1. Introduction
Designers of laws and constitutions have long prioritized the issue of centralization versus decentralization. The concern is natural, as the assignment of authority is consequential for policy outcomes. Many of the trade-offs are by now familiar. Decentralization can encourage the discovery of good policies and adaption to local conditions, while centralization can control externalities, implement best practices and prevent a wasteful “race to the bottom.”
An important but less explored rationale for allocating policy-making authority is ideological objectives. Centralization may bring wayward localities into line, while decentralization can protect against adverse national-level developments. Moreover, these arrangements may be applied selectively. For example, the U.S. Clean Air Act centralized air quality regulatory authority at the federal level by superseding state standards. It also allowed California to adopt standards at least as stringent as federal ones and gave other states a choice over whether to adopt California or federal standards. This arrangement persisted for decades until the Trump administration re-centralized federal authority in 2019, only to be reversed by the Biden administration in 2022.Footnote 1
This paper develops a theory of the role of ideology in allocating policy-making powers across levels of government. While several models have considered the role of ideology in various ways (Crémer and Palfrey, Reference Crémer and Palfrey1999, Reference Crémer and Palfrey2000; Volden et al., Reference Volden, Ting and Carpenter2008), this institutional setting is, to our knowledge, unique and empirically well-grounded. Consistent with the preceding example, our model has three important institutional features. First, there is uncertainty about the ideology of future politicians. Second, institutional rigidities may bind future politicians to pre-established centralization structures. Finally, politicians have the ability to centralize only partially.
Our model features ideological policy choices in two localities over two periods. All players care about policies, which have spillovers that induce some benefit from coordination. In each period, there are three players: a right-leaning locality, a left-leaning locality, and a central executive who is either right- or left-leaning and cares about social welfare. The initial executive cares about outcomes in both periods and chooses whether to centralize or decentralize each locality’s policy authority. Under the former, the executive chooses a policy, while under the latter, the locality chooses. Full centralization does not bind the executive to choose the same policies across localities. An election between periods may replace the incumbent executive with an ideological opponent.
A key parameter in the model is institutional rigidity. With some probability, the second period executive cannot change the polity’s centralization profile, and policy-making proceeds according to the first-period arrangement. Rigidity captures the idea that opportunities for changing governance arrangements are rare due to the need for political consensus in resolving fundamental (and sometimes constitutional) questions. High and low rigidity might correspond to strong and weak checks and balances systems, respectively.
The model shows that rigidity and political competition in conjunction produce greater decentralization. Centralization is desirable for a second-period executive as it allows her to impose policy and internalize externalities. For the first-period incumbent executive, the choice depends on rigidity. With high rigidity, centralization raises the risk of centrally mandated policies set by the opposition. This outcome becomes worse as polarization, or the ideological distance between left and right executives, increases.
Decentralization provides insurance against a bad electoral outcome. In equilibrium, the executive often centralizes her ideological enemy and decentralizes her ideological ally. This pattern is consistent with the U.S. practice of selectively granting state waivers for implementing alternatives to federal programs (e.g., Richardson, Reference Richardson2019). The result contrasts with many existing models of federalism, which either assume that complete centralization or decentralization is the only option or derive conditions for the optimality of such arrangements. At the extreme, full decentralization insulates policy completely from national election results when rigidity and polarization are high.
Our model suggests two ways to sharpen empirical analyses of the determinants of centralization. A large body of literature examines the relationship between electoral prospects and decentralization (e.g., Escobar-Lemmon, Reference Escobar-Lemmon2003; Dickovick, Reference Dickovick2007; Mardones, Reference Mardones2007; Sorens, Reference Sorens2009). In particular, O’Neill (Reference O’Neill2003; Reference O’Neill2005) finds that incumbents across Latin America were more likely to decentralize when their party’s national vote share decreased or the number of subnational electoral contests their party won increased. Tellingly, most countries in these studies have presidential systems, where multiple veto players could thwart re-centralization attempts. Additionally, we are not aware of work linking ideological polarization with decentralization. Studies of ethnic fragmentation, which may play a similar role, have produced mixed results (Treisman, Reference Treisman2006; Blume and Voigt, Reference Blume and Voigt2011; Spina, Reference Spina2013). Our model predicts that both polarization and rigidity are necessary for decentralization.
