey

We study Chile’s ideology distribution of voters from the CEP political
opinion survey because it intends to be nationally representative, and it has
been published periodically since the 90s. We mainly focus in the May 2019
version.999The field work last 2 months approximately.101010This data has been
used to analyze Chilean politics in the empirical Public Choice literature,
see Bonilla et al. [2011]. We choose this version because it precedes Chile’s
political unrest event of October 2019. The study surveyed 1,380 citizens of
the 128 most important counties in Chile. In addition to different socio-
demographic questions, the study also ask about political opinions of well-
recognized politicians, and their self-reported ideology, in a discrete 1 to 5
scale. In Figure 4, we highlight how the estimated non-parametric distribution
is far from a normal distribution, where most of voters would be bunched
around the center. It is worth mentioning that Figure 4 considers the roughly
55% of people that do not self-identify with any of these categories, a common
phenomena in Latin American politics [Ruth, 2016].111111In our calibration of
the model, unknown voters are going to be uniformly distributed in the 1 to 5
axis. From the same opinion survey, we can recover politicians ideology using
the self-reported ideology variable described above, and the public opinion of
well-known politicians.121212Our proposed method is explained in B. In Figure
8, we plot the regression coefficients that measure politicians’ ideology.
Interestingly, our estimates suggest that voters would not see a lack of
supply of politicians with different ideologies.131313For a more detailed
analysis of the sampled 28 politicians see Figure 5.

####  4.1.2 Twitter

Twitter “likes” are obtained using Twitter API. We generate a script to
collect the last 500 “likes” for every Chilean deputy that can be tracked in
Twitter. Data extraction occurs at different points of time during the
2019-2020 period, which covers October 2019 Chile’s political unrest, and the
first year of the COVID crisis.141414For a description of time periods see
Table 3. The Twitter database is structured as a panel dataset, where we can
track the number of “likes” between deputies during the studied time window.
In addition, from the same source we can record if one politician follows
another. On average, politicians in our sample send 2.74 messages in Twitter
(“tweet”) a day. However, the number of messages per day by politician is
highly skewed, with the top ten users “tweeting” more than 8 times a day. In
Table 1 we can see that the number of interactions that we are following in
Twitter is increasing over time. This is explained by the higher number of
deputies start using Twitter after the Chilean unrest event of October 2019,
and also after the COVID crisis started. The average number of “likes” is 0.45
for the whole period. However, this number can vary over time as is observed
in Table 1. From the same table, we can see that the probability of observing
a deputy giving a “like” to an opponent (Opponents Mean) is less than a tenth
of the pooled mean (Opponents All). On the other hand, we also find that the
unconditional probability that a deputy follows an intra-coalition mate is
roughly 47%, which compares higher with the approximately 18% probability that
a politician follows an opponent.

####  4.1.3 Chilean Chamber of Deputies

Voting records are obtained from the website of the Chilean Chamber of
Deputies. Using data scrapping, we collected all voting records by politician,
before Twitter data is collected. We collected bills voted around 40 days
before interactions in Twitter are retrieved. We do this as an intent to study
the interactions in Twitter and Congress during the same time window. In Table
1 we can see that, on average, the number of bills voted in favor among all
deputies is not very different to the number of bills voted between opponents.
This finding is consistent with politicians disagreeing more in Twitter than
in Congress.

Table 1: Summary Statistics | Tweet likes | May-19 | Oct-19 | Feb-20 | Jun-20 | Dec-20
---|---|---|---|---|---|---
All | Mean | 0.47 | 0.48 | 0.41 | 0.39 | 0.49
Median | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
Std. Dev. | 5.80 | 5.84 | 5.12 | 4.50 | 5.49
N | 8113 | 8640 | 8640 | 10530 | 12727
Opponents | Mean | 0.02 | 0.02 | 0.04 | 0.03 | 0.05
Median | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
Std. Dev. | 0.21 | 0.21 | 0.45 | 0.29 | 0.48
N | 3980 | 4252 | 4252 | 5180 | 6339
| Votes in favor | May-19 | Oct-19 | Feb-20 | Jun-20 | Dec-20
All | Mean | 77.02 | 91.78 | 82.52 | 72.93 | 82.33
Median | 77.00 | 92.00 | 76.00 | 74.00 | 75.00
Std. Dev. | 23.72 | 28.25 | 35.33 | 17.19 | 41.36
N | 8113 | 8640 | 8640 | 10530 | 12727
Opponents | Mean | 68.64 | 91.96 | 85.30 | 73.61 | 81.29
Median | 68.00 | 92.00 | 78.00 | 75.00 | 77.00
Std. Dev. | 19.32 | 27.44 | 37.59 | 16.20 | 32.15
N | 3980 | 4252 | 4252 | 5180 | 24003

###  4.2 Network construction

In this section we describe the construction of indirect networks based on the
interactions of politicians in Twitter and Congress. Specifically, we
construct weighted networks $G_{i}=(V_{i},E_{i},W_{i})$, where $V_{i}$ is the
set of nodes corresponding to “likes” or votes in favor between politicians,
$E_{i}$ is the set of edges between them, and edge weights ($W_{i}$)
corresponds to the Pearson correlation coefficient. By setting a threshold
$\theta=0.1$, we can transform correlation matrices into correlation networks.
In Figures 1 and 2 the networks of votes in favor and “likes” are presented.
As we can see, consistently with the summary statistics presented in Table 1,
the density of “likes” between politicians is lower than in Congress. In other
words, agreement between deputies appear to be more common in Congress than in
Twitter. On the other hand, the network figures also suggest that deputies
tend to interact more with politicians from the same coalition, which is
consistent with the evidence of homophily documented by Halberstam and Knight
[2016] using Twitter data related to politically-engaged users.

