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\begin{center}
\bigskip

\Large \textbf{Online appendix for:\\ International Treaty Ratification and Party Competition: Theory and Evidence from the EU's Constitutional Treaty}

\bigskip
\bigskip

\normalsize
\begin{tabular}
[c]{cc}%
Andreas D\"{u}r & Nikitas Konstantinidis\\
University of Salzburg & LSE\\
andreas.duer@sbg.ac.at & n.konstantinidis@lse.ac.uk\\
\end{tabular}

\end{center}

\bigskip
\bigskip



\pagenumbering{roman}%
%EndExpansion


\section*{Appendix I: Theory}

\subsection*{A Probabilistic Model of Referendum Voting}

Let the country's electorate be represented by a continuum of mass one. Each
voter $j$ will vote for the referendum option (`Yes' or `No') that maximizes
his/her quasi-linear utility with respect to integration policy and the
incumbent's relative political capital. For reasons of analytical parsimony we
rule out voter abstention as a possibility. The two dimensions of electoral
competition are assumed orthogonal. Integration policy preferences are
represented by a quasi-concave Euclidean utility function $u:X\times
X\rightarrow%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ that maps ideal positions $x^{j}$ (levels of integration) and policy
proposals $x$ into real pay-offs. This implies that preference profiles over a
continuum of policy alternatives increasing in the depth of integration will
be single-peaked.

For a continuous population of mass one we can define a Benthamite aggregate
welfare function as the (unweighted) average policy-derived utility, that is,
$W\left(  x\right)  :=\underset{X}{\int}u\left(  x;x^{j}\right)  f_{x}\left(
x^{j}\right)  dx^{j}\equiv u\left(  x;\overline{x}\right)  $. For any generic
distribution function $F_{x}\left(  \cdot\right)  $ average utility will be
distinct from the utility of the median voter, that is, $u\left(
x;\overline{x}\right)  \neq u\left(  x;F_{x}^{-1}\left(  \frac{1}{2}\right)
\right)  $. Furthermore, as political parties pursue both policy-seeking and
office-seeking objectives, their policy preferences are equivalent to those of
some particular individual generically distinct from the average voter. Again,
by the `continuum of mass one' property of the model, one can capture
interparty ideological divergence along the integration dimension through
distinct partisan-weighted aggregate utility functions as follows:%
\[
W^{i}\left(  x\right)  :=\underset{X}{\int}u\left(  x;x^{j}\right)
g^{i}\left(  x^{j}\right)  f_{x}\left(  x^{j}\right)  dx^{j}\equiv u\left(
x;x^{i}\right)  ,i=I,O.
\]


Throughout the model we make use of the following intuitive assumption about
the content of the negotiated agreement in light of unanimity voting
requirements and veto rights:

\begin{assumption}
\label{assum}$\Delta W\left(  x_{c},x_{SQ}\right)  \geq0$ and $\Delta u\left(
x_{c},x_{SQ};x^{I}\right)  >0.$
\end{assumption}

In the run-up to a referendum, each voter $j$ receives a private and
independently distributed signal $\widehat{\delta}^{j}$ of the incumbent's
political capital (or else popularity) relative to its main opposition rival
at that particular moment in the electoral cycle.\footnote{We posit that the
underlying stochastic process of relative political capital accumulation is
subject to a downward stationary trend and the stochastic white noise
component of the process captures unexamined positive or negative shocks to a
government's popularity (for example, political scandals, economic crises,
etc.).} We assume that $\widehat{\delta}^{j}=\delta+\eta^{j}+\varepsilon$,
where $\delta\in%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ is the true underlying level of relative political capital, $\eta^{j}$ is an
ideological bias term independently distributed according to a regular
distribution function, and $\varepsilon$ is an independent white noise
disturbance term (with zero mean, finite variance, and no serial correlation)
that captures aggregate uncertainty over the true value of this latent and
unobservable state variable. The $\eta^{j}$ variable captures the fact that
political information is subjectively perceived, distorted, and filtered
through individual ideological prisms (for example, partisan media outlets).
Voters base their decision both on the merits of the issue at hand and the
weighted relative popularity of the incumbent responsible for the negotiation
of the agreement. Parameter $\gamma>0$ captures the relative salience of the
orthogonal valence dimension.\footnote{Within the framework of an underlying
probabilistic voting model, this relative salience variable is assumed to be
common for both voters and parties as they will tend to converge to a similar
assessment of the domestic political environment.} Parties across the spectrum
then arrive at the common belief that voter $j$ will vote in favor of treaty
ratification \textit{if and only if}%
\begin{equation}
\Delta u\left(  x_{c},x_{SQ};x^{j}\right)  +\gamma\widehat{\delta}^{j}=\Delta
u\left(  x_{c},x_{SQ};x^{j}\right)  +\gamma\left(  \delta+\eta^{j}%
+\varepsilon\right)  >0\text{,} \tag{Yes}\label{yesvotej}%
\end{equation}
where $\Delta u\left(  x_{c},x_{SQ};x^{j}\right)  $ denotes the relative
policy desirability of the treaty \textit{vis-\`{a}-vis} the \textit{status
quo} for voter $j$. Since the decision is dichotomous, voting will be sincere.

As is typical in probabilistic voting models, politicians are only aware of
the (twice continuously differentiable and of full support) joint distribution
function $F\left(  \cdot,\cdot\right)  $ of private types $\left(  x^{j}%
,\eta^{j}\right)  \in X\times%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ across the population but not their individual realization. Let $f\left(
\cdot,\cdot\right)  >0$ be the corresponding joint density function and
$f_{x}\left(  \cdot\right)  $, $f_{\eta}\left(  \cdot\right)  $ the respective
marginal density functions.\footnote{Assuming that ideal policy types $x^{j}$
and ideological bias types $\eta^{j}$ are independent across the population
would simplify the calculation of a closed-form solution for the probability
of a `Yes' vote, as marginal densities would be separable. However, this
assumption is not necessary for our results. In fact, the observation that
Euroskeptics tend to be clustered in the two extremes of the spectrum should
make it more apposite to assume correlated types across the traditional
ideological (left/right) and the integration dimensions.} Individual types are
thus treated as measurable random variables and the referendum outcome becomes
probabilistic. To arrive at the probability of a successful referendum in such
a model, we first need to define the vote share in each country as the
fraction of votes in favor of the treaty barring abstentions. This is
equivalent in our model to the total fraction of voter type pairs $\left(
x^{j},\eta^{j}\right)  $ that satisfy condition \ref{yesvotej} above.
Formally, expected vote share is given by%
\[
VS\left(  \varepsilon;\gamma,\delta\right)  =\underset{\left(  \ref{yesvotej}%
\right)  }{\iint}f\left(  x^{j},\eta^{j}\right)  dx^{j}d\eta^{j}=\underset
{X}{\int}\overset{+\infty}{\underset{\text{ }-\frac{\Delta u^{j}}{\gamma
}-\delta-\varepsilon}{\int}}f\left(  x^{j},\eta^{j}\right)  d\eta^{j}dx^{j}%
\]