The literature on political centralization is vast enough to have spawned multiple review articles (Oates, Reference Oates1999; Bednar, Reference Bednar2011; Graham et al., Reference Graham, Shipan and Volden2012; Mookherjee, Reference Mookherjee2015; Gilardi, Reference Gilardi2016). Most previous theoretical work focuses on quality. In these models, centralization allows the imposition of better policies, while decentralization aids in their discovery (e.g., Kollman et al., Reference Kollman, Miller and Page2000; Strumpf, Reference Strumpf2002; Volden et al., Reference Volden, Ting and Carpenter2008; Cai and Treisman, Reference Cai and Treisman2009; Callander and Harstad, Reference Callander and Harstad2015; Cheng and Li, Reference Cheng and Li2019). Our model suppresses uncertainty over the quality of policies and thus is more appropriate for settings like the Clean Air Act example, which had seemingly more to do with ideological conflict than policy failures.
In Oates’s (Reference Oates1972) seminal model, centralization helps a welfare-oriented center control externalities, while decentralization allows local units to produce superior public goods. In contrast, outputs in our model are ideological policies and not public goods, and we provide for—but do not require—cross-unit policy spillovers and executive welfare motivations. We show that policy motivation, coupled with rigidity and electoral concerns, can be an alternative driver of decentralization in an otherwise similar framework.
While we are not the first to consider the role of ideology, the literature on the interactions between ideology and centralization remains small (e.g., Bulman-Pozen, Reference Bulman-Pozen2014; von Wilpert, Reference von Wilpert2017; Gordon and Landa, Reference Gordon and Landa2021). Perhaps closest to our model are Crémer and Palfrey (Reference Crémer and Palfrey1999, Reference Crémer and Palfrey2000), who show that centralization can not only reduce policy risk but also welfare. These models share with ours the idea that centralization can be a tool for achieving ideological gains but focus on voters in a single period. We examine elites who face incentives to insulate policy over time.
The paper proceeds as follows. Section 2 describes the model, Section 3 presents our results, and Section 4 concludes. The appendix develops an infinite horizon extension.
2. Model
We consider a two-period game of policy-making across two localities. The players are an incumbent executive I, her opponent O, who can replace the incumbent in the second period, and two local governments, denoted by 
$i \in \{1,2 \}$. In each period 
$t \in \left\{1,2\right\}$, a policy vector 
$\mathbf{x}_{t} = (x_{1,t}, x_{2,t})$ is chosen, where 
$x_{i,t}$ is implemented in locality i. There is no discounting.
All players derive utility from policy choices. Local government i has an ideal point yi, where 
$y_{1} \lt 0 \lt y_{2}$ and, for tractability, 
$y_{2} \equiv - y_{1}$. Each receives utility over xt according to
\begin{equation}
U_{i} (\mathbf{x}_{t}, y_{i}) \equiv - \gamma \left( x_{i,t} - y_i \right)^2 - (1-\gamma) \left( x_{-i,t} - y_i \right)^2 .
\end{equation} Local governments assign weight 
$\gamma \in (0,1]$ to their policy and 
$1 - \gamma$ to the policy in the other locality.Footnote 2 Allowing localities to care about policy in other jurisdictions connects our framework to models of centralization that feature cross-unit externalities (e.g.,Oates, Reference Oates1972).
Executive 
$j \in \{I, O\}$ has a time-invariant ideal point zj, where (without loss of generality) the incumbent executive is left-leaning, i.e., 
$z_I \lt 0$. These ideal points are symmetric around 0: 
$z_{I} = - z_{O}$. Consequently, lower values of zI increase polarization. In a given period, a party j executive earns the following utility from xt regardless of whether she holds power:
\begin{equation}
U^{e}_{j} (\mathbf{x}_t, \mathbf{y}) \equiv - \omega \sum_{i = 1}^{2} \left( x_{i,t} - z_j \right)^2 + (1 - \omega ) \sum_{i = 1}^{2} U_{i} (\mathbf{x}_t, y_{i}) .