In order to provide a further characterization of the networks we follow
[Zhang et al., 2008], which proposes modularity as a measure of political
polarization. We calculate the modularity of the network following Newman
[2006] 151515See A for more details.. In our application of his method we need
to first identify relevant communities in Congress and Twitter to then
quantify the severity of such a divisions. Intuitively, modularity measures
network segregation into these distinct identified communities. For example, a
network with high modularity would be divided into clusters having many
internal connections among nodes, and few connections to other communities. In
the literature, we find different ways to identify communities [Ribeiro et
al., 2018]. In our paper we use the Louvain algorithm [Blondel et al., 2008],
as well as the Edge betweenness algorithm [Newman and Girvan, 2004] as a
robustness check.161616The Louvain method is based on a greedy optimization
method, while the edge betweeness algorithm is an iterative process based on
betweenness centrality. In Figure 3 we present the evolution of the modularity
of the networks constructed with data from Congress and Twitter. Our
quantitative analysis confirm the intuition provided by Figure 1 and Figure 2.
First, estimated polarization is notably higher in Twitter than in Congress,
until the Chilean political unrest event of October 2019. However, our results
suggest that this event, as well as the COVID crisis are associated with an
important increase in the polarization in Congress.171717The decline in
modularity of the network of votes in favor by June 2020 is related to the
cross-party agreement of an emergency coronavirus plan.181818Our results
appear to be robust to the methodological choice of community detection
algorithm. Finally, is important to highlight that our measured levels of
polarization in Twitter ($\approx 0.4$) are consistent with the highest levels
of modularity found by Waugh et al. [2009] using roll call votes from the U.S.
House during the 1788-2004 period, and Conover et al. [2011] findings obtained
from a network of “retweets” related to politically relevant “hashtags” during
the congressional midterm election of 2010.

Figure 1: Network analysis of bills voted in favor. Figure 2: Network analysis
of “likes”. Figure 3: Evolution of the modularity measurement. We considered
the groups obtained via community detection method.

##  5 Theoretical model

In this section, we outline a public choice model that is used to interpret
the cross-section of “likes” in Twitter among Congress members. The model
considers a finite number of politicians that compete in a voting market. We
assume that the voting market is populated by politicians that have different
ideology types. An ideology type $i$ is well described by draws from a normal
distribution with parameters $\mu_{i}$ and $\sigma_{i}$.191919The practical
implication of this assumption is that, in our model, some politicians are,
exogenously more ideologically flexible than others, regardless of their
ideological positions. On the other hand, voters form beliefs about
politicians’ ideological positions. Voters can be simply characterised by a
discrete distribution in a one dimension political axis (right to left wing).
Society is fragmented into K political groups with ideology ($i_{k}$) and a
population weight ($p_{k}$).202020The specific parameter assumptions that
govern the electoral population are shown C. Specifically, we highlight that
in our model a more normally distributed electoral population is related to
less polarization among elected politicians.

The dynamic of the political competition in the model occurs within
coalitions, or ideology groups. This assumption is related to the D’Hondt
proportional representation rule that governs the Chilean Chamber of Deputies,
which seeks to elect Congress members in proportions that better represent the
electoral population.212121Until 2017 Chile had a modified D’Hondt system with
two seats by electoral entity [Dow, 2001]. It has been argued by this system
forced bipartisanship trough the formation of two coalitions in order to
maintain political stability [Riquelme et al., 2018]. In the model, $N$
politicians sort into $n$ coalitions. Then, within the coalition, politicians
gain electoral power based on the minimum distance to all competitors in the
group. Ideological distance between politician’s $i$ with respect to group of
voters $k$ is calculated as follows:

$\displaystyle d_{i,k}=\big{(}\mu_{i}-i_{k}\big{)}\dfrac{1}{w_{k}}$ (1)

where a positive (negative) value for $d_{i,k}$ measures how much to the left
(right) is politician’s $i$ from group $k$, and $\dfrac{1}{w_{k}}$ is a factor
that penalizes the focus on smaller groups of voters.

