The Ceuta Signal

1. Introduction

The Ceuta episode is analytically useful because it separates two questions that democratic discourse often conflates. The first is epistemic: which political actor offers the best statistical description of the migration risk? The second is strategic: which actor changes enough voters' expected utilities to obtain an electoral advantage? The first question concerns inference. The second concerns equilibrium.

In the public exchange, Sánchez's reply relied on accumulated detections of irregular border crossings. The figures he circulated and attributed to Frontex placed Italy above Spain over the 2021–2026 interval. Meloni's move did not directly disprove those counts. Instead, it altered the temporal and conditional object of comparison. The relevant question for her target voter became not "Which route generated more detections during the previous five years?" but "Which government will reduce the probability that the present external shock reaches me?"

That transformation is game-theoretically nontrivial. A historical frequency is a base rate; a mass border event is a public signal; an internal-border intervention is both an action and a signal of governmental type; the European reaction affects higher-order beliefs; and the voter's decision is conditioned by loss aversion, limited attention and the opportunity to delegate responsibility. These mechanisms can make a low-probability event electorally decisive without making it objectively probable.

The paper contributes a compact formal synthesis. It embeds Bayesian updating, salience weighting, maxmin expected utility, costly signalling, strategic information transmission and issue ownership in a single electoral framework. The purpose is not to claim that every voter literally solves the equations below. The model instead identifies the incentives that can emerge from stable behavioural regularities and from the strategic structure of political communication.

The central thesis can be expressed in one line:

A message may maximise accuracy while an action maximises votes. Conversely, an electorally profitable action may be weakly connected to the modal factual state. This divergence is not an anomaly outside game theory; it is precisely what one should expect when players have different objectives, information sets and payoff functions.

The remainder of the paper proceeds as follows. Section 2 reconstructs the empirical and institutional setting. Section 3 places the model in the literature. Sections 4–10 develop the game. Section 11 states the main theorem. Section 12 provides a numerical calibration. Section 13 discusses interpretation and limitations, and Section 14 concludes.

2. Institutional and empirical background

2.1. The shock and the policy response

During the late-July 2026 border emergency, tens of thousands of people crossed from Morocco into the Spanish autonomous city of Ceuta. Contemporary reporting converged on a final Spanish estimate of approximately 50,000 irregular entries, while 48,300 people were reported to have returned voluntarily to Morocco by the following day, leaving fewer than 2,000 in the enclave at that stage (El País, 2026). Reuters reported both the rapid return movement and the fatalities associated with the border rush (Reuters, 2026).

Italy responded by temporarily reintroducing controls at internal air and sea borders with Spain. The European Commission's Schengen notification page records the Italian measure for 1 August to 1 September 2026 and identifies the stated rationale as a threat to public policy, internal security and migration management, including a perceived risk of secondary movements from Ceuta (European Commission, 2026a). Under the Schengen Borders Code, such controls are legally conceived as exceptional, time-limited, necessary and proportionate measures of last resort (European Parliament and Council, 2016; European Commission, 2026a).

The important distinction for the model is that the event was large relative to the population and reception capacity of Ceuta but not automatically equivalent to a large realised flow into continental Europe, still less into Italy. Its electoral relevance depended on the conversion of a local realised shock into a prospective transnational risk.

2.2. The Sánchez base-rate argument

Sánchez answered the Italian position by publicising route-level values attributed to Frontex for 2021–2026: 478,600 detected irregular entries through Italy, 340,600 through the Western Balkans, 259,800 through Greece and 234,760 through Spain (Cadena SER, 2026). The argument was designed to show that the Spanish route was not the Union's principal structural vulnerability and that Italy had historically experienced a substantially larger volume. Let $M_I$ denote the reported Italian count and $M_S$ the reported Spanish count:

Within that restricted comparison, the Italian value is slightly more than twice the Spanish value. The descriptive point is strong but must be interpreted carefully. Frontex data concern detections of irregular border crossings along routes and need not correspond one-for-one to unique persons; individuals can in some circumstances be detected more than once. More importantly, accumulated route detections estimate a historical frequency, whereas Meloni's claim concerned a conditional future risk following an exceptional event.

Table 1 summarises the empirical inputs used in the model. The paper does not attempt an independent forensic reconstruction of the event; it studies the strategic consequences of the public information environment available on 3 August 2026.