Note that the vote share becomes a strictly increasing and (twice)
continuously differentiable function of the aggregate uncertainty disturbance
term $\varepsilon$, that is, $VS:%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
^{2}\times%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
_{++}\longrightarrow\left(  0,1\right)  $ and%
\[
VS^{\prime}\left(  \varepsilon;\gamma,\delta\right)  =\underset{X}{\int
}\left(  -\right)  \left(  -\right)  f\left(  x^{j},-\frac{\Delta u^{j}%
}{\gamma}-\delta-\varepsilon\right)  dx^{j}>0.
\]
By the Inverse Function Theorem, inverse function $VS^{-1}:\left(  0,1\right)
\times%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\times%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
_{++}\longrightarrow%
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
$ exists and is also strictly increasing and continuously differentiable.
Partial differentiation with respect to parameters $\delta$ and $\gamma$
yields the following: $\frac{\partial VS\left(  \varepsilon;\gamma
,\delta\right)  }{\partial\delta}=\underset{X}{\int}\left(  -\right)  \left(
-\right)  f\left(  x^{j},-\frac{\Delta u^{j}}{\gamma}-\delta-\varepsilon
\right)  dx^{j}>0$ and $\frac{\partial VS\left(  \varepsilon;\gamma
,\delta\right)  }{\partial\gamma}=-\frac{1}{\gamma^{2}}\underset{X}{\int
}\Delta u^{j}f\left(  x^{j},-\frac{\Delta u^{j}}{\gamma}-\delta-\varepsilon
\right)  dx^{j}\leq0$. Moreover, the vote share is (weakly) decreasing with
respect to the relative salience parameter $\gamma$ \textit{if and only if}
the expected aggregate welfare differential of swing voters, that is, those
who are indifferent between voting `Yes' or `No' in a referendum (condition
\ref{yesvotej} just binds), is non-negative. So we need the following to hold:

\begin{assumption}
{\normalsize \label{assum2}$\underset{X}{\int}\Delta u^{j}f\left(
x^{j},-\frac{\Delta u^{j}}{\gamma}-\delta-\varepsilon\right)  dx^{j}\geq0.$ }
\end{assumption}

This is a generalization of assumption \ref{assum} above. Finally, partial
differentiation of identity $VS^{-1}\left(  VS\left(  \varepsilon
;\gamma,\delta\right)  ;\gamma,\delta\right)  =\varepsilon$ with respect to
$\gamma$ and $\delta$ implies that $\frac{\partial VS^{-1}}{\partial\gamma
}=-\left(  VS^{-1}\right)  ^{\prime}\times\frac{\partial VS}{\partial\gamma
}\geq0$ and $\frac{\partial VS^{-1}}{\partial\delta}=-\left(  VS^{-1}\right)
^{\prime}\times\frac{\partial VS}{\partial\delta}<0$.

We may now provide a general proof of proposition \ref{prob} below:

\begin{proposition}
\label{prob}The probability of successful ratification by referendum $P\left(
\gamma,\delta,\Delta W\right)  $ is decreasing in the relative salience of
valence $\left(  \gamma\right)  $ and increasing in the relative political
capital of the incumbent $\left(  \delta\right)  $ and the aggregate welfare
differential of achieving a higher level of international cooperation $\left(
\Delta W\right)  $.
\end{proposition}

\textit{Proof}. Winning a referendum by majority vote is tantamount to a vote
share of at least $50\%$ (where ties are assumed to happen with zero
probability). Hence, the probability $P$ of a successful referendum vote is
calculated as follows:%
\begin{align*}
P\left(  \gamma,\delta\right)   &  =\Pr\left(  VS\left(  \varepsilon
;\gamma,\delta\right)  >\frac{1}{2}|\varepsilon\text{ is independent white
noise with zero mean and finite variance}\right) \\
&  =\Pr\left(  \varepsilon>VS^{-1}\left(  \frac{1}{2};\gamma,\delta\right)
|\varepsilon\sim F_{\varepsilon}\left(  \cdot\right)  \text{, where
}F_{\varepsilon}^{\prime}>0,\forall\varepsilon\right) \\
&  =1-F_{\varepsilon}\left(  VS^{-1}\left(  \frac{1}{2};\gamma,\delta\right)
\right)
\end{align*}
Again, partially differentiating the above expression gives us $\frac{\partial
P\left(  \gamma,\delta\right)  }{\partial\gamma}=-F_{\varepsilon}^{\prime
}\left(  VS^{-1}\left(  \frac{1}{2};\gamma,\delta\right)  \right)  \times
\frac{\partial VS^{-1}\left(  \frac{1}{2};\gamma,\delta\right)  }%
{\partial\gamma}\leq0$ and $\frac{\partial P\left(  \gamma,\delta\right)
}{\partial\delta}=-F_{\varepsilon}^{\prime}\left(  VS^{-1}\left(  \frac{1}%
{2};\gamma,\delta\right)  \right)  \times\frac{\partial VS^{-1}\left(
\frac{1}{2};\gamma,\delta\right)  }{\partial\delta}>0$. We have thus shown
that for any generic distribution functions $F\left(  \cdot,\cdot\right)  $
and $F_{\varepsilon}\left(  \cdot\right)  $ and if assumption \ref{assum2}
holds, then the probability of successful ratification via referendum is
weakly decreasing in the relative salience of the valence dimension and
strictly increasing in the incumbent's relative popularity.

In the simple case where all three variables are independently and uniformly
distributed, that is, $x^{j}\sim U\left[  0,1\right]  $, $\eta^{j}\sim
U\left[  -\frac{1}{2\theta},\frac{1}{2\theta}\right]  $, and $\varepsilon\sim
U\left[  -\frac{1}{2\mu},\frac{1}{2\mu}\right]  $, where$\ \theta>0$ and
$\mu>0$ capture the levels of ideological dispersion and aggregate uncertainty
(or else the instantaneous volatility of political capital around its trend)
respectively, calculations are simplified in the following manner:%
\begin{align*}
VS\left(  \varepsilon;\gamma,\delta\right)   &  =\underset{0}{\overset{1}%
{\int}}\overset{\frac{1}{2\theta}}{\underset{-\frac{\Delta u^{j}}{\gamma
}-\delta-\varepsilon}{\int}}\theta d\eta^{j}dx^{j}=\underset{0}{\overset
{1}{\int}}\theta\left(  \frac{1}{2\theta}+\frac{\Delta u^{j}}{\gamma}%
+\delta+\varepsilon\right)  dx^{j}=\frac{1}{2}+\theta\left(  \frac{\Delta
W}{\gamma}+\delta+\varepsilon\right) \\
P\left(  \gamma,\delta,\Delta W\right)   &  =\Pr\left(  VS\left(
\varepsilon;\gamma,\delta\right)  >\frac{1}{2}|\varepsilon\overset
{i.i.d.}{\sim}U\left[  -\frac{1}{2\mu},\frac{1}{2\mu}\right]  \right)
=\Pr\left(  \varepsilon>-\frac{\Delta W}{\gamma}-\delta\right) \\
&  =\frac{1}{2}+\mu\left(  \frac{\Delta W}{\gamma}+\delta\right)  .
\end{align*}


For the rest of the analysis we will employ the simple specification of the
probability function provided above (equation 1 in the text).