Politicians, within a coalition, compete based on distance $d_{i,k}$.
Political power within the coalition is related to votes, which are
endogenously determined by the distance between politician $i$ and political
group $k$:

$\mathbbm{1}_{i,k}=\begin{cases}1&\text{if
}d_{i,k}=min\big{\\{}d_{i,1},...,d_{i,K}\big{\\}},\\\ 0&\text{if
}$\text{otherwise}$\end{cases}$

By assumption, within the group, political power depends on the number of
votes (weighted by population) that politician obtain:

$\displaystyle v_{i}=\sum_{k=1}^{K}\mathbbm{1}_{i,k}w_{k}$ (2)

The ideology of the political front-runner, within the coalition, is based on
the highest number of votes within the coalition:

$\mu^{f}_{k}=\begin{cases}\mu_{i}&\text{if}\;\;v_{i,k}=max\big{\\{}v_{1},...,v_{N_{k}}\big{\\}},\\\
0&\text{if}\;\;$\text{otherwise}$\end{cases}$

where $N_{k}$ is the number of politicians that compete in coalition $k$.

In our model, politicians use Twitter to manipulate voters’ posterior beliefs
(as in a Bayesian persuasion game?). Manipulation occurs trough the effect of
a signal that a politician $i$ sends to voters at the moments of giving a
“like” to a message sent by another politician $j$ ($\delta_{i,j}$). Under the
assumption that signals come from a normally distributed likelihood function
with known variance equal to $\sigma_{i}$. Posteriors beliefs from the voters
perspective can be determined as simple weighted average:

$\mu_{i}^{*}=\dfrac{\mu_{i}}{1+\omega}+\dfrac{\omega}{1+\omega}\delta_{i,j}$
(3)

where $\omega$ captures how much voters weight the signal ($\delta_{i,j}$)
versus their prior view ($\mu_{j}$) on politician $j$.

We define the endogenous variable $l_{i,j}$ as a dummy variable that takes a
1, if and only if, politician $i$ gives a “like” to politician $j$’s message,
and zero otherwise. Assuming self interest preferences, a politician decides
to “like” a message of another politician $j$ if it increases politicians’
popularity ($\Delta P(l_{i,j})$). Politician’s popularity is measured by
distance, or proximity, in a right-left axis as has been empirically suggested
by Busch [2016] using data from Europe.

On the other hand, we incorporate an additional factor that influences
politicians’ behavior motivated by the idea of authenticity developed by
Trilling [2009]. We include an authenticity parameter ($\gamma$) that measures
politician’s capacity to reach agreement in public argumentation [Haberrmas,
2006]. In other words, politicians apply a factor $\gamma$ to the disutility
of giving a “like” to some political message that is far from its own ideology
($\mu_{i}$). In Section 5.2 we show that his parameter generates ideological
consistency. However, at the same time reinforces the propensity to give a
like to a message that is ideologically appealing, regardless of the identity
of the message sender. In our model, this ideological distance is measured by
$\Delta A(l_{i,j})$. The decision of politician $i$ to give a “like” to
politician $j$’s message ($\delta_{i,j}$) can be formulated as follows:

$\displaystyle\max_{l_{i,j}}$ $\displaystyle\Delta P(l_{i,j})-\gamma\Delta
A(l_{i,j})$ (4)

where $\Delta P(l_{i,j}=1)$ measures the absolute change of politician $i$’s
ideological distance with her front-runner candidate ($f$), before
($|\mu_{i}-\mu^{f}_{k}|$) and after giving the “like”
($|\mu_{i}^{*}-\mu^{f}_{k}|$). A positive (negative) value for $\Delta P$
measures electoral gains (losses) out of giving a “like” to a message
$\delta_{i,j}$. On the other hand, $\Delta A(l_{i,j}=1)$ measures how far is
the message from politician’s own ideology
($|\delta_{i,j}-\mu_{i}|/\sigma_{i}$).

###  5.1 Model Parameters

We solve the model for a set of parameters that we took from the CEP opinion
survey. In the simulations of the model, we use the ideological levels, as
well as the proportion of voters documented in Figure 4.222222In C we show
that the assumed distribution of voters has implications that are related to
violations of the median voter theorem. In our baseline case, some politicians
have incentives to move toward the extremes of the political spectrum.

Parameters that describe politicians’ ideology ($\mu_{i}$ and $\sigma_{i}$)
are also taken from the same opinion survey. Estimates are obtained by an OLS
regression of surveyed subjective evaluation of a set of 28 politicians on
self reported ideology. Our estimates allow us to have a measure of public
opinion perceived ideology for a set of Chilean politicians. Intuitively, this
measure is based on the correlation between subjective opinion and self
reported ideology .232323For a detailed description of our estimation see B
The mean and standard error of the coefficients plotted in Figure 5 determine
politicians’ ideology ($\mu_{i}$ and $\sigma_{i}$).

Figure 4: The figure measures the percentage of people in Chile that is
associated with each ideology group, a scale from 1 to 5. Null responses are
uniformally distributed. Figure 5: The figure plots the mean and the standard
deviation of the ideological distribution of each politician in the model.
Politicians are sorted from right to left.

###  5.2 Model Simulation

In this section, we present the predictions of our proposed model. It is
important to highlight first that our results are based on $\omega=1$, which
is equivalent to assuming that voters equally weight politicians’ prior
ideology and the observed signal related to the given “like”. Second, in the
model the political market (e.g. politician and voters’ ideology distribution)
is well described by the parameters presented Section 5.1.