3. Relation to the literature

The model combines several literatures that are usually studied separately. Bayesian games with incomplete information originate in Harsanyi's formalisation of type spaces and common priors. Political actors and voters in the present model possess different information and incentives; equilibrium therefore requires both strategies and beliefs.

The distinction between Sánchez's verbal rebuttal and Meloni's action follows the theory of strategic communication. Crawford and Sobel show that cheap talk becomes less informative as sender and receiver preferences diverge. Even truthful data may have little marginal effect when the audience knows that the sender would defend the same national position across states. By contrast, Spence-style costly signalling allows an observable action to reveal type when the cost is lower for a genuinely committed type than for an opportunistic type.

The treatment of attention and vividness draws on salience theory and rational inattention. Bordalo, Gennaioli and Shleifer formalise the overweighting of states that stand out relative to a reference set. Sims shows that information processing is itself costly. A dramatic mass event may consequently dominate a statistically richer but cognitively expensive time series.

The decision under uncertainty combines prospect theory, reference dependence and ambiguity aversion. Loss aversion makes preventive policies attractive even when their perceived effectiveness is small. Gilboa and Schmeidler's maxmin criterion explains why voters may optimise against a worst plausible probability rather than a central estimate. Kőszegi and Rabin provide a framework in which losses are evaluated relative to expectations rather than absolute outcomes.

The responsibility-transfer component is related to experimental work showing that delegation can diffuse responsibility for self-interested or harmful choices. Hamman, Loewenstein and Weber and Bartling and Fischbacher demonstrate that principals may use agents to shift perceived responsibility even when they retain substantial control over the outcome. In electoral politics, a protective leader can perform an analogous function by converting uncertain collective agency into delegated executive ownership.

Finally, the issue-salience mechanism connects to the literature on issue ownership and agenda manipulation. Petrocik argues that parties benefit when elections are fought on issues for which voters perceive them as comparatively competent. Riker's concept of heresthetic emphasises that political victory can result from changing the dimensions of choice rather than persuading opponents within a fixed dimension. Meloni's strongest strategic move is therefore not necessarily her estimate of migration risk; it is her capacity to make migration security the dimension on which the election is evaluated.

4. The basic Bayesian political game

4.1. Players, states and timing

Consider a finite Bayesian game $\Gamma =(N,\Theta ,A,P,U)$. The set of strategic players is $N=\{G,S,V\}$, where $G$ is the Italian government, $S$ is the Spanish government and $V$ is a representative pivotal voter. A continuum version is introduced in Section 9.

The state $\theta \in \{0,1\}$ represents whether the Ceuta event generates a materially significant onward-movement risk toward Italy. State $\theta =1$ denotes a high-risk state and $\theta =0$ a contained state. Before the public shock, the voter has prior probability ${\pi }_0=\mathrm{Pr}(\theta =1)$.

The timing is: (i) nature draws $\theta$; (ii) the Ceuta shock $x_C$ becomes public; (iii) the Italian government chooses an action $a_G$; (iv) Spain sends a message $m_S$; (v) European institutions and other governments generate a public-response vector $K$; (vi) the voter updates beliefs and votes.

Assumption A1 (Common prior). All players begin from a common prior ${\pi }_0$, but they may process public information with different attention and salience parameters.

Assumption A2 (Governmental action set). The Italian government selects $a_G\in \{N,C,E\}$: no exceptional action, selective controls, or broader European escalation.

Assumption A3 (Spanish message set). Spain selects $m_S\in \{D,R,A\}$: data-based rebuttal, operational reassurance, or accusation of political exploitation.

Assumption A4 (Voting). The voter chooses $v\in \{M,O\}$, where $M$ denotes support for Meloni's coalition and $O$ the relevant opposition alternative.

Assumption A5 (Issue advantage). Conditional on migration security being salient, the voter weakly prefers Meloni's coalition: $\Delta u_m(\pi )=u_m(M,\pi )-u_m(O,\pi )$ is non-decreasing in perceived risk $\pi$.

4.2. Objective and perceived posteriors

The objective Bayesian posterior following the event is:

The voter does not necessarily act on ${\pi }_1$. Let ${\pi }_1$ denote the behaviourally and politically mediated posterior. The electoral outcome is generated by ${\pi }_1$, while ex post factual evaluation is generated by ${\pi }_1$. The central wedge is therefore $\omega ={\tilde{\pi }}_1-{\pi }_1$.

