Reaching for the Threshold: How Minimum Participation Rules Facilitate Multilateral Treaty Ratification

Abstract

Uncertainty about other states’ willingness to cooperate often impedes collective action. Many multilateral agreements address this by incorporating Minimum Participation Rules (MPRs), which are provision-point mechanisms that specify the minimum coalition size required for a treaty to enter into force. Public and institutional choice theories suggest that such mechanisms lower barriers to participation by reducing coordination problems and limiting opportunities for freeriding. To test this assumption, we introduce a survival estimator to evaluate how the inclusion and design of MPRs impact treaty ratification across diverse issue areas. Drawing on data from agreements deposited with the United Nations Secretary-General, this study offers the first systematic analysis of MPRs in multilateral treaty cooperation. We find that threshold provisions accelerate ratification, even in contexts where incentives to freeride are unlikely to be significant.

Introduction

Global challenges, from pandemics to the climate crisis, demand sustained international cooperation. Yet uncertainty about other states’ willingness to collaborate often hampers collective action. To manage uncertainty over shifting preferences and varying commitments to cooperation, states have developed a range of institutional devices (see Helfer 2013; Koremenos et al. 2001). ¹ Foremost among these instruments, multilateral treaties are deliberately designed to facilitate collaboration. Many international agreements, for example, make provisions for reservations (McKibben and Western 2020; McLaughlin Mitchell and Powell 2009; Neumayer 2007; Simmons 2009; Zvobgo et al. 2020), derogations (Hafner-Burton et al. 2011), safeguards (Baccini 2010; Kucik and Reinhardt 2008; Pelc 2009; Rosendorff and Milner 2001), amendments (Laurens et al. 2023), or withdrawals (Helfer 2005; Koremenos and Nau 2010) to mitigate the effects of uncertainty on international cooperation.

Minimum participation rules (MPRs) are another flexibility device that specifies the minimum coalition required for a treaty to enter into force. ² This mechanism functions as a provision-point arrangement under which pledged contributions toward a collective goal become binding only once a predetermined threshold has been met. Scholars in the public choice tradition argue that, by operating in this way, MPRs facilitate cooperation and help overcome collective action problems (Olson 1965). Environmental and resource economists, for example, have likewise examined how threshold provisions can enhance participation in public-goods agreements, and note that environmental treaties such as the Paris Agreement (2016) often incorporate carefully crafted MPRs (see Barrett 2003). Similar provision-point mechanisms are used in other domains, including infrastructure projects (Rose et al. 2002) and crowdfunding campaigns (Agrawal et al. 2014). Nor are these mechanisms novel: the US Constitution entered into force only after ratification by at least nine of the thirteen original state legislatures (Lenowitz 2022).

Although the logic of MPRs and their anticipated effects is well established in theory, most scholarly work has been limited to simulation models and experimental studies of public goods (Isaac et al. 1989; Van de Kragt et al. 1983). Despite the widespread use of MPRs in international treaty-making, the institutional design literature typically treats them only in passing (see Arnold 2017, 652; Cole 2009, 576–578; Milewicz and Snidal 2016, 825; von Stein 2018, 13–14; Laurens et al. 2023, 3). Consequently, we still lack systematic analyses of how provision-point mechanisms shape cooperation in real-world settings.

This paper addresses this empirical gap by examining how MPRs shape treaty ratification in practice. We focus on two key dynamics. First, we assess how the inclusion and design of entry-into-force thresholds influence states’ decisions to ratify. Second, we examine whether MPRs help curb freeriding. Treaties with MPRs enter into force only once a participation threshold is met. This means states cannot benefit from others’ contributions without first committing themselves. Only when a sufficient number of parties ratify does the treaty take effect and begin to generate collective benefits, making strategic delay less attractive. While this mechanism abstracts from the complexity of real-world politics, we expect MPRs to be particularly effective in issue areas where freeriding pressures are most pronounced.

Answering these questions with observational data entails several methodological challenges. Outside experimental settings, the design of MPRs reflects political negotiation: whether an MPR is included and how it is structured, is closely linked to states’ interests and their willingness to cooperate. Moreover, the impact of MPRs on ratification is inherently dynamic, as they are likely to shape state behavior differently before and after a treaty enters into force. Finally, states that ratify after a treaty has taken effect are more