In Figure 9 we can see that our model generates a behavior that can explain
how politicians at the extremes of the spectrum do not have incentives to move
toward the center. Second, although not all politicians have incentives to
interact with their political opponents, in the first panel of Figure 6(e) we
can see that our model still generates a fair amount of “likes” between
political opponents. And this occurs in our self interest setting. In the
following panels of Figure 6(e), we show how the simulated networks of “likes”
changes for different levels of authenticity ($\gamma$), assuming homogeneous
preferences. Visually, we can see that if all politicians are more authentic
at the same time, the model generates “echo chambers” where only some
politicians interact among each other. As we proposed in Section 4.2, in
Figure 7 we confirm that a systematic increase in politicians’ authenticity is
related to higher polarization, measured by networks’ modularity.

Finally, we present a simulation based on heterogeneous levels of politicians’
authenticity, which are randomly endowed independently of politicians’
ideology. By assumption, authenticity is normally distributed with mean and
standard deviation of 0.1, with a bound at zero. The simulated networks of
“likes” is analyzed based on the following regression analysis:

$\text{Likes}_{i,j}=\alpha+\beta\cdot\text{Opponents}_{i,j}+\epsilon_{i,j}$
(5)

where $\text{Likes}_{i,j}$ measures the number of simulated “likes” between
politician $i$ and $j$; Opponents is a a dummy variable that takes a 1 if
politicians $i$ and $j$ are opponents; $\epsilon_{i,j}$ is the residual.

The estimated coefficient ($\beta$) of the regression is presented in Table 4.
As we can see, in our model opponents have a lower propensity to “like” each
other’s messages. In Figure X we present the relationship between the residual
of Equation 5 and the first principal component of politicians’ ideology and
authenticity. This relationship shows that “likes” between opponents are
confined to politicians that have higher levels of authenticity and that are
ideologically close. Importantly, this analysis suggest that, to the extent
that we understand politicians’ incentives, “likes” between opponents can be
informative of politicians authenticity.

(a)

(b)

(c)

(d)

(e)

Figure 6: Simulated Network Analysis by Authenticity

This figure plots the estimated network of simulated “likes”. Panel (a) shows
the case of politicians with no authenticity ($\gamma=0$); Panel (b)
$\gamma=0.05$; Panel (c) $\gamma=0.1$; Panel (d) $\gamma=0.15$; Panel (e)
$\gamma=0.2$

Figure 7: The figure plots the modularity of the simulated networks presented
in Figure 6(e) for different levels of authenticity ($\gamma$).

##  6 Empirical framework

In Section 5 we outline a public choice model to highlight the effect of
political incentives and politicians’ intrinsic authenticity on their
propensity to “like” messages of other Congress members. The model generates
the following main predictions. First, a politician that is less authentic is
more willing to “like” an opponent’s message even if she disagrees with the
ideological content of the message. Second, controlling for the electoral
incentives, if a politician “likes” the message of an opponent, this observed
behavior can be informative of politicians’ authenticity and the ideological
agreement between the two Congress members. Based upon our combination of
voting data from Chilean Deputies and their corresponding interactions in
Twitter, we empirically analyze the relationship between the interactions of
the politician in Twitter and Congress. Our analysis is conducted using a
fixed effect regressions on the combined panel data that describes the
historical interactions of politicians in Twitter and Congress. Our regression
model is presented below:

$\displaystyle
Y_{i,j,t}=\alpha_{i}+\alpha_{t}+\beta\cdot\,\text{Likes}_{i,j,t}+\lambda\cdot\,\text{Likes}_{i,j,t}^{2}+\beta^{O}\cdot\,\text{Likes}_{i,j,t}\text{Opp}_{i,j}+$
(6)
$\displaystyle\lambda^{O}\cdot\,\text{Likes}_{i,j,t}^{2}\cdot\text{Opp}_{i,j}+\theta_{i,j}+\epsilon_{i,j,t}$

where $Y_{i,j,t}$ is the numbers of “likes” or bills voted in favor between
politician $i$ and $j$ during time window $t$, which are used interchangeable
in the different specifications presented in Table 4;
$\text{Likes}_{i,j,t}^{2}$ measures the number of “likes” between politician
$i$ and $j$ squared, to capture potential nonlinear effects in the
relationship of votes and “likes”; $\text{Opp}_{i,j,t}$ is a dummy variable
that takes a 1 if politician $i$ and $j$ are opponents;242424The Opponent Opp
variable is constructed based on party affiliation. $\alpha_{i}$ and
$\alpha_{t}$ are politicians and time fixed effects, respectively;
$\theta_{i,j}$ are two dummy variables that are used as non-time-varying
controls, these are indicator functions that identify if politician $i$
follows politician $j$, and if politician $i$ and $j$ are opponents;
$\epsilon_{i,j,t}$ is the residual.

Our main focus of analysis is related to the parameters $\lambda+\beta$ and
$\lambda+\beta+\lambda^{O}$ of Equation 6 because they measure how “likes” to
political opponents is associated with the number of bills voted in favor by
the two deputies. These estimates allow us to test our hypothesis of Twitter
working as a public sphere. To the extent that these estimates are positive
and significant, this would suggest that “likes” between political opponents
are relevant signals of agreement.