\subsection*{Nash Equilibria of the Treaty Ratification Subgame}

We now present the formal exposition of the Nash equilibria of the game. We
make the assumption of symmetric valence pay-offs mainly for reasons of
notational parsimony, which can also be rationalized by the fact that this is
a partial equilibrium setting, whereby the incumbent has no control over the
content of the new treaty and, therefore, is not primarily judged on its
ability to negotiate a favorable agreement.\footnote{Presumably, however, the
incumbent party should be expected to incur higher costs (benefits) of being
on the losing (winning) side of a popular vote, as it reflects badly (well) on
a) the popular perception of its performance to date and b) its reputation for
`getting things done', that is, its ability to mobilize its party resources
and rank-and-file with the goal of `selling' the treaty. Luxembourgian Prime
Minister Juncker, for example, threatened to resign in the event of a `No'
vote in the referendum on the Constitutional Treaty. Choosing either
assumption has no effect on the qualitative nature of the results.} To solve
for the Nash equilibria of the strategic-form game in Table 1
we derive the pure-strategy best-response correspondences with respect to the
probability of popular ratification $P\left(  \gamma,\delta,\Delta W\right)
\in\left(  0,1\right)  $. Define such correspondences as $BR^{i}:A^{j}%
\times\left(  0,1\right)  \rightrightarrows A^{i},i=I,O,i\neq j,$ where the
$A$'s denote the action sets of each player. Then for each action taken by the
opposition the incumbent's best response as a function of the probability of a
`Yes' vote is the following:%
\begin{equation}
BR^{I}\left(  \alpha^{O}\right)  =\left\{
\begin{array}
[c]{lc}%
\begin{array}
[c]{lc}%
\{C\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
>\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)  }{G\left(  x^{I}\right)
+2\left(  1+b\right)  }\\
\{NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
<\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)  }{G\left(  x^{I}\right)
+2\left(  1+b\right)  }\\
\{C,NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
=\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)  }{G\left(  x^{I}\right)
+2\left(  1+b\right)  }%
\end{array}
& ,\alpha^{O}=\{EN\}\\%
\begin{array}
[c]{lc}%
\{C\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
>\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)  }\\
\{NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
<\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)  }\\
\{C,NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
=\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)  }%
\end{array}
& ,\alpha^{O}=\{EY\}\\%
\begin{array}
[c]{lc}%
\{C\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
>\frac{G\left(  x^{I}\right)  +\left(  1-d\right)  }{G\left(  x^{I}\right)
+\left(  1+b\right)  }\\
\{NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
<\frac{G\left(  x^{I}\right)  +\left(  1-d\right)  }{G\left(  x^{I}\right)
+\left(  1+b\right)  }\\
\{C,NC\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
=\frac{G\left(  x^{I}\right)  +\left(  1-d\right)  }{G\left(  x^{I}\right)
+\left(  1+b\right)  }%
\end{array}
& ,\alpha^{O}=\{NE\}
\end{array}
\right.  \label{BRI}%
\end{equation}
The above probability threshold values make use of some new notation $G\left(
x^{j}\right)  =\frac{\Delta u\left(  x_{c},x_{SQ};x^{j}\right)  }{\gamma
},j=I,O$ for the salience-weighted utility differential from adopting the
proposed treaty. Similarly for given incumbent pure strategies the
opposition's best responses are:%
\begin{equation}
BR^{O}\left(  \alpha^{I}\right)  =\left\{
\begin{array}
[c]{ll}%
\begin{array}
[c]{ll}%
\{EN\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
\in\left(  0,\min\{\frac{d+b}{1+b},\frac{1}{2}\}\right) \\%
\begin{array}
[c]{c}%
\{EN,NE\}\text{ }\\
\text{\textit{or} }\{EN,EY\}
\end{array}
& \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)  =\min
\{\frac{d+b}{1+b},\frac{1}{2}\}\\
\{NE\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
\in\left(  \min\{\frac{d+b}{1+b},\frac{1}{2}\},\max\{\frac{1-d}{1+b},\frac
{1}{2}\}\right) \\%
\begin{array}
[c]{c}%
\{EN,NE\}\text{ }\\
\text{\textit{or} }\{EN,EY\}
\end{array}
& \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)  =\max
\{\frac{1-d}{1+b},\frac{1}{2}\}\\
\{EY\} & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta W\right)
\in\left(  \max\{\frac{1-d}{1+b},\frac{1}{2}\},1\right)
\end{array}
& ,\alpha^{I}=\{C\}\\
\{EN,EY\} & ,\alpha^{I}=\{NC\}
\end{array}
\right.  \label{BRO}%
\end{equation}


Define pure-strategy Nash equilibria as pairs of pure strategies that are
mutual best responses, that is, $\left(  \alpha^{I\ast},\alpha^{O\ast}\right)
$ such that $\alpha^{I\ast}\in BR^{I}\left(  \alpha^{O\ast}\right)  $ and
$\alpha^{O\ast}\in BR^{O}\left(  \alpha^{I\ast}\right)  $. Then the
best-response correspondences in (\ref{BRI}) and (\ref{BRO}) give rise to the
following pure-strategy Nash equilibria profile with respect to the
exogenously determined probability $P\left(  \gamma,\delta,\Delta W\right)  $:%
\begin{equation}
\left(  \alpha^{I\ast},\alpha^{O\ast}\right)  =%
\begin{array}
[c]{ll}%
\left(  C,EN\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \geq\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)  }{G\left(
x^{I}\right)  +2\left(  1+b\right)  }\text{ \textit{and }}P\left(
\gamma,\delta,\Delta W\right)  \leq\min\{\frac{d+b}{1+b},\frac{1}{2}\}\\
\left(  C,EY\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \geq\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)  }\text{
\textit{and }}P\left(  \gamma,\delta,\Delta W\right)  \geq\max\{\frac
{1-d}{1+b},\frac{1}{2}\}\\
\left(  NC,EN\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \leq\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)  }{G\left(
x^{I}\right)  +2\left(  1+b\right)  }\\
\left(  NC,EY\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \leq\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)  }%
\end{array}
\label{psNE1}%
\end{equation}


A close examination of the above best-response correspondences reveals the
existence of multiple equilibria at various points in the parameter
space.\footnote{In this case the equilibria are not strict, which means that
they do not consist of strict best responses. For at least one player not all
possible deviations leave him strictly worse off.} Whenever pure-strategy Nash
equilibria do not exist, there are always corresponding mixed-strategy Nash
equilibria. Overall the expectation derived from this model is that the
incumbent party $\left(  I\right)  $ is more likely to initiate a referendum
$\left(  C\right)  $ and the opposition $\left(  O\right)  $ more prone to
positively endorse it $\left(  EY\right)  $ when the commonly perceived
probability of a `Yes' vote is relatively high. Whenever the domestic
political climate appears to be highly polarized (that is, high $\gamma$) and
the incumbent's gains from closer international cooperation relatively low,
(that is, low $\Delta u\left(  x_{c},x_{SQ};x^{I}\right)  $), then the main
opposition party is more likely to adopt a more confrontational and polarising
stance by calling for a negative popular vote $\left(  EN\right)  $, thereby
inducing a midterm assessment of government performance through a second-order
type of election. However, it rarely appears to be the case that such partisan
policy confrontation takes place at the ballot box rather than the
parliamentary arena.\footnote{In light of our assumption about party cohesion
and simple majority rules and the assertion that voters only care about policy
outcomes insofar as they are excluded from the ratification process, the
rhetorical intensity of the main opposition party in parliament has no effect
on the payoffs of the game or the hypothetical outcome of the referendum vote;
parliamentary debate is deemed to be insulated from external audiences.} The
adversarial outcome $\left(  C,EN\right)  $ arises as an unlikely equilibrium
prediction, supported by a small range of parameter configurations that
eventually vanishes for infinitesimal levels of the reputational gain from
reflecting majority will $\left(  b\right)  $. Finally, the possibility of
pure strategy randomization (that is, the section of the parameter space that
only supports unique mixed-strategy Nash equilibria) is decreasing in $b$
relative to $d$, becoming non-existent for $b\in\left[  1-2d,1\right)  $. Note
that $\left(  C,NE\right)  $ can never arise as a pure-strategy Nash
equilibrium as there is no feasible parameter configuration that satisfies
both $P\left(  \gamma,\delta,\Delta W\right)  \geq\frac{G\left(  x^{I}\right)
+\left(  1-d\right)  }{G\left(  x^{I}\right)  +\left(  1+b\right)  }$ and
$\frac{d+b}{1+b}\leq P\left(  \gamma,\delta,\Delta W\right)  \leq\frac
{1-d}{1+b}$ given that $G\left(  x^{I}\right)  >0$. The same applies for
$\left(  NC,NE\right)  $, that is, the outcome where neither the government
nor the opposition favor popular ratification, since for any parameter
configuration $O$ will want to rhetorically endorse a referendum, in order to
reap the strictly positive reputational reward of appearing more democratic
$\left(  d>0\right)  $.