5. Salience-distorted updating

5.1. Log-odds representation

Let $s_C\ge 0$ denote the visual and emotional salience of the Ceuta event. Let $a\ge 0$ measure the observable intensity of the Italian response, $K\ge 0$ the degree of common institutional attention, and $D\ge 0$ the informational force of Sánchez's data-based rebuttal. The perceived posterior is represented in log-odds form as:

The parameters $\alpha$, $\beta$, $\phi$ and $\gamma$ are non-negative. The first three capture salience, elite signalling and public-coordination effects; $\gamma$ captures the voter's responsiveness to base-rate correction. Equation (10) does not require the voter to be irrational in a global sense. It can arise from rational inattention when processing a table is more costly than processing a vivid event, or from uncertainty about whether the government possesses private information.

The equation separates four channels. First, $x_C$ affects the objective likelihood ratio. Second, $s_C$ increases the accessibility of the adverse state. Third, the costly action $a$ can be interpreted as evidence. Fourth, institutional attention $K$ raises higher-order beliefs. Sánchez's rebuttal works in the opposite direction through $D$.

Proposition 1 (Perceptual dominance condition). Holding the objective likelihood ratio fixed, Meloni's frame raises the voter's perceived posterior relative to the data-corrected benchmark if and only if $\alpha s_C+\beta a+\phi K>\gamma D$.

Proof. From equation (10), define the net political-information term $Z=\alpha s_C+\beta a+\phi K-\gamma D$. Because the logistic function is strictly increasing, ${\tilde{\pi }}_1$ exceeds the posterior obtained after applying only the objective signal whenever $Z>0$. Thus the government's salience, action and coordination effects dominate the opponent's data correction exactly when $\alpha s_C+\beta a+\phi K>\gamma D$. □

Proposition 1 formalises the intuitive claim that "having the numbers" is not sufficient. The relevant comparison is not between the amount of information in the two interventions, but between their effects on the voter's log-odds after attention, credibility and public coordination are taken into account.

5.2. Availability priors

A second mechanism changes the prior itself. Let $q_C$ be the risk suggested by the most cognitively available event and let $\rho \in [0,1]$ be its weight. The voter behaves as if the prior were:

When $\rho$ approaches one, historical frequencies are displaced by the local shock. Sánchez reasons from ${\pi }_0$; Meloni encourages the electorate to reason from ${\pi }_A$. The disagreement is therefore partly a contest over which prior is legitimate.

The distinction also explains why an argument based on cumulative Italian detections may fail to reassure. A voter can accept that Italy has historically received more arrivals while assigning a high conditional probability to a new Spanish-origin shock. Historical and conditional claims can coexist without logical inconsistency.

6. Threat externalisation and responsibility transfer

Political risk is psychologically different when it is represented as an external threat rather than an endogenous consequence of collective choice. Let $L>0$ be the loss attached to the adverse state. Let $\kappa >0$ be the disutility of acknowledging personal or collective responsibility for the policy outcome. The voter may delegate responsibility to a protective executive by choosing Meloni's coalition.

Let $d\in \{0,1\}$ denote delegation. The voter's utility is:

where $c_d$ is the ideological, distributive or reputational cost of supporting the protective actor. The first term is the expected material or symbolic loss; the second is responsibility cost; the third is delegation cost.

Proposition 2 (Responsibility-delegation threshold). The voter delegates responsibility to the protective government if and only if $\kappa >c_d$. This choice can occur independently of the objective probability of onward migration.

Proof. The voter delegates when $U_V(1)>U_V(0)$. Substitution into equation (12) yields $-{\pi }_{1}L-c_d>-{\pi }_{1}L-\kappa$. The expected-loss terms cancel. Rearranging gives $\kappa >c_d$. Therefore the act of delegation can be driven entirely by the value of transferring responsibility rather than by a belief that the policy substantially changes the physical risk. □

The result clarifies why reassurance can be electorally valuable even when the underlying danger is small. The political product is not only risk reduction. It is an allocation of agency: the voter purchases the claim that someone else has taken control.

This mechanism is particularly strong when the external event is outside the voter's action set. A threat generated in Ceuta is naturally coded as something done by others. Once a leader announces a preventive response, supporting that leader becomes a low-cost way of converting diffuse anxiety into delegated executive action.