##  7 Results

This section presents the results of a test that relates deputies’ voting
behavior to their propensity to “like” other politicians’ messages in Twitter.

We begin with the study of deputies’ behavior in Twitter. In columns (1) to
(3) of Table 7 we document the coefficient estimates related to Equation 6
using the number of “likes” as the dependent variable. Our findings suggest
that deputies have a lower propensity to “like” their opponents messages,
consistent with our theoretical model and the empirical evidence documented by
Halberstam and Knight [2016]. At the same time, our results also suggest that
following links cannot explain “likes” when we control for political
affiliation, which is consistent with the fact that politicians do want to
read other congress members’ “tweets”.

Columns (4) to (6) of Table 7 use the number of bills voted in favor as the
dependent variable. Interestingly, our results finds no relationship between
bills voted in favor and coalition membership. This result is consistent with
low levels of coalition unity during the analyzed period. Moreover, when we
analyze columns (7) to (9) we can see that, during the studied period, the
number of “likes” in Twitter is negatively related to the number of bills
voted in favor. This finding suggest that a deputy could “like” the “tweet” of
a coalition mate as a signal of group loyalty [Brennan and Hamlin, 1998], even
when she opportunistically deviate from its coalition in Congress. Finally, in
columns (8) and (9) we document our main finding. Giving a “like” to an
opponent is positive and significantly correlated with future cross-cutting
coalition in Congress. The differential effect between intra- and inter-
coalition suggest that “likes” between political opponents work as costly
signals of ideological agreement.

Table 2: Politicians interactions in Twitter and Congress | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
---|---|---|---|---|---|---|---|---|---
| Likes | Likes | Likes | Votes | Votes | Votes | Votes | Votes | Votes
Opponents | -0.812*** |  | -0.811*** | 0.275 |  | 0.763 |  | 0.612 | 0.486
| (0.045) |  | (0.043) | (3.939) |  | (4.029) |  | (4.045) | (4.026)
Following |  | 0.315*** | 0.003 |  | 1.461 | 1.754* | 1.488 | 1.663* | 1.735*
|  | (0.041) | (0.032) |  | (1.375) | (0.686) | (1.368) | (0.721) | (0.695)
Likes |  |  |  |  |  |  | -0.088** | -0.088*** | -0.345***
|  |  |  |  |  |  | (0.022) | (0.005) | (0.068)
Likes $\times$ Opponent |  |  |  |  |  |  |  | 1.717* | 2.957**
|  |  |  |  |  |  |  | (0.797) | (0.771)
Likes2 |  |  |  |  |  |  |  |  | 0.002**
|  |  |  |  |  |  |  |  | (0.000)
Likes2 $\times$ Opponent |  |  |  |  |  |  |  | -0.123 |
|  |  |  |  |  |  |  |  | (0.102)
Observations | 48650 | 48650 | 48650 | 48650 | 48650 | 48650 | 48650 | 48650 | 48650
Adjusted R-squared | 0.011 | 0.005 | 0.011 | 0.091 | 0.092 | 0.092 | 0.092 | 0.092 | 0.092
Fixed Effects | Time & Deputy FE

##  8 Conclusion

This paper tests the hypothesis that Twitter provides relevant information
about politicians’ legislative decisions. As opposed to other papers that have
used politicians’ Twitter data, we focus on the number of “likes” as an
observable measure of agreement between Congress members. Our empirical test
intends to isolate the relationship between agreement in Twitter and Congress.
We find that “likes” are negative and significantly related to the number of
bills voted in favor. We do, however, find a heterogeneous propensity to vote
bills in favor if the “like” is given to an opponent. Our results can be
rationalized by “likes” to coalition mates being signals of group loyalty
instead of political agreement. On the other hand, “likes” to opponents would
work as costly signals of ideological agreement as in our proposed political
economy model. The implications of our results are related to voters ability
to distinguish politicians’ epistemic impartiality, an important condition for
reaching political agreement as suggested by [Taylor and Bosworth, 2020].

Table 3: Analyzed time periods Votes |
---|---
Start date | End date | Likes
April 2, 2019 | May 28, 2019 | May 27, 2019
September 3, 2019 | October 20, 2019 | October 28, 2019
December 30, 2019 | January 30, 2020 | February 21, 2020
May 12, 2020 | June 10, 2020 | June 11, 2020
November 3, 2020 | December 2, 2020 | December 2, 2020
Table 4: Regression of Simulated Model | Coefficients
---|---
Opponents | -172.043***
| (10.614)
Constant | 177.401***
| (10.467)
Observations | 784
Adjusted R-squared | 0.251

##  Appendix A Network modularity

A network cluster (communities) is a region of the network that is strongly
connected within and relatively sparsely connected to the rest of the network.
The common way of measuring how well a subdivision of a network into clusters
capture the modular structure of the network is by network modularity [Newman,
2006]. Mathematically, the network modularity $Q$ is given by:

$Q=\frac{1}{2m}\sum_{i,j}\Big{(}\text{a}_{i,j}-\frac{\text{k}_{i}\text{k}_{j}}{2m}\Big{)}\delta(\text{c}_{i},\text{c}_{j})$
(7)

where $\text{a}_{i,j}=1$ if nodes $i$ and $j$ are connected and
$\text{a}_{i,j}=0$, otherwise. $m=\frac{1}{2}\sum_{i,j}\text{a}_{i,j}$ is the
total number of edges in the network and
$\text{k}_{i}=\sum_{j}a_{i,j}\delta(\text{c}_{i},\text{c}_{j})=1$ only if
nodes $i$ and $j$ are in the same community. Otherwise,
$\delta(c_{i},\text{c}_{j})=0$.