\subsection*{Comparative Statics and Utility Differentials}

A close examination of the normal form of the simple majority ratification
game depicted in Table 1 in the text yields the following expressions for
the utility differentials of both parties $I$ and $O$, where $\Delta
U^{i}\left(  a^{i},a^{i\prime}|a^{j}\right)  =U^{i}\left(  a^{i}|a^{j}\right)
-U^{i}\left(  a^{i\prime}|a^{j}\right)  ,a^{i}\in A^{i},\forall i=I,O,i\neq
j$:%
\begin{align}
\Delta U^{I}\left(  C,NC|EY\right)   &  =\Delta u\left(  x_{c},x_{SQ}%
;x^{I}\right)  P\left(  \gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  -\gamma d\right]
\nonumber\\
\Delta U^{I}\left(  C,NC|NE\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{I}\right)  +\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  +\gamma\left(
1-d\right)  \right] \nonumber\\
\Delta U^{I}\left(  C,NC|EN\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{I}\right)  +2\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  +\gamma\left(
1+b-d\right)  \right] \label{udifs}\\
\Delta U^{O}\left(  EN,NE|C\right)   &  =-\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  +\gamma\left(  b+d\right) \nonumber\\
\Delta U^{O}\left(  EY,NE|C\right)   &  =\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1-d\right) \nonumber\\
\Delta U^{O}\left(  EY,EN|C\right)   &  =2\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1+b\right) \nonumber\\
\Delta U^{O}\left(  EN,NE|NC\right)   &  =\gamma d\nonumber\\
\Delta U^{O}\left(  EY,NE|NC\right)   &  =\gamma d\nonumber\\
\Delta U^{O}\left(  EY,EN|NC\right)   &  =0\nonumber
\end{align}


\subsection*{Equilibria under Extreme Policy Positions}

Even for some prior ideological commitment to a stated and commonly known pro-
or anti- integration stance we assume that moderate opposition parties
$\left(  x^{O}\in\left[  x_{SQ},x_{c}\right]  \right)  $ may freely and
costlessly switch positions as dictated by the strategic contours of the game;
to boot, voters are arguably only aware of openly stated positions, that is,
ideal points $x^{j}$, not the full ranking of policy alternatives, that is,
utility functions $u\left(  \cdot,\cdot\right)  $. However, when parties have
an established reputation of extremist views with respect to say European
integration, then a directional assessment on the part of voters allows them
to impose `rhetorical consistency' costs on the opposition in the form of
dwindling political capital. This implies that a position in favor or against
the new treaty that runs counter to the party's established reputation becomes
non-credible and thus strictly dominated. In the remainder of this subsection
we consider the following two cases: i) integration-skeptic parties $\left(
x^{O}<x_{SQ}\right)  $ and ii) pro-integration parties $\left(  x^{O}%
>x_{c}\right)  $. In both cases we make the simplifying assumption of infinite
rhetorical costs (which discontinuously drop to zero within the interval of
moderate ideological preferences $\left[  x_{SQ},x_{c}\right]  $).

For anti-integration opposition parties $\left(  x^{O}<x_{SQ}\right)  $ it is
no longer a credible option to come out in favor of the new treaty $\left(
EY\right)  $\ because of the irreparable damage done to their long-term
reputation. That essentially locks them in an anti-integration ideological
position, which they may either choose to defend in a popular vote $\left(
EN\right)  $ or in parliament $\left(  NE\right)  $. In game-theoretic terms,
the elimination of a strictly dominated strategy renders the ratification
subgame a $2\times2$ normal-form game. A straightforward recalculation of best
responses gives rise to the following set of pure-strategy Nash equilibria:%

\begin{equation}
\left(  \alpha^{I\ast},\alpha^{O\ast}\right)  =%
\begin{array}
[c]{ll}%
\left(  NC,EN\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \in\left[  0,\frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)
}{G\left(  x^{I}\right)  +2\left(  1+b\right)  }\right] \\
\left(  C,EN\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \in\left[  \frac{G\left(  x^{I}\right)  +\left(  1+b-d\right)
}{G\left(  x^{I}\right)  +2\left(  1+b\right)  },\frac{b+d}{1+b}\right] \\
\left(  C,NE\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \geq\max\left\{  \frac{G\left(  x^{I}\right)  +\left(  1-d\right)
}{G\left(  x^{I}\right)  +\left(  1+b\right)  }.\frac{b+d}{1+b}\right\}
\end{array}
\label{psNE2}%
\end{equation}


As is evident from the above characterization of pure-strategy Nash
equilibria, an increase in the probability of successful ratification by
referendum has opposite effects on the two parties' equilibrium choice of
ratification mechanism. The more likely the treaty is to pass a popular vote,
the keener is the incumbent to call a referendum $\left(  C\right)  $ in the
first place and the more inclined is the opposition not to endorse one
$\left(  NE\right)  $. Note that in contrast to the equilibrium correspondence
in equation \ref{psNE1} of the original $2\times3$ game it is now possible for
$\left(  C,NE\right)  $ to become a pure-strategy Nash equilibrium for a high
enough probability of successful ratification by referendum. This refers to
cases of integration-skeptic opposition parties that would rather fight out
their cause in parliament (without losing face to their core supporters) than
lose a highly skewed popular contest.

In the case of strongly pro-integration opposition parties $\left(
x^{O}>x_{c}\right)  $ coming out against the new treaty becomes a strictly
dominated strategy. This leads to the following set of pure-strategy Nash equilibria:%

\begin{equation}
\left(  \alpha^{I\ast},\alpha^{O\ast}\right)  =%
\begin{array}
[c]{ll}%
\left(  NC,EY\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \in\left[  0,\frac{G\left(  x^{I}\right)  -d}{G\left(  x^{I}\right)
}\right] \\
\left(  C,EY\right)  & \text{\textit{iff} }P\left(  \gamma,\delta,\Delta
W\right)  \geq\max\left\{  \frac{G\left(  x^{I}\right)  -d}{G\left(
x^{I}\right)  }.\frac{1-d}{1+b}\right\}
\end{array}
\label{psNE3}%
\end{equation}
We find that strongly pro-integration opposition parties never favor
parliamentary ratification as part of a pure-strategy Nash equilibrium. Of
course mixed-strategy equilibria may arise for a certain range of
probabilities \textit{if and only if} $G\left(  x^{I}\right)  <\frac{d\left(
1+b\right)  }{b+d}$.

\subsection*{Alternative Constitutional Provisions for Referendum Initiation}

As explained before, the strategic interplay between the incumbent party's
prerogatives for referendum initiation and the opposition's rhetorical powers
should be examined within the context of specific institutional rules for
referendum initiation. The benchmark model is predicated on the presumption
that only the incumbent has referendum initiation prerogatives, which is the
most common rule amongst parliamentary democracies in Europe. In a few
countries, however, government majority in parliament is either oversufficient
(minority provisions) or insufficient (supermajority provisions).

In countries like Denmark and Slovenia the parliamentary vote threshold for
referendum initiation is low enough such that even minority opposition parties
have such prerogatives. In this case, the specification of the normal-form
game of ratification changes (see Table \ref{normalform2} below) with the main
difference from the benchmark model in Table 1 in the text being that the
incumbent no longer possesses full control over the policy component of the
ratification gamble, even though the opposition retains its influence over the
political stakes of the valence component. Guaranteed parliamentary
ratification of the treaty now only ensues when both mainstream parties opt
against the referendum option.%

%TCIMACRO{\TeXButton{B}{\begin{table}[htbp] \centering}}%
%BeginExpansion
\begin{table}[htbp] \centering
%EndExpansion%
%TCIMACRO{\TeXButton{footnotesize}{\footnotesize}}%
%BeginExpansion
\tiny
%EndExpansion%
\begin{tabular}
[c]{cc|c|c|c}
& \multicolumn{4}{c}{\textbf{\textquotedblleft O\textquotedblright}}\\
&  & \textbf{$EN$} & \textbf{$EY$} & \textbf{$NE$}\\\cline{2-5}%
\textbf{\textquotedblleft I\textquotedblright} & $\mathbf{C}$ &
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  ,$\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  ,$\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{NE}^{I}\right)  +d\right)  ,$\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{NE}^{I}\right)  +d\right)  $}%
\end{tabular}
\\\cline{2-5}
& $\mathbf{NC}$ &
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  -d\right)  ,$\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  -d\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  -d\right)  ,$\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma\left(  EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  -d\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$u\left(  x_{c};x^{I}\right)  ,$\\
\multicolumn{1}{r}{$u\left(  x_{c};x^{O}\right)  $}%
\end{tabular}
\end{tabular}%
%TCIMACRO{\TeXButton{normalsize}{\normalsize}}%
%BeginExpansion
\normalsize
%EndExpansion


\begin{center}
\caption{Ratification game with minority referendum initiation provisions}
\label{normalform2}
\end{center}