7. Loss aversion, ambiguity and robust choice

7.1. Loss-averse policy evaluation

Let the voter evaluate outcomes through a prospect-theoretic value function:

where $0<\eta \le 1$ and $\lambda >1$ is the coefficient of loss aversion. Let $p_M$ and $p_O$ be the voter's subjective probabilities of the adverse event under Meloni and the opposition, respectively, and let $c_M$ be the perceived cost of restrictive controls.

Proposition 3 (Loss-aversion adoption threshold). The voter supports the protective policy whenever $p_O-p_M>c_M/(\lambda L)$. The required perceived effectiveness of the policy decreases in both $\lambda$ and $L$.

Proof. Support for Meloni requires $EU(M)>EU(O)$. From equation (14), $-\lambda p_{M}L-c_M>-\lambda p_{O}L$. Rearranging yields $\lambda L(p_O-p_M)>c_M$ and therefore $p_O-p_M>c_M/(\lambda L)$. The right-hand side is decreasing in $\lambda$ and $L$. □

Only a small perceived reduction in risk is needed when the imagined loss is large or losses are heavily weighted. The policy can therefore win support even if voters believe its direct effectiveness is modest.

7.2. Ambiguity and the maxmin criterion

The Ceuta shock also produces ambiguity: voters do not know the correct probability model for onward movements. Let $\Pi$ be a set of plausible distributions and let $\bar{\pi }={\max }_{\pi \in \Pi }\pi$ be the worst-case probability. A maxmin voter evaluates action $a$ according to:

Let $C$ denote controls, $N$ no controls, $e\in [0,1]$ perceived effectiveness and $c$ the policy cost.

Proposition 4 (Robust-control threshold). An ambiguity-averse voter selects controls if and only if $\bar{\pi }>c/(eL)$. A communication strategy can increase support for controls by enlarging the perceived upper bound $\bar{\pi }$ even when it does not change the mean probability $E[\pi ]$.

Proof. Controls are preferred when $W(C)>W(N)$. Using equation (16), $-c-\bar{\pi }(1-e)L>-\bar{\pi }L$. After cancellation, $\bar{\pi }eL>c$. Thus $\bar{\pi }>c/(eL)$. Since the decision depends on the upper bound rather than the mean, a worst-case frame can be effective without altering the central estimate. □

Sánchez's base-rate argument primarily lowers the mean or modal estimate. Meloni's framing emphasises the upper tail. For ambiguity-averse voters, the second intervention may dominate because the relevant object is $\bar{\pi }$ rather than $E[\pi ]$.

8. Costly signalling, cheap talk and commitment

8.1. Government types and separating behaviour

Suppose the Italian government has a privately known type $t\in \{H,L\}$. Type $H$ is strongly committed to restrictive border enforcement; type $L$ prefers symbolic rhetoric and finds actual controls more costly. Let $c_H<c_L$ be the type-dependent cost of choosing $C$.

The government chooses $C$ or $N$. Let $B_t(C)$ and $B_t(N)$ be the electoral benefits to type $t$. A separating equilibrium in which $H$ chooses $C$ and $L$ chooses $N$ requires:

Proposition 5 (Costly-signal equilibrium). If the incremental electoral return from controls lies weakly between $c_H$ and $c_L$, there exists a separating perfect Bayesian equilibrium in which type $H$ chooses controls, type $L$ chooses inaction, and voters assign posterior probability one to $H$ after observing controls.

Proof. Under the stated inequalities, $C$ is incentive-compatible for $H$ because its incremental benefit covers $c_H$, while $C$ is not incentive-compatible for $L$ because its incremental benefit does not cover $c_L$. Bayes' rule then assigns $\mu (H\mid C)=1$ and $\mu (H\mid N)=0$ on the equilibrium path. The voter's response sustains the benefit differential assumed in the incentive constraints. □

In practice, opportunistic types can imitate controls, so the equilibrium may be pooling. Yet even a pooling action can reinforce an established reputation. Let $r_t$ be the perceived stock of toughness and let it evolve as:

The present action creates a discounted stream of reputational returns. Its value therefore cannot be evaluated solely by its immediate operational effect.

8.2. Why correct data can function as cheap talk

Sánchez's message can be true and nevertheless weakly informative in equilibrium. If voters believe that a Spanish prime minister would defend Spain under both $\theta =0$ and $\theta =1$, then the message strategy pools across states:

Consequently, the message does not separate states and may leave posterior beliefs largely unchanged. This is a credibility problem, not a factual refutation. The sender's predictable strategic interest reduces the marginal information conveyed by a truthful statement.