\end{equation} 
$U^{e}_{j} (\cdot)$ combines policy utility and concern for locality-level welfare, with the former weighted by ω. The concern for welfare internalizes externalities across localities and resembles that of Oates Reference Oates(1972) in the special case of ω = 0. To focus on the role of ideology, we assume 
$\omega \in (0,1]$.Footnote 3
Each locality can be either centralized or decentralized. Under centralization, the executive chooses the locality’s policy, while the locality chooses under decentralization. We denote the centralization status of locality i in period t by 
$c_{i, t} \in \{0,1\}$, where 0 corresponds to decentralization and 1 corresponds to centralization. A centralization profile 
$\mathbf{c}_{t} = (c_{1, t}, c_{2, t})$ is the set of period t centralization statuses. We denote the set of possible centralization profiles as 
$\mathcal{C} = \{0,1\} \times \{0,1\}$.
The game proceeds as follows. At the beginning of period 1, the incumbent executive chooses a centralization profile c1. Next, the actors with policy-making authority simultaneously choose local policies x1. At the end of period 1, there is an election, where the incumbent executive I remains in office in period 2 with probability p and is replaced by O otherwise.
Whether the period 2 executive can change the centralization profile depends on institutional constraints. With known probability q > 0, the period 2 executive is weak and cannot change the centralization profile, and thus 
$\mathbf{c}_{2} = \mathbf{c}_{1}$. With probability 
$1- q$, the period 2 executive is strong and free to choose c2. We refer to q as rigidity. After c2 is determined, the actors who have policy-making authority simultaneously choose local policies x2 and the game ends.
We derive the unique subgame perfect Nash equilibrium of this game. For localities and executives in each period, this consists of optimal policy choices from 
$\mathbb{R}$ when decentralized and centralized, respectively. Additionally, the period 1 executive chooses the initial centralization profile from 
$\mathcal{C}$ and the period 2 executive chooses a centralization profile if she is strong.
3. Equilibrium
3.1. One period
We begin by characterizing actors’ policy preferences. For a local government, maximizing equation 1 produces its ideal point:
\begin{equation}
x^{*}_{i} = \mathrm{arg\,max}_{x_{i}} U_{i} (\mathbf{x}, y_{i}) = y_{i}.
\end{equation}Maximizing equation 2 produces an executive’s optimal policy for a centralized locality:
\begin{equation}
x^{*}_{i} = \mathrm{arg\,max}_{x_{i}} U^{e}_{j} (\mathbf{x}, \mathbf{y}) = \omega z_{j} + (1 - \omega) \left[ \gamma y_{i} + (1 - \gamma) y_{-i} \right].
\end{equation}The executive’s optimal policy takes externalities into account and thereby deviates from her ideal point. Changes in γ shift the policy that each executive desires by the same amount. Thus, externalities do not affect policy conflict between executives but increase policy conflict between each executive and the more ideologically distant locality (hereafter adversary). When executives’ preferred policies are less extreme than those of the localities, externalities also increase policy conflict between each executive and the more ideologically proximate locality (hereafter ally). Stronger welfare concerns (lower ω) move the ideal policies of the two executives closer together and thus reduce policy conflict on the executive level. Note also that the executive’s optimal policy for each locality does not depend on whether the other locality is centralized.
While centralization profiles may persist across the two periods, there is no policy persistence. Therefore, policy choices in period 1 have no implications for any player’s payoffs from period 2. Conditional upon ct, the myopic optimal policies given in equations 3 and 4 thus fully describe policy choices in both periods.
To characterize executives’ preferences over centralization profiles in a single period, we begin with a simple intuition. Centralization in the first period raises the incumbent executive I’s cost of losing power in the second period. Party control of the executive is irrelevant for policy under complete decentralization (
$\mathbf{c}_{t} = (0,0)$). The relative benefit of holding power increases under the partial centralization profiles 
$\mathbf{c}_{t} = (1,0)$ and 
$\mathbf{c}_{t} = (0,1)$ and is maximized under full centralization (
$\mathbf{c}_{t} = (1,1)$).Footnote 4 Hence, decentralization can reduce the stakes of an election loss and play an insurance role for I.