##  Appendix B Estimated Politicians Ideology

In this section we propose a simple method for estimating politicians
perceived ideology from public opinion surveys. The measure is constructed
using a simple OLS regression:

$\text{Opinion}_{j,k}\,=\alpha+\,\beta_{k}\,\text{Ideology}_{j}+\epsilon_{j}$
(8)

where $Opinion_{j}$ captures how favorable is the opinion of surveyed $j$
about politician $k$. Voters opinion is measured in a 1 (very bad) to 5 (very
good) scale. $Ideology_{j}$ measures self reported ideology of surveyed $j$.
Parameters that describe politicians ideology in the model ($\mu$ $\sigma$)
are obtained from the mean and standard error of coefficients $\beta_{k}$. In
the right and left extremes we have politicians with ideologies of 1 and 5,
respectively. Ideology of the other politicians are re-adjusted using
coefficients presented in Figure 5 in order to have a supply of politicians
that go from 1 (right) to 5 (left). In Figure 8 we show the estimated levels
of politicians from the CEP public opinion study as of May 2009.

Figure 8: The figure plots the mean ideology of each politician in the model.
Politicians are sorted from right to left.

##  Appendix C Median Voter Theorem

A standard benchmark in the public choice theory is the Median Voter Theorem
of Dow [1998]. In Figure 9 we show that our calibration of voters introduces
an incentive to some politicians to move toward the extremes. Contrarily, a
normal distribution of voters’ ideology (same mean and standard deviation)
increases the incentives to move toward the center. This incentive is
enhanced, if the population is more continuously distributed in the whole
political spectrum.

Figure 9: The figure shows how the electoral incentives are shaped by the
distribution of voters. In the X-axis (Politician Ideology) is politicians’
original ideology. In the Y-axis (Target Ideology), we have the ideology of
the front-runner of the coalition for each politician. Empirical Discrete
refers to the observed discrete distribution in the CEP opinion survey. Normal
Discrete is a discrete distribution with the same mean and standard deviation
of the voters’ ideology. Normal Continuous corresponds to a continuous version
of Normal Discrete.

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¡!DOCTYPE HTML PUBLIC¿ ¡html¿¡head¿¡title¿ EPTCS 374: Graph Computation Models
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¡center¿ ¡h1¿EPTCS 374¡/h1¿ ¡h1¿¡font size=5¿Proceedings of the Thirteenth
International Workshop on¡/font¿ ¡br¿Graph Computation Models ¡br¿¡font
size=3¿Nantes, France, 6th July 2022¡/font¿¡/h1¿ Edited by: Reiko Heckel and
Christopher M. Poskitt ¡/center¿ ¡hr class=sep¿ ¡table width=100¡tr¿¡td
class=fill¿¡i¿¡a href=”#EPTCS374.0”¿ Preface¡/a¿¡/i¿¡/br¿ Reiko Heckel and
Christopher M. Poskitt¡/td¿¡/tr¿ ¡tr¿¡td class=fill¿¡i¿¡b¿Invited
Presentation:¡/b¿ ¡a href=”#EPTCS374.1”¿ Graph Representations in Traditional
and Neural Program Analysis¡/a¿¡/i¿¡/br¿ Elizabeth Dinella¡/td¿¡td
align=”right”¿1¡/td¿¡/tr¿ ¡tr¿¡td class=fill¿¡i¿¡b¿Panel Discussion:¡/b¿ ¡a
href=”#EPTCS374.2”¿ Learning Graph Transformation Rules¡/a¿¡/i¿¡/br¿ Reiko
Heckel¡/td¿¡td align=”right”¿2¡/td¿¡/tr¿ ¡tr¿¡td class=fill¿¡i¿¡a
href=”http://dx.doi.org/10.4204/EPTCS.374.3”¿ Graph-Based Specification and
Automated Construction of ILP Problems¡/a¿¡/i¿¡/br¿ Sebastian Ehmes,
Maximilian Kratz and Andy Schürr¡/td¿¡td align=”right”¿3¡/td¿¡/tr¿
¡tr¿¡td class=fill¿¡i¿¡a href=”http://dx.doi.org/10.4204/EPTCS.374.4”¿ Time
and Space Measures for a Complete Graph Computation Model¡/a¿¡/i¿¡/br¿ Brian
Courtehoute and Detlef Plump¡/td¿¡td align=”right”¿23¡/td¿¡/tr¿ ¡tr¿¡td
class=fill¿¡i¿¡a href=”http://dx.doi.org/10.4204/EPTCS.374.5”¿ A Foundation
for Functional Graph Programs: The Graph Transformation Control Algebra
(GTA)¡/a¿¡/i¿¡/br¿ Jens H. Weber¡/td¿¡td align=”right”¿45¡/td¿¡/tr¿ ¡tr¿¡td
class=fill¿¡i¿¡a href=”http://dx.doi.org/10.4204/EPTCS.374.6”¿ Towards
Mechanised Proofs in Double-Pushout Graph Transformation¡/a¿¡/i¿¡/br¿ Robert
S#x00f6;ldner and Detlef Plump¡/td¿¡td align=”right”¿59¡/td¿¡/tr¿ ¡tr¿¡td
class=fill¿¡i¿¡a href=”http://dx.doi.org/10.4204/EPTCS.374.7”¿ A Graph-
Transformational Approach for Proving the Correctness of Reductions between
NP-Problems¡/a¿¡/i¿¡/br¿ Hans-J#x00f6;rg Kreowski, Sabine Kuske, Aaron Lye and
Aljoscha Windhorst¡/td¿¡td align=”right”¿76¡/td¿¡/tr¿ ¡/table¿ ¡hr
class=sep¿¡h1 align=left¿¡a name=’EPTCS374.0’¿Preface¡/a¿¡/h1¿