%

%TCIMACRO{\TeXButton{E}{\end{table}}}%
%BeginExpansion
\end{table}%
%EndExpansion


The normal form of the minority ratification game depicted in Table
\ref{normalform2} above gives us the following expressions for the utility
differentials of both parties $I$ and $O$:%

\begin{align}
\Delta U^{I}\left(  C,NC|EY\right)   &  =\gamma d\nonumber\\
\Delta U^{I}\left(  C,NC|NE\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{I}\right)  +\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  +\gamma\left(
1-d\right)  \right] \nonumber\\
\Delta U^{I}\left(  C,NC|EN\right)   &  =\gamma d\nonumber\\
\Delta U^{O}\left(  EN,NE|C\right)   &  =-\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  +\gamma\left(  b+d\right) \nonumber\\
\Delta U^{O}\left(  EY,NE|C\right)   &  =\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1-d\right) \nonumber\\
\Delta U^{O}\left(  EY,EN|C\right)   &  =2\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1+b\right) \label{udifsmin}\\
\Delta U^{O}\left(  EN,NE|NC\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{O}\right)  -2\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{O}\right)  -\gamma\left(
1+b+d\right)  \right] \nonumber\\
\Delta U^{O}\left(  EY,NE|NC\right)   &  =\Delta u\left(  x_{c},x_{SQ}%
;x^{O}\right)  P\left(  \gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{O}\right)  -\gamma d\right]
\nonumber\\
\Delta U^{O}\left(  EY,EN|NC\right)   &  =2\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1+b\right) \nonumber
\end{align}


On the other hand, the political system of a country such as Belgium contains
supermajority parliamentary provisions for referendum initiation. This implies
that both the incumbent and the main opposition party (depending on seat
allocation) need to concur for an international treaty to be submitted to a
popular vote.\footnote{A special case is Estonia, where a failed referendum
leads to the dissolution of parliament and new elections. This increases the
stakes of referendum initiation for all parties.} In this case, electoral
competition along the policy dimension is captured by the model specification
in Table \ref{normalform3} below:%

%TCIMACRO{\TeXButton{B}{\begin{table}[htbp] \centering}}%
%BeginExpansion
\begin{table}[htbp] \centering
%EndExpansion%
%TCIMACRO{\TeXButton{footnotesize}{\footnotesize}}%
%BeginExpansion
\footnotesize
%EndExpansion%
\begin{tabular}
[c]{cc|c|c|c}
& \multicolumn{4}{c}{\textbf{\textquotedblleft O\textquotedblright}}\\
&  & \textbf{$EN$} & \textbf{$EY$} & \textbf{$NE$}\\\cline{2-5}%
\textbf{\textquotedblleft I\textquotedblright} & $\mathbf{C}$ &
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  ,${\small \ \ }\\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EN}^{I}\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$Eu\left(  \Pi;x^{I}\right)  +\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  ,$ \ \\
\multicolumn{1}{r}{$Eu\left(  \Pi;x^{O}\right)  -\gamma EV\left(
%TCIMACRO{\tciLaplace}%
%BeginExpansion
\mathcal{L}%
%EndExpansion
_{EY}^{I}\right)  $}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$u\left(  x_{c};x^{I}\right)  +\gamma d,$ \ \\
\multicolumn{1}{r}{$u\left(  x_{c};x^{O}\right)  -\gamma d$}%
\end{tabular}
\\\cline{2-5}
& $\mathbf{NC}$ &
\begin{tabular}
[c]{l}%
$u\left(  x_{c};x^{I}\right)  -\gamma d,$ \ \\
\multicolumn{1}{r}{$u\left(  x_{c};x^{O}\right)  +\gamma d$}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$u\left(  x_{c};x^{I}\right)  -\gamma d,$ \ \\
\multicolumn{1}{r}{$u\left(  x_{c};x^{O}\right)  +\gamma d$}%
\end{tabular}
&
\begin{tabular}
[c]{l}%
$u\left(  x_{c};x^{I}\right)  ,$ \ \\
\multicolumn{1}{r}{$u\left(  x_{c};x^{O}\right)  $}%
\end{tabular}
\end{tabular}%
%TCIMACRO{\TeXButton{normalsize}{\normalsize}}%
%BeginExpansion
\normalsize
%EndExpansion


\begin{center}
\caption{Ratification game with supermajority referendum initiation provisions}
\label{normalform3}
\end{center}

%

%TCIMACRO{\TeXButton{E}{\end{table}}}%
%BeginExpansion
\end{table}%
%EndExpansion


The normal form of the supermajority ratification game depicted in Table
\ref{normalform3} above gives us the following expressions for the utility
differentials of both parties $I$ and $O$:%

\begin{align}
\Delta U^{I}\left(  C,NC|EY\right)   &  =\Delta u\left(  x_{c},x_{SQ}%
;x^{I}\right)  P\left(  \gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  -\gamma d\right]
\nonumber\\
\Delta U^{I}\left(  C,NC|NE\right)   &  =\gamma d\nonumber\\
\Delta U^{I}\left(  C,NC|EN\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{I}\right)  +2\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{I}\right)  +\gamma\left(
1+b-d\right)  \right] \nonumber\\
\Delta U^{O}\left(  EN,NE|C\right)   &  =\left[  \Delta u\left(  x_{c}%
,x_{SQ};x^{O}\right)  -2\gamma\left(  1+b\right)  \right]  P\left(
\gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{O}\right)  -\gamma\left(
1+b+d\right)  \right] \label{udifssuper}\\
\Delta U^{O}\left(  EY,NE|C\right)   &  =\Delta u\left(  x_{c},x_{SQ}%
;x^{O}\right)  P\left(  \gamma,\delta,\Delta W\right) \nonumber\\
&  -\left[  \Delta u\left(  x_{c},x_{SQ};x^{O}\right)  -\gamma d\right]
\nonumber\\
\Delta U^{O}\left(  EY,EN|C\right)   &  =2\gamma\left(  1+b\right)  P\left(
\gamma,\delta,\Delta W\right)  -\gamma\left(  1+b\right) \nonumber\\
\Delta U^{O}\left(  EN,NE|NC\right)   &  =\gamma d\nonumber\\
\Delta U^{O}\left(  EY,NE|NC\right)   &  =\gamma d\nonumber\\
\Delta U^{O}\left(  EY,EN|NC\right)   &  =0\nonumber
\end{align}


As a final note, we remark some of the changes in the comparative statics
behavior of the model compared to the results presented in Table
2 in the main text as a consequence of alternative constitutional provisions
for referendum initiation (see utility differentials in equations
\ref{udifsmin}\ and \ref{udifssuper}\ above). The effect of the aggregate
welfare differential variable $\left(  \Delta W\right)  $ on the relative odds
of $EN$ vs. $NE$ is ambiguous for $I$ both in the minority and supermajority
cases and strictly negative for $O$ unless $\Delta u^{O}$ is very high. The
partial effect of government popularity $\left(  \delta\right)  $ on the
relative odds of $EN$ vs. $NE$ is also ambiguous under both sets of provisions
unless $\Delta u^{O}>2\gamma\left(  1+b\right)  $, in which case the effect
becomes - counterintuitively so - positive. Finally, we need to distinguish
between the policy preferences of $I$ and $O$ with respect to their effect on
the choice of $EY$ vs. $EN$, which remains strictly positive for $\Delta
u^{I}$ and becomes zero for $\Delta u^{O}$.\pagebreak