We state our result from the perspective of I; a symmetric result holds for the opponent O. The result depends on the following threshold values of zI:
\begin{align}
\underline{z}_{I} &= \phantom{\dfrac{1}{3}} \left( 2 \gamma + \frac{2(1 - \gamma)}{\omega} - 1 \right) y_{1},
\end{align}
\begin{align}
\overline{z}_{I} &= \dfrac{1}{3} \left( 2 \gamma + \frac{2(1 - \gamma)}{\omega} - 1 \right) y_{1}.
\end{align} Note that the parenthesized term is at least 1 and hence 
$\underline{z}_{I} \lt y_1$ and 
$\underline{z}_{I} \lt \overline{z}_{I} \lt 0$.
Lemma 1. Executive preferences in a single period
For the incumbent executive I:
(i) When I is in power,
$(1,1) \succ (0,1) \succ (1,0) \succ (0,0)$.(ii) When O is in power,
\begin{align*}
(1,1) \succ (0,1) \succ (1,0) \succ (0,0) &\ \textrm{if } \overline{z}_{I} \lt z_{I} \lt 0, \\
(0,1) \succ (1,1) \succ (1,0), (0,1) \succ (0,0) \succ (1,0) &\ \textrm{if } \underline{z}_{I} \lt z_{I} \lt \overline{z}_{I}, \\
(0,0) \succ (0,1) \succ (1,0) \succ (1,1) &\ \textrm{if } z_{I} \lt \underline{z}_{I}.
\end{align*}
An executive in power has a unique preference ordering over centralization profiles, with more centralization preferred to less. In a single period, an executive can always increase her utility by centralizing a locality. Thus, the period 2 executive will attempt complete centralization. Moreover, whether in power or not, executives prefer centralizing their adversary to centralizing their ally.
The non-incumbent executive’s preference ordering additionally depends on the degree of polarization, as given by the location of zI relative to 
$\underline{z}_{I}$ and 
$\overline{z}_{I}$. When polarization is low (
$\overline{z}_{I} \lt z_{I} \lt 0$), the non-incumbent executive prefers full centralization, and when polarization is high (
$z_{I} \lt \underline{z}_{I}$), she prefers full decentralization. As 
$\underline{z}_{I} \lt y_1$, the preference for full decentralization arises only if executives are more polarized than the localities. The reason is that a decentralized adversary locality would choose a more moderate policy than the opposing executive. When localities are more polarized than executives, a non-incumbent executive prefers the opposing executive’s policy choice, thus centralizing her adversary. In this manner, high polarization incentivizes the first-period incumbent to decentralize to guard against a transition of power.
3.2. Two periods
In the full game, the incumbent executive I may be replaced by the opponent executive O in period 2. A strong election winner will choose full centralization (
$\mathbf{c}_{2} = (1,1))$ and implement her optimal policy for both localities. A weak winner will set second-period policies under the centralization profile c1 implemented in period 1. This implies the following two-period objective 
$V_{I} \left( \mathbf{c}_{1} \right)$ for I:
\begin{eqnarray}
V_{I} \left( \mathbf{c}_{1} \right) &=& U^{e}_{I,I}( \mathbf{x}^{*} (z_{I}, \mathbf{c}_{1}) ) + p \left[ q U^{e}_{I,I}( \mathbf{x}^{*} (z_{I}, \mathbf{c}_{1}) ) + (1 - q) U^{e}_{I,I}( \mathbf{x}^{*} (z_{I}, (1,1)) ) \right] + \nonumber \\
& & \quad (1 - p) \left[q U^{e}_{I,O}( \mathbf{x}^{*} (z_{R}, \mathbf{c}_{1}) ) + (1 - q) U^{e}_{I,O}( \mathbf{x}^{*} (z_{R}, (1,1)) ) \right] .
\end{eqnarray}Note that her predecessor’s centralization profile does not constrain a strong second-period executive. What matters for the incumbent’s first-period choice of centralization profile is thus the case in which the period 2 executive is weak.
Recall that 
$(1,0)$ is dominated for the incumbent executive I in a single period. Hence, setting 
$\mathbf{c}_1 = (1,0)$ is never optimal, and I effectively chooses between three “increasing” levels of centralization (
$(0, 0)$, 
$(0, 1)$, and 
$(1, 1)$). The incumbent can maximize her period 1 utility by setting 
$\mathbf{c}_1 = (1,1)$. In period 2, however, she may no longer be in office, and greater centralization increases the stakes of losing power. The incumbent, therefore, trades off the benefit of choosing policy today and potentially tomorrow against the risk of having her opponent set policies in centralized localities tomorrow.