Meloni's action, by contrast, changes administrative procedures and generates political or diplomatic costs. It therefore has a commitment component. The voter compares not merely proposition against proposition but costless speech against an observable change in behaviour.

Total value of $C$ = operational effect + signalling effect + reputational effect. (22)

9. Endogenous issue salience and electoral competition

The most important strategic effect may be the endogenous selection of the issue dimension. Let voter $i$'s utility difference between Meloni and the opposition be:

where $b_i$ is an ideological predisposition, ${\lambda }_m$ is the salience weight on migration, $\Delta u_m$ is Meloni's comparative utility advantage on migration and $r(C)$ is the reputational return from decisive action. The voter supports Meloni when $\Delta U_i>0$. Meloni's communication affects both ${\tilde{\pi }}_1$ and ${\lambda }_m$. This is a heresthetic move: it changes not only the perceived value within a dimension but the weight of the dimension itself. Sánchez's response contests the first element while accepting the second. He argues about the size of the migration risk inside a game whose dominant issue has already been selected by his opponent.

If $\Delta u_m({\tilde{\pi }}_1)>0$, any increase in migration salience benefits Meloni even when the underlying factual dispute remains unresolved.

9.1. The pivotal-voter formulation

Let ideological predisposition $b$ be distributed with cumulative distribution $F$ and density $f$. The threshold voter $b^{\ast }$ satisfies:

Under Assumption A5, the derivative is non-negative and is strictly positive whenever there is positive voter density at the threshold. The government does not need to persuade the median citizen in an abstract sense. It needs to move enough voters located near $b^{\ast }$.

10. Public signals, coordination and common knowledge

European reactions matter because they create higher-order beliefs. Let each voter receive a private signal $s_i=\theta +{\epsilon }_i$ and a public signal $y=\theta +\eta$. Private information can be more precise in aggregate, but the public signal is observed by everyone and therefore coordinates expectations. The relevant hierarchy is:

When other governments reinforce controls, request emergency discussions or publicly characterise the event as a European security problem, a voter may infer not only that the risk exists but that other voters and institutions also treat it as relevant. Let $K$ summarise this common-knowledge amplification. Equation (10) then shows why institutional attention can increase perceived risk even when the institutions' substantive conclusions are cautious.

This creates a potential informational externality. A government adopting controls for domestic electoral reasons may raise $K$ for every other government, encouraging further controls and thereby validating the original frame. The process can become self-reinforcing:

The resulting equilibrium can display strategic complementarity. Each government's precaution makes precaution by others more electorally valuable.

11. Strategic-dominance theorem

We now combine the mechanisms. Let the net electoral payoff from the Ceuta intervention be:

where $G_B$ is the belief-updating gain, $G_S$ the issue-salience gain, $G_R$ the reputational gain, $G_A$ the ambiguity-aversion gain, $G_D$ the responsibility-delegation gain, and $C_P$, $C_L$ and $C_D$ are policy, legal-institutional and diplomatic costs. Using the pivotal-voter approximation, write:

Theorem 1 (Strategic dominance under epistemic inferiority). Suppose Sánchez's historical base-rate claim is accurate, but the Italian action produces a positive perceived-risk shift $\Delta {\tilde{\pi }}_1$, a positive issue-salience shift $\Delta {\lambda }_m$, and non-negative reputational, ambiguity and responsibility-transfer gains. Meloni's strategy yields a strictly positive electoral payoff whenever the following inequality holds:

This condition is logically independent of the truth of the historical comparison $M_I>M_S$.

Proof. By equations (30)–(32), the left-hand side is the sum of all marginal electoral gains generated by belief movement, endogenous issue selection, reputation, ambiguity and delegation. The right-hand side is the total cost of intervention. If the stated inequality holds, $\Delta E_M>0$ by direct substitution. The historical comparison $M_I>M_S$ affects the data term $D$ and potentially the objective likelihood ratio, but it does not algebraically determine $\Delta {\lambda }_m$, $\Delta r$, $\bar{\pi }$, $\kappa$, the density $f(b^{\ast })$ or the policy costs. Hence the electoral inequality can hold while Sánchez's descriptive claim remains true. □

Corollary 1 (The technocratic-correction failure). A strategy that increases $\gamma D$ but leaves ${\lambda }_m$, $K$, $r$ and $\bar{\pi }$ unchanged can lose electorally even when it improves the accuracy of average beliefs.