¡p¿ This volume contains the post-proceedings of the 13th International
Workshop on Graph Computation Models (¡a href=”https://gcm2022.github.io/”¿GCM
2022¡/a¿), which was held in Nantes, France on 6th July 2022 as part of ¡a
href=”https://staf2022.univ-nantes.io/”¿STAF 2022¡/a¿. ¡/p¿

¡p¿ Graphs are common mathematical structures that are visual and intuitive.
They constitute a natural and seamless way for system modelling in science,
engineering, and beyond, including computer science, biology, and business
process modelling. Graph computation models constitute a class of very high-
level models where graphs are first-class citizens. The aim of the
International GCM Workshop series is to bring together researchers interested
in all aspects of computation models based on graphs and graph transformation.
It promotes the cross-fertilising exchange of ideas and experiences among
senior and young researchers from different communities interested in the
foundations, applications, and implementations of graph computation models and
related areas. ¡/p¿

¡p¿ Previous editions of the GCM series were held in Natal, Brazil (2006);
Leicester, UK (2008); Enschede, The Netherlands (2010); Bremen, Germany
(2012); York, UK (2014); L’Aquila, Italy (2015); Wien, Austria (2016);
Marburg, Germany (2017); Toulouse, France (2018); Eindhoven, The Netherlands
(2019); online (2020); and online (2021). ¡/p¿

¡p¿ This post-proceedings volume contains revised versions of five selected
papers presented at GCM 2022. All submissions were subject to careful
refereeing (at least three reviews per paper), and span a wide range of topics
from the foundations and applications of graph computation models. ¡/p¿

¡p¿ We would like to thank everyone who contributed to the success of this
volume, including our contributing authors, as well as our Programme Committee
and additional reviewers, who provided several valuable insights throughout
the selection process. ¡/p¿

¡p¿Reiko Heckel and Chris Poskitt¡br /¿ ¡em¿Programme Committee Co-
Chairs¡/em¿¡br /¿ ¡em¿Leicester (UK) and Singapore (Singapore), December
2022¡/em¿ ¡/p¿

¡h2¿GCM 2022 Programme Committee¡/h2¿

¡ul¿ ¡li¿Andrea Corradini (Universit#x00e0; di Pisa, Italy)¡/li¿ ¡li¿Frank
Drewes (Ume#x00e5; University, Sweden)¡/li¿ ¡li¿Rachid Echahed (CNRS and
University of Grenoble, France)¡/li¿ ¡li¿Annegret Habel (University of
Oldenburg, Germany)¡/li¿ ¡li¿Reiko Heckel (University of Leicester, UK)¡/li¿
¡li¿Berthold Hoffmann (Universit#x00e4;t Bremen, Germany)¡/li¿ ¡li¿Gabor
Karsai (Vanderbilt University, USA)¡/li¿ ¡li¿Barbara K#x00f6;nig (University
of Duisburg-Essen, Germany)¡/li¿ ¡li¿Leen Lambers (Brandenburgische Technische
Universit#x00e4;t Cottbus-Senftenberg, Germany)¡/li¿ ¡li¿Mark Minas
(Universit#x00e4;t der Bundeswehr M#x00fc;nchen, Germany)¡/li¿ ¡li¿Fernando
Orejas (Universitat Polit#x00e8;cnica de Catalunya, Spain)¡/li¿ ¡li¿Detlef
Plump (University of York, UK)¡/li¿ ¡li¿Chris Poskitt (Singapore Management
University, Singapore)¡/li¿ ¡/ul¿