\clearpage


\section*{Appendix II: The Data}

For space reasons, the exposition of the control variables included in the empirical analysis remained very brief in the main part of this paper. Here, we discuss these variables in more detail: first, we include a measure of the party's policy benefits from ratifying the Treaty $(\Delta u\left(x_{c},x_{SQ};x^{j}\right)  )$ (\textit{Party benefit}). In most models we rely on data obtained by hand-coding parties' programmes for the 2004 European Parliament elections to operationalize this variable (Braun et al. 2007). More specifically, we use a measure of a party's general stance with respect to European integration that is an aggregate of nine different coding categories.\footnote{The variable used is the log ratio of pro- and anti- European integration statements in party programs. See Veen (2011).} The advantage of these data is that they reflect party positions from 2004 when parties concretized their stance with respect to the Constitutional Treaty. We managed to find values for this variable for 169 of the 175 parties included in our analysis (in two cases we use the position of the European party family as a proxy for the position of the national party). We cross-check our results with the help of the Chapel Hill expert survey from 2002 (Hooghe et al. 2010).  This variable ranges from 1 (strongly opposed) to 7 (strongly in favor). For some parties that were not included in the 2002 Chapel Hill survey we rely on the 2006 survey (which includes more parties) and, if the party was also not included in the 2006 survey, we use the mean for the European party family. Even after doing so, we have missing data for ten parties.\footnote{The results reported are not sensitive to this imputation strategy.}  The correlation between the Veen and Hooghe et al. data is 0.57.

Second, we operationalize the democratic legitimacy benefits of a referendum $(d)$ by way of a Eurobarometer poll from spring 2003 (Eurobarometer 2003a) that asked respondents whether they considered it essential, useful but not essential, or useless \textquotedblleft that all citizens of the European Union could give their opinion, by referendum, on the draft Constitution\textquotedblright%
(\textit{Legitimacy}). The disadvantage of the wording of this
question is that it refers to \textquotedblleft\textit{all}
citizens\textquotedblright\ (emphasis added), suggesting a response on the desirability of a Europe-wide referendum (which is different from the need for a national referendum on a treaty). Because most respondents were probably not aware of this distinction, we decided to stick to these data. The fact that this poll is from spring 2003, and thus before  most political parties decided on whether to back a referendum, allows us to avoid a potential endogeneity problem that arises if parties' public support for a referendum influences
public opinion on that question. The variable is calculated as the percentage of respondents that considered a
referendum essential divided by the sum of the percentages that considered a referendum essential and useless. 

Third, the variable \textit{Minority} takes the value 1 for parties in the Czech Republic, Denmark, and Slovenia, that is, countries in which a parliamentary minority could force the holding of a referendum on the Constitutional Treaty either by refusing to accept parliamentary ratification (in countries with a qualified majority requirement for parliamentary ratification) or by using constitutional provisions that allow a minority of parliament to call a referendum. Fourth, \textit{New member} is a dummy variable for countries that acceded to the EU in May 2004. Fifth, since relative valence salience $\left(  {\normalsize \gamma}\right)  $ is arguably conditional on how adversarial a political system is, we include a control variable that captures the competitiveness of the political system (\textit{Competitiveness}). This variable is measured as the number of effective parties at the electoral level in the last elections prior to the start of the intergovernmental conference (Gallagher and Mitchell 2008). Finally, we include a dummy variable for left-wing and liberal parties, which tend to be more supportive of direct democracy and, therefore, of referendums than right-wing ones (\textit{Ideology}).\footnote{This variable is based on the classification in http://www.parties-and-elections.de/.}  In Table \ref{descript} we present a summary of the variables and data sources used.


\singlespacing
\begin{table}[h]
\begin{tabular}
[c]{lccccccc}%
Variables (parameter) & N & Mean & SD & Min & Max & Operationalisation & Source\\\hline
Party position & 175 & 1.88 & 0.85 & 1 & 3 & & 1\\
Political capital ($\delta$) & 175 & 38.92 & 15.98 & 7.6 & 78.1 & Public opinion & 2\\
Timing ($\gamma$) & 175 & 8.09 & 3.70 & 0.7 & 15.6 & Days left as of 01/01/04 & 3\\
& & & & & & (divided by 100) & \\
Public support ($\Delta W$) & 175 & 83.92 & 8.77 & 63.0 & 94.6 & Public opinion & 4\\
Party benefit ($\Delta u$) & 169 & 13.10 & 22.86 & -61.4 & 58.5 & Party programmes & 5\\
Legitimacy ($d$) & 175 & 74.41 & 13.57 & 40.7 & 94.7 & Public opinion & 6\\
Minority & 175 & 0.11 & 0.32 & 0 & 1 & Constitutional provisions & 7\\
New member & 175 & 0.37 & 0.48 & 0 & 1 & 2004 accession & 8\\
Competitiveness & 175 & 5.07 & 1.72 & 2.0 & 8.9 & Effective parties & 9\\
Ideology & 175 & 0.46 & 0.50 & 0 & 1 & Left and liberal parties & 3\\\hline
\end{tabular}
\begin{center}
\caption*{Sources: 1 D\"{u}r and Mateo 2011; 2 Eurobarometer 2004b; 3 www.parties-and-elections.de; 4 Eurobarometer 2004a; 5 Veen 2011; Eurobarometer 2003; 7 verfassungsvergleich.de; 8 Own data; 9 Gallagher and Mitchell 2008.} 
\caption{Descriptive statistics and data sources (Model 1)}
\label{descript}%
\end{center}%
\end{table}


\singlespacing
\begin{table}[h]
\begin{tabular}
[c]{llll}%
Country & Provision & Country & Provision\\\hline
Austria & Simple majority & Latvia & Simple majority\\
Belgium & No provision & Lithuania & Simple majority\\
Cyprus & No provision & Luxembourg & Simple majority\\
Czech Republic & Simple majority & Malta & No provision\\
Denmark & Minority right & Netherlands & No provision\\
Estonia  & Simple majority & Poland & Absolute majority\\
Finland & Simple majority & Portugal & Simple majority\\
France & Simple majority & Slovakia & Simple majority\\
Germany & No provision & Slovenia & Minority right\\
Greece & Simple majority & Spain & Simple majority\\
Hungary & Simple majority & Sweden & Simple majority\\
Italy & Simple majority & United Kingdom & Simple majority\\\hline

\end{tabular}
\begin{center}
\caption*{Note: based on \url{http://www.servat.unibe.ch/law/icl/index.html} (except for France: \url{http://www.assemblee-nationale.fr/english/8ab.asp}). Certain assumptions have to be made to derive the coding from the legal texts; i.e. that the Constitutional Treaty does not imply a change in national constitutions and that no additional transfer of powers is required (otherwise some constitutions foresee mandatory referendums). In most cases, ``no provision'' means that a change of the constitution is required (mostly by two thirds majority). In some cases, a non-binding referendum may be called with simple majority in the absence of a constitutional provision. In France, the President can also call a referendum on the proposal of the government. In Italy, only an initiative can be called (Art. 71 of the Constitution); a referendum on an international treaty is prohibited under Art. 75.} 
\caption{Constitutional provisions for referendum initiation}
\label{const}%
\end{center}%
\end{table}