How the incumbent resolves this trade-off depends on her re-election probability p. Centralization will be more appealing if she is likely to remain in office; otherwise, greater decentralization will be more attractive. Indeed, the expected two-period utility of the incumbent increases linearly with p and more so with higher period 1 centralization levels. Since the benefits of greater centralization are increasing in the incumbent’s electoral prospects, equilibrium centralization must be monotonically increasing in p.
To derive conditions under which the incumbent switches between centralization profiles, we compare 
$V_{I} \left( \mathbf{c}_{1} \right)$ under different centralization profiles and find the values of p at which she is indifferent. Indifference between 
$(0,0)$ and 
$(0,1)$ obtains when p equals
\begin{equation}
\underline{p} = 1 - \frac{1 + q}{q} \left( \frac{z_{I} + \left( 2 \gamma + 2(1 - \gamma) / \omega - 1 \right) y_{1} }{2 z_{I}} \right)^{2}.
\end{equation} Analogously, indifference between 
$(1,1)$ and 
$(0,1)$ requires p to be
\begin{equation}
\overline{p} = 1 - \frac{1 + q}{q} \left( \frac{z_{I} - \left( 2 \gamma + 2(1 - \gamma) / \omega - 1 \right) y_{1} }{2 z_{I}} \right)^{2}.
\end{equation}The following result summarizes the incumbent’s optimal choice of centralization profile given her electoral prospects.
Proposition 1. Optimal centralization
The optimal centralization profile for the first-period executive I is
\begin{equation}
\mathbf{c}_{1}^{*} = \left\{
\begin{array}{ll}
(0,0) & \textrm{if } p \lt \underline{p} \\
(0,1) & \textrm{if } \underline{p} \leq p \lt \overline{p} \\
(1,1) & \textrm{if } p \geq \overline{p}.
\end{array}
\right.
\end{equation}Proposition 1 confirms our intuition about the insurance value of decentralization: incumbent executives who are unlikely to be re-elected decentralize the ally or even both localities to insure against losing office. With some rigidity, this choice deprives their opponent of future policy-making power. By contrast, a high probability of re-election makes executives more “greedy.” Full centralization becomes appealing in period 1 because rigidity might not allow them to change the centralization level after re-election.
It is clear from equations 8 and 9 that 
$\underline{p} \lt \overline{p} \le 1$. Proposition 2 characterizes the conditions under which either cutoff is interior such that partial or, respectively, full decentralization can arise in equilibrium. The result distinguishes between two kinds of polities.
Definition 1. Rigidity
A polity has high rigidity if 
$q \gt \frac{1}{3}$ and low rigidity if 
$q \lt \frac{1}{3}$.
In addition, the result depends on two critical values of zI.
Proposition 2. Polarization and centralization
There exist zc and zp, where 
$z_p \lt z_c$, such that
(i) if
$z_I \ge z_c$, then
$\overline p \le 0$ and thus
$c^* = (1,1)$,(ii) if
$z_I \in [z_p, z_c)$, then
$\overline p \gt 0 \gt \underline p$ and thus
$c^* \ne (0, 0)$,(iii) if
$z_I \lt z_p$ and rigidity is low, then
$\overline p \lt 0$ and thus
$c^* = (1, 1)$,(iv) if
$z_I \lt z_p$ and rigidity is high, then
$\underline p \gt 0$ and thus all centralization profiles are possible.
When polarization is low (
$z_I \geq z_c$), executives are ideologically moderate and would prefer the policy choices of opposing executives to those of their own ideological allies. Hence, full centralization is always preferred. As polarization becomes moderate 
$(z_I \in [z_p, z_c))$, the incumbent loses more if policies are set by her opponent in the second period. At the same time, the ideal policies of the incumbent and her ally roughly coincide. Rigidity may then let the incumbent preserve the ally’s policy autonomy. The first-period incumbent thus partially centralizes if she is pessimistic about re-election and fully centralizes otherwise.