Proof. Increasing $D$ lowers ${\tilde{\pi }}_1$ through equation (10), but it need not alter the issue weight ${\lambda }_m$, the public-coordination term $K$, the protective reputation $r$ or the ambiguity bound $\bar{\pi }$. If these remaining terms satisfy Theorem 1, the data intervention is insufficient to reverse the electoral payoff. □

Corollary 2 (Small-risk, large-payoff result). For any objective posterior ${\pi }_1>0$, there exist sufficiently large values of $\lambda$, $L$, $\alpha$, $\beta$, $\phi$, $\kappa$ or $f(b^{\ast })$ such that the intervention is electorally profitable.

Proof. Propositions 1–4 and equation (27) show that electoral gains are increasing in these parameters. Because the cost side is finite, at least one sufficiently large gain parameter makes the inequality in Theorem 1 hold even when ${\pi }_1$ is arbitrarily small but positive. □

12. Numerical calibration

The following calibration is illustrative rather than empirical estimation. Suppose the pre-event probability of material onward movement to Italy is ${\pi }_0=0.02$. Let the objective likelihood ratio generated by the Ceuta shock be $\Lambda =1.5$. The objective posterior odds are:

The evidence-based estimate therefore rises from 2 per cent to approximately 3 per cent. Now suppose the combined salience, elite-action and common-knowledge multiplier is $\exp (\alpha s_C+\beta a+\phi K-\gamma D)=5$. The perceived odds and posterior become:

The perceived probability is now 13.3 per cent despite an objective estimate close to 3 per cent. Let $L=100$, $\lambda =2.5$, perceived policy effectiveness $e=0.20$ and policy cost $c=4$. The perceived benefit of controls is:

Because $6.65>4$, the voter supports controls. Under the objective posterior:

The same voter rejects the policy under data-calibrated beliefs and accepts it under salient beliefs. The strategic territory is the wedge ${\tilde{\pi }}_1-{\pi }_1$.

To connect the example to vote share, suppose $f(b^{\ast })=0.9$, ${\lambda }_m=0.35$ and $\Delta u_m^{\prime }({\tilde{\pi }}_1)=1.2$. A ten-point increase in perceived risk produces approximately:

The implied shift is 3.78 percentage points among the modelled electorate. The value is not a forecast; it demonstrates how a modest posterior movement can be electorally large when voter density near the threshold is high.

13. Discussion, interpretation and limitations

13.1. What the model explains

First, the model explains why the statement "Sánchez is right about the numbers" does not settle the strategic evaluation. His statistic concerns an unconditional historical comparison. Meloni's claim concerns a conditional future event and a comparative competence judgement. A voter can consistently accept both.

Second, it explains why the scale of the Ceuta shock matters even if onward movement remains limited. Salience enters separately from the likelihood ratio. A locally enormous event can be globally contained and still alter beliefs, issue weights and common knowledge.

Third, the model shows why action often dominates explanation. A border-control measure is observable, administratively concrete and costly enough to function as a commitment signal. A statistical rebuttal is cognitively expensive and strategically predictable. The former may therefore have greater belief impact even when the latter has greater factual content.

Fourth, the model identifies reassurance as an electoral good. The voter may value not only lower risk but also the transfer of responsibility to an actor who claims control. This helps explain the appeal of preventive action under uncertainty.

13.2. Normative non-equivalence

Electoral rationality is not equivalent to social welfare. A strategy can be privately optimal for a party and collectively inefficient. Internal-border controls can impose transaction costs, legal friction, diplomatic damage and distributive burdens that are not internalised by the pivotal voter. Likewise, raising perceived risk can generate externalities for migrants, minority groups and other Member States.

Let social welfare be $W$ and party payoff be $E_M$. There is no reason to assume:

The model therefore predicts strategic success, not policy desirability. A full welfare analysis would require humanitarian outcomes, enforcement costs, Schengen spillovers, legal constraints and the probability that restrictive signalling induces copycat measures.

13.3. Empirical limitations

The paper uses a stylised binary state, whereas migration movements are continuous, networked and path dependent. It treats the pivotal voter as a reduced-form agent and does not estimate heterogeneous responses by ideology, geography, age or prior attitudes.