\clearpage

\newpage

%\thispagestyle{empty}

\section*{Appendix III: Additional Empirical Results}

\singlespacing
\begin{table}[h]
\begin{small}
\begin{tabular}
[c]{lcccccc}
& \multicolumn{2}{c}{Model A1} & \multicolumn{2}{c}{Model A2} & \multicolumn{2}{c}{Model A3}\\
& \multicolumn{2}{c}{(probit)} &
\multicolumn{2}{c}{(probit)} &
\multicolumn{2}{c}{(probit)}\\
& $EN/NE$ & $EY/NE$ & $EN/NE$ & $EY/NE$ & $EN/NE$ & $EY/NE$\\\hline
\textsc{Predictors:}&  &  &  &  &  & \\
&  &  &  &  &  & \\
\hskip .3cm  Political capital&-0.05***&-0.03*&-0.03&-0.01&-0.05***&-0.03*\\
&(0.01)&(0.02)&(0.02)&(0.01)&(0.02)&(0.02)\\
\hskip .3cm Timing&-1.46***&-0.37&-0.01***&-0.00***&-0.00&0.00\\
&(0.36)&(0.25)&(0.00)&(0.00)&(0.00)&(0.00)\\
\hskip .3cm Timing\textsuperscript{2}&0.08***&0.02&0.00***&0.00***&0.00***&0.00\\
&(0.02)&(0.02)&(0.00)&(0.00)&(0.00)&(0.00)\\
\hskip .3cm Public support&-0.15***&-0.06&-0.26***&-0.17***&-0.15***&-0.06\\
&(0.05)&(0.05)&(0.05)&(0.05)&(0.04)&(0.05)\\
\hskip .3cm Political capital*Timing&&&0.00***&0.00***&&\\
&&&(0.00)&(0.00)&&\\
\hskip .3cm Welfare*Timing&&&&&-0.00*&-0.00\\
&&&&&(0.00)&(0.00)\\
\textsc{Controls:}&  &  &  &  &  & \\
&  &  &  &  &  & \\
\hskip .3cm Party benefit&-0.08***&0.01&-0.08***&0.01&-0.08***&0.01\\
&(0.02)&(0.01)&(0.02)&(0.01)&(0.02)&(0.01)\\
\hskip .3cm Legitimacy&-0.02&0.05**&-0.07**&-0.01&-0.02&0.05**\\
&(0.02)&(0.02)&(0.03)&(0.04)&(0.02)&(0.02)\\
\hskip .3cm Minority&0.84&1.32&1.34&1.44&1.01&1.42\\
&(1.04)&(1.07)&(0.83)&(0.93)&(0.91)&(0.92)\\
\hskip .3cm New member&-1.39***&-1.07**&-1.45***&-1.30***&-1.00&-0.64\\
&(0.51)&(0.48)&(0.47)&(0.44)&(0.62)&(0.56)\\
\hskip .3cm Competitiveness&0.22*&-0.02&-0.18&-0.53**&0.12&-0.09\\
&(0.13)&(0.16)&(0.21)&(0.24)&(0.13)&(0.16)\\
\hskip .3cm Ideology&0.20&0.82***&0.14&0.76**&0.10&0.79**\\
&(0.40)&(0.30)&(0.43)&(0.37)&(0.40)&(0.31)\\
\hskip .3cm Constant&20.36***&2.82&6.86**&3.91&12.26***&0.84\\
&(4.20)&(3.77)&(3.04)&(3.67)&(3.26)&(3.48)\\
N (clusters)&169 (24)&169 (24)&169 (24)&169 (24)&169 (24)&169 (24)\\
Log.lik.&-112.91&-112.91&-98.65&-98.65&-109.81&-109.81\\
BIC&338.68&338.68&315.28&315.28&337.60&337.60\\
\hline
\multicolumn{7}{l}{Standard errors clustered by country in parentheses; *** p$<$0.01, **
p$<$0.05, * p$<$0.1.}\\
&  &  &  &  &  &
\end{tabular}
\begin{center}
\caption{\protect Robustness checks, Models A1-A3}
\label{robust0}%
\end{center}%
\end{small}
\end{table}


\begin{table}
{\normalsize
\begin{tabular}
[c]{lcccccc}
& \multicolumn{2}{c}{Model A4} &
\multicolumn{2}{c}{Model A5}\\
& \multicolumn{2}{c}{(no government)} &
\multicolumn{2}{c}{(no extreme)}\\
& EN/NE & EY/NE & EN/NE & EY/NE\\\hline
\textsc{Predictors:}  &  &  &  & \\
&  &  &  & \\
\hskip .3cm Political capital&-0.06**&-0.03&-0.08***&-0.05**\\
&(0.03)&(0.02)&(0.02)&(0.02)\\
\hskip .3cm Timing&-2.02***&-0.60&-2.42***&-0.53\\
&(0.62)&(0.39)&(0.79)&(0.40)\\
\hskip .3cm Timing\textsuperscript{2}&0.12***&0.03&0.15***&0.03\\
&(0.04)&(0.03)&(0.05)&(0.03)\\
\hskip .3cm Public support&-0.19***&-0.07&-0.14&-0.03\\
&(0.07)&(0.08)&(0.09)&(0.06)\\
\textsc{Controls:} &  &  &  & \\
 &  &  &  & \\
\hskip .3cm Party benefit&-0.09***&0.03&-0.11**&0.02\\
&(0.03)&(0.02)&(0.05)&(0.02)\\
\hskip .3cm Legitimacy&-0.02&0.10**&-0.04&0.05\\
&(0.04)&(0.05)&(0.03)&(0.03)\\
\hskip .3cm Minority&0.97&0.96&0.09&1.33\\
&(1.37)&(1.25)&(1.60)&(1.46)\\
\hskip .3cm New member&-1.07&-1.44*&-1.00&-1.47**\\
&(0.81)&(0.74)&(0.95)&(0.63)\\
\hskip .3cm Competitiveness&0.36&0.19&-0.00&-0.21\\
&(0.24)&(0.32)&(0.29)&(0.25)\\
\hskip .3cm Ideology&0.78&1.75***&0.95&1.38***\\
&(0.61)&(0.61)&(0.77)&(0.38)\\
Constant&24.47***&0.04&24.71***&1.99\\
&(6.86)&(5.89)&(8.35)&(4.59)\\
N (clusters)&109 (24)&109 (24)&118 (24)&118 (24)\\
Pseudo R2 & 0.39 & 0.39 & 0.31 & 0.31\\
BIC &  248.67 & 248.67 & 237.81 & 237.81\\\hline
\multicolumn{5}{l}{Standard errors clustered by country in parentheses.}\\
\multicolumn{5}{l}{*** p$<$0.01, ** p$<$0.05, * p$<$0.1.}\\
&  &  &  &  &  &
\end{tabular}
}\begin{center}
\caption{\protect Robustness checks, Models A4-A5}
\label{robust1}%
\end{center}%
\end{table}