When polarization is high (
$z_I \lt z_p$), the character of the equilibrium depends on rigidity. Under low rigidity, there is little point for the incumbent to give up policy-making authority today to “lock in” decentralization. Given that partial centralization is unlikely to survive, an extreme incumbent hesitates to give up present policy-making authority even to a moderate ally. Hence, the incumbent chooses full centralization. By contrast, high rigidity allows decentralization to insure against adverse electoral outcomes. An extreme first-period incumbent who is pessimistic about re-election will then find it optimal to exploit rigidity to preserve the policy autonomy of her ally or, if very pessimistic, of both localities. Full decentralization thus requires both high rigidity and polarization. Indeed, as foreshadowed in the analysis of a single period, executives must be more extreme than the localities (
$z_{I} \lt z_p \lt y_{1}$) for full decentralization to arise.
How do executive welfare motivations and externalities affect our results? Because a higher welfare motivation (lower ω) aligns executives’ policy preferences, it expands the scope for centralization: 
$\underline{p}$, zc, and zp increase in ω.Footnote 5 In the extreme case of pure welfare motivation (ω = 0), executives have perfectly aligned policy preferences and hence always desire full centralization, even when out of power.Footnote 6 The incentive to decentralize in our model thus stems from executive policy preferences coupled with the risk of losing power—and not, as in Oates Reference Oates(1972), from the wish to adapt policy to local conditions. Under the standard view that politicians are office motivated and assuming that improving citizens’ welfare increases popularity, one may interpret a greater welfare-orientation as a reduced form way to capture electoral concerns. Even though election probabilities are exogenous in our model, our framework thus suggests that decentralization may become less likely when it has electoral implications.
Greater externalities (lower γ) have a similar effect on 
$\underline{p}$, zc, and zp. Like in other models of decentralization, externalities in our model provide an impetus for centralization. The reason is that externalities create a divergence in policy preferences between localities and executives.
In sum, if executives and localities are more ideologically motivated (high ω and γ), the initial executive has incentives to “lock in” either full decentralization or centralization of the adversary, especially if the electoral environment is unfavorable and the second-period executive is unlikely to be strong.
4. Discussion
The allocation of policy-making authority is a key factor in determining policy outcomes. Therefore, the question of centralization versus decentralization has long been a concern to institution designers. Extensive literature has addressed the role of decentralization in producing externalities, generating information, and diffusing policies. However, as recent examples make clear, ideology is often a primary driver of such decisions. This paper isolates the roles of ideology, institutions, and electoral turnover in generating a purely political account of centralization choices.
Our two-period model shows that ideological polarization and re-election prospects push politicians away from centralization. The intuition is that decentralization can allow politicians to insure against their successors’ efforts at imposing unfavorable policies. For this mechanism to work, institutional rigidities such as checks and balances are crucial. Majorities can undo decentralization in a system without rigidities, making insurance impossible. In an environment with rigidities, centralization is increasing in an incumbent’s re-election prospects. We show that partial centralization is the norm, with complete decentralization predicted only when polarization is very high.
Our model produces comparative statics that align with existing evidence on rigid presidential systems in Latin America (e.g., O’Neill, Reference O’Neill2005) and produces novel implications for empirical work. First, as full decentralization is predicted to depend on polarization, a more comprehensive test could incorporate data on the ideological dimension of party competition. Second, several papers have examined the role of ethnic fragmentation in centralization decisions, with unclear results. Polarization and ethnic fragmentation are plausibly related because both imply the absence of mutually beneficial policies. Future work could assess whether rigidity plays a role in this relationship.
Opportunities for theoretical expansion exist as well. The appendix shows that our model’s results extend to an infinite horizon setup. A more comprehensive extension would endogenize elections by letting a decisive voter arise from one locality in each period. The need to both cater to this voter and react to their preferences may play an important role in disciplining the choices of national politicians.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/psrm.2025.13.
Acknowledgements
We thank Georg Vanberg, Craig Volden, and panel participants at the 2019 Annual Meeting of the Southern Political Science Association and 2020 Emory Conference on Institutions and Law Making for helpful comments.
Competing interests
The authors declare none.
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