The route-level values circulated by Sánchez are accepted as public inputs to the political game. They are not independently reconstructed from the underlying Frontex microdata. Moreover, border-crossing detections are not necessarily unique-person counts and are shaped by enforcement intensity.

The numerical calibration is illustrative. Estimating the model would require panel survey data collected before and after the Ceuta shock, measures of media exposure, experimental variation in the presentation of base rates, and data on perceived policy effectiveness.

Finally, the model abstracts from humanitarian ethics and international law except insofar as legal constraints enter the cost function. These dimensions are not secondary in policy evaluation; they are simply outside the paper's positive-theory objective.

13.4. Testable implications

• H1. Exposure to vivid Ceuta imagery should increase perceived onward-movement risk more than exposure to route-level historical tables, controlling for factual knowledge.
• H2. The effect of imagery should be larger among voters with high loss-aversion or ambiguity-aversion scores.
• H3. Announcing a concrete control should increase perceived governmental competence more than issuing an equally restrictive verbal statement.
• H4. Sánchez's base-rate correction should reduce perceived risk more among high-numeracy and high-attention voters than among the general electorate.
• H5. The electoral effect should be concentrated among voters close to indifference and among voters who already attribute migration-issue ownership to Meloni's coalition.
• H6. Multilateral reactions by other governments should amplify the effect by increasing common knowledge, even if those reactions are explicitly precautionary rather than accusatory.

14. Conclusion

The Ceuta controversy is best understood as a contest over the architecture of choice. Sánchez sought to correct the common prior by showing that Italy had historically registered more irregular-entry detections than Spain. Meloni changed the information structure, raised the salience of a new risk, signalled willingness to act and moved the decision onto an issue dimension favourable to her coalition.

The difference can be summarised by two conditional claims:

The first is a historical descriptive comparison. The second is a prospective competence claim. Demonstrating the first does not logically refute the second in the voter's utility function.

The formal results show that a low-probability external event can generate a positive electoral payoff when salience, costly signalling, ambiguity aversion, responsibility transfer and threshold-voter density are sufficiently strong. The political actor who controls these variables can win even while conceding the opponent's base rate.

In Bayesian terms, Sánchez optimises the accuracy of the posterior. Meloni influences the prior, the likelihood weighting, the public signal, the action cost, the issue coefficient and the electoral threshold. She does not merely play the game more aggressively. She changes the game being played.

That is the central analytical lesson: one may be right about the world and still lose the equilibrium.

Appendix A. Proofs and extensions

A.1. Comparative statics of the perceived posterior

Let $z=\mathrm{logit}({\pi }_0)+\ln \Lambda +\alpha s_C+\beta a+\phi K-\gamma D$. Since ${\tilde{\pi }}_1=1/(1+e^{-z})$, the derivative with respect to any additive parameter $x$ is:

The marginal effect is maximised near ${\tilde{\pi }}_1=1/2$ and becomes small near zero or one. Political persuasion is therefore most productive when the voter is uncertain rather than fully reassured or fully alarmed.

A.2. Endogenous media amplification

Let media attention $h$ be an increasing function of governmental action and event salience: $h=h(a,s_C)$, with $h_a>0$ and $h_s>0$. Suppose the effective salience term is $s_C+\nu h$. Equation (10) becomes:

The total derivative with respect to action is:

Action thus affects beliefs directly through signalling and indirectly through media amplification. This creates an incentive to choose visible policies rather than technically effective but low-visibility policies.

A.3. Strategic complementarity across governments

Let government $j$'s payoff from controls be $E_j(C_j,C_{-j})$. If other governments' controls raise common knowledge $K$, then:

is a sufficient condition for strategic complementarity. Multiple equilibria can emerge: a low-control equilibrium with limited common alarm and a high-control equilibrium in which each precaution validates the others. A salient external shock can move the system from the first basin of attraction to the second.

A.4. Welfare wedge

Let the party internalise only a fraction $\tau \in [0,1]$ of the social cost $X$ generated by controls. Its private cost is $C_P+\tau X$, while the social cost is $C_P+X$. The action can be electorally optimal and socially inefficient whenever:

This interval is non-empty whenever $\tau <1$. Political competition can therefore overproduce visible precautions whose costs fall on diffuse actors.