\begin{table}
{\normalsize
\begin{tabular}
[c]{lcccccc}
& \multicolumn{2}{c}{Model A6} & \multicolumn{2}{c}{Model A7} &
\multicolumn{2}{c}{Model A8}\\
& \multicolumn{2}{c}{(multilevel)} & \multicolumn{2}{c}{(Hooghe et al.)} &
\multicolumn{2}{c}{(gov. approval)}\\
& EN/NE & EY/NE & EN/NE & EY/NE & EN/NE & EY/NE\\\hline
\textsc{Predictors:}&  &  &  &  &  & \\
&  &  &  &  &  & \\
\hskip .3cm Political capital & -3.96*** & -2.42*** & -0.10*** & -0.04* & -0.05* & -0.04*\\
  & (1.29) & (0.75) & (0.02) & (0.02) & (0.03) & (0.02)\\
\hskip .3cm Timing & -1.15 & -1.57 & -1.95*** & -0.49 & -2.16*** & -0.57*\\
  & (0.96) & (0.96) & (0.51) & (0.34) & (0.66) & (0.33)\\
\hskip .3cm Timing\textsuperscript{2} & 9.39*** & -0.73 & 0.11*** & 0.03 & 0.12*** & 0.03\\
  & (2.32) & (1.48) & (0.03) & (0.02) & (0.04) & (0.02)\\
\hskip .3cm Public support & -4.64*** & 0.11 & -0.14** & -0.07 & -0.20*** & -0.06\\
  & (1.17) & (1.00) & (0.07) & (0.07) & (0.07) & (0.07)\\
\textsc{Controls:}&  &  &  &  &  & \\
&  &  &  &  &  & \\
\hskip .3cm Party benefit & -5.59*** & 0.93 & -1.77*** & 0.19 & -0.12*** & 0.01\\
  & (1.10) & (0.64) & (0.34) & (0.24) & (0.03) & (0.01)\\
\hskip .3cm Legitimacy & -1.00 & 1.83** & -0.05 & 0.06* & -0.03 & 0.06*\\
  & (0.78) & (0.85) & (0.04) & (0.04) & (0.03) & (0.03)\\
\hskip .3cm Minority & 0.51 & 0.51 & -1.53 & 1.58 & 1.14 & 1.87\\
  & (0.66) & (0.74) & (1.57) & (1.39) & (1.25) & (1.21)\\
\hskip .3cm New member & -2.41** & -1.84*** & -1.39* & -1.44** & -1.53** & -1.56***\\
  & (0.95) & (0.69) & (0.76) & (0.62) & (0.67) & (0.55)\\
\hskip .3cm Competitiveness & 0.85 & -1.25 & -0.21 & -0.01 & 0.30 & -0.03\\
  & (0.81) & (0.89) & (0.23) & (0.21) & (0.21) & (0.23)\\
\hskip .3cm Ideology & 0.22 & 1.18** & -0.62 & 1.14*** & 0.15 & 0.95**\\
  & (0.61) & (0.52) & (0.67) & (0.40) & (0.57) & (0.39)\\
Country level variance & 3.58 & 3.58 &  &  &  & \\
  & -1.78 & -1.78 &  &  &  & \\
Constant & -4.16*** & -0.54 & 35.93*** & 3.56 & 27.81*** & 4.28\\
  & (0.86) & (0.46) & (8.12) & (4.47) & (6.89) & (4.93)\\
N (clusters) & 169 (24) & 169 (24) & 165 (24) & 165 (24) & 169 (24) & 169 (24)\\
Pseudo R\textsuperscript{2} &  &  & 0.4 & 0.4 & 0.38 & 0.38\\
BIC & 338.68 & 338.68 & 321.59 & 321.59 & 338.64 & 338.64\\\hline
\multicolumn{7}{l}{Standard errors (clustered by country in Models A7 and A8) in parentheses}\\ 
\multicolumn{7}{l}{*** p$<$0.01, **
p$<$0.05, * p$<$0.1.}\\
&  &  &  &  &  & \\
\end{tabular}
}\begin{center}
\caption{\protect Robustness checks, Models A6-A8}
\label{robust2}%
\end{center}%
\end{table}

\singlespacing

\begin{table}
{\normalsize
\begin{tabular}
[c]{lcccc}
& \multicolumn{2}{c}{Model A9} & \multicolumn{2}{c}{Model A10} \\
& \multicolumn{2}{c}{(internal divisions)} & \multicolumn{2}{c}{(drop Germany)}\\
& EN/NE & EY/NE & EN/NE & EY/NE \\\hline
\textsc{Predictors:}&  &  &  & \\
&  &  &  &   \\
\hskip .3cm Political capital & -0.11** & -0.13*** & -0.06*** & -0.04* \\
  & (0.05) & (0.04) & (0.02) & (0.02) \\
\hskip .3cm Timing & -3.32*** & -1.41*** & -2.10*** & -0.39 \\
  & (1.01) & (0.44) & (0.56) & (0.32) \\
\hskip .3cm Timing\textsuperscript{2} & 0.21*** & 0.11*** & 0.12*** & 0.02  \\
  & (0.07) & (0.03) & (0.04) & (0.02)  \\
\hskip .3cm Public support & -0.24*** & -0.09* & -0.22*** & -0.06  \\
  & (0.08) & (0.05) & (0.07) & (0.07)\\
\textsc{Controls:}&  &  &  &  \\
&  &  &  &  \\
\hskip .3cm Party benefit & -0.16*** & 0.02 & -0.11*** & 0.02  \\
  & (0.05) & (0.02) & (0.03) & (0.01) \\
\hskip .3cm Legitimacy & -0.05 & 0.07* & -0.03 & 0.07** \\
  & (0.04) & (0.04) & (0.03) & (0.03) \\
\hskip .3cm Minority & -0.84 & 2.77** & 1.05 & 1.74  \\
  & (1.41) & (1.27) & (1.41) & (1.36)  \\
\hskip .3cm New member & 0.16 & -1.48* & -1.49** & -1.43**  \\
  & (1.18) & (0.83) & (0.69) & (0.61)\\
\hskip .3cm Competitiveness & -0.20 & -0.40* & 0.32* & -0.06 \\
  & (0.29) & (0.23) & (0.19) & (0.21) \\
\hskip .3cm Ideology & 1.51** & 1.24** & 0.19 & 1.11*** \\
  & (0.77) & (0.52) & (0.59) & (0.41) \\
\hskip .3cm Cohesiveness & -0.75* & 0.15 &  & \\
  & (0.40) & (0.38) &  &  \\
Constant & 42.21*** & 10.11 & 28.49*** & 2.66  \\
  & (12.28) & (6.54) & (6.13) & (4.90) \\
N (clusters) & 136 (24) & 136 (24) & 163 (23) & 163 (23)  \\
Pseudo R\textsuperscript{2} & 0.49 & 0.49 & 0.49 & 0.49 \\
BIC & 241.82 & 241.82 & 323.69 & 323.69\\\hline
\multicolumn{5}{l}{Standard errors clustered by country in parentheses.}\\
\multicolumn{5}{l}{*** p$<$0.01, **p$<$0.05, * p$<$0.1.}\\
\end{tabular}
}\begin{center}
\caption{\protect Robustness checks, Models A9-A10}
\label{robust3}%
\end{center}%
\end{table}


\begin{table}
{\normalsize
\begin{tabular}
[c]{lcccccc}
 & \multicolumn{2}{c}{NE} & \multicolumn{2}{c}{EN} & \multicolumn{2}{c}{EY}\\
Country & Observed & Predicted & Observed & Predicted & Observed & Predicted\\
\hline
AT & 3 & 3 & 1 & 1 & 0 & 0\\
BE & 4 & 4 & 2 & 4 & 4 & 2\\
CY & 5 & 7 & 0 & 0 & 2 & 0\\
CZ & 0 & 3 & 2 & 1 & 3 & 1\\
DE & 2 & 1 & 1 & 0 & 3 & 5\\
DK & 0 & 0 & 3 & 2 & 5 & 6\\
EE & 4 & 6 & 0 & 0 & 2 & 0\\
EL & 1 & 0 & 2 & 1 & 1 & 3\\
ES & 0 & 0 & 7 & 9 & 5 & 3\\
FI & 4 & 6 & 2 & 1 & 1 & 0\\
FR & 0 & 0 & 3 & 2 & 5 & 6\\
HU & 3 & 4 & 0 & 0 & 1 & 0\\
IT & 10 & 11 & 1 & 1 & 1 & 0\\
LA & 9 & 9 & 0 & 0 & 0 & 0\\
LI & 6 & 7 & 1 & 0 & 1 & 1\\
LU & 0 & 1 & 2 & 2 & 4 & 3\\
MA & 2 & 1 & 0 & 0 & 0 & 1\\
NE & 3 & 4 & 2 & 2 & 4 & 3\\
PL & 0 & 2 & 3 & 3 & 4 & 2\\
PO & 1 & 0 & 2 & 2 & 3 & 4\\
SI & 5 & 2 & 0 & 1 & 0 & 2\\
SK & 5 & 5 & 3 & 3 & 0 & 0\\
SW & 5 & 0 & 2 & 2 & 0 & 5\\
UK & 0 & 0 & 5 & 6 & 4 & 3\\
\textbf{TOTAL} & \textbf{72} & \textbf{76} & \textbf{44} & \textbf{43} & \textbf{53} & \textbf{50}\\
\hline
\end{tabular}
}\begin{center}
\caption*{Note: The ``observed'' columns exclude 6 parties for which we have missing observations on at least one covariate.}
\caption{\protect Intra-country variation of \textit{observed} and \textit{predicted} party stances with respect to the ratification of the Constitutional Treaty}
\label{intracountry}%
\end{center}%
\end{table}


\end{document}