¡h2¿Additional Reviewers¡/h2¿

¡ul¿ ¡li¿Brian Courtehoute (University of York, UK)¡/li¿ ¡li¿Okan #x00d6;zkan
(University of Oldenburg, Germany)¡/li¿ ¡li¿Sven Schneider (Hasso Plattner
Institute, Germany)¡/li¿ ¡/ul¿ ¡hr class=sep¿¡h1 align=left¿¡a
name=’EPTCS374.1’¿Graph Representations in Traditional and Neural Program
Analysis¡/a¿¡/h1¿

¡b¿Elizabeth Dinella¡/b¿ (¡i¿University of Pennsylvania, USA¡/i¿) ¡p¿ ¡p¿
Traditional program analysis techniques often represent programs as graphs
where nodes are program entities and edges represent various relations (data
flow, control flow, call graphs, etc). Graphs are a standard representation
for programs as they can capture syntactic and semantic structure with long
range dependencies. Recently, ”neural” program analysis has been proposed for
traditional analysis tasks. Representing a program as input to a machine
learning model is an active area of research. Popular representations include
sequences of tokens, relational databases, and graph neural networks. In many
cases, a graph representation is preferable. Program repair is an example of
such a task. In this talk I will discuss the advantages and challenges of
representing programs as graphs in both traditional and neural program repair.
¡/p¿

¡p¿ ¡strong¿Speaker Biography.¡/strong¿ Elizabeth is a PhD student at the
University of Pennsylvania advised by Mayur Naik. She works on models of code
for program analysis tasks such as program repair (¡a
href=”https://openreview.net/pdf?id=SJeqs6EFvB”¿Hoppity¡/a¿). As an intern at
Microsoft Research, Elizabeth worked on the ¡a
href=”https://www.microsoft.com/en-us/research/publication/deepmerge-learning-
to-merge-programs/”¿DeepMerge¡/a¿ project contributing an edit-aware neural
approach to merge programs. More recently, her interests lie in neural test
suite generation (¡a href=”https://www.seas.upenn.edu/ edinella/icse-camera-
ready.pdf”¿TOGA¡/a¿), and web3 security. In her free time, Elizabeth enjoys
hot coffee and her chow chow puppy Cinnabon. ¡/p¿¡hr class=sep¿¡h1
align=left¿¡a name=’EPTCS374.2’¿Learning Graph Transformation Rules¡/a¿¡/h1¿

¡b¿Reiko Heckel¡/b¿ (¡i¿University of Leicester, UK¡/i¿) ¡p¿ ¡p¿ As with any
detailed model of a complex problem, creating a graph transformation system is
hard. An alternative in some situations is to learn models from historical or
observed data or derive them by optimising a basic model based on some
objective function using feedback from simulations or real-world processes.
The session is dedicated to discussing application scenarios and solutions for
learning, in particular, the rules of a graph transformation system with the
aim of inspiring collaborative research on this topic. A preliminary
classification of rule learning problems could distinguish these two aspects.
¡/p¿

¡p¿ ¡strong¿Prescriptive vs descriptive model.¡/strong¿ A model is
¡em¿prescriptive¡/em¿ if it is intended as a design of a system to be built,
¡em¿descriptive¡/em¿ if it represents an existing system to be analysed. ¡/p¿
¡p¿ In the prescriptive case, creating a model that best suits certain
requirements is a form of optimisation based on a given objective function. In
order to assess the fitness of a model, we have to either run the model
directly (e.g., in a simulation) or use it to control a real-world process we
can measure. For example, we may want to optimise the topology management for
a decentralised network, maximising connectivity while minimising the number
of links to be maintained. Such requirements should be expressed by the
objective function and the aim should be to optimise the application of a set
of basic rules, e.g. for nodes joining or leaving, making or breaking links.
¡/p¿ ¡p¿ In the descriptive case, we infer the model from existing data
observed from a real process, e.g., the version history of a software project.
This can be a precursor to a prescriptive use of the model in a re-engineering
scenario, e.g., inferring a model of how faults are detected and fixed in
software projects in order to recommend typical fixes. Rules in this case
should represent typical fault patterns and their repair actions. ¡/p¿

¡p¿ ¡strong¿Online vs offline learning.¡/strong¿ In either of the above
scenarios, learning can be ¡em¿online¡/em¿ (at runtime, using a form of
reinforcement learning) or ¡em¿offline¡/em¿ (based on historical data). In the
online case we make continuous observations and use them to modify the model,
e.g., in a stochastic or probabilistic model, adding weight to successful
rules (in the prescriptive scenario) or frequently observed rules (in the
descriptive case). In the offline case, there is no direct feedback or
continuous update, but for prescriptive models learning can happen in longer
cycles of model inference, usage and feedback. ¡/p¿

¡p¿ Based on the above we would like to collect, describe and classify
application scenarios for rule learning, such as network topology management
or fault detection and repair, and discuss possible solutions. The result
could be a position paper summarising our findings. ¡/em¿

¡p¿ ¡strong¿Acknowledgements.¡/strong¿ The topic for this panel arose from a
series of discussions between the chair, Nicolas Behr, Bello Shehu Bello, and
Sebastian Ehmes, with further input from Marc Santolini and Ashiq Anjum. ¡/p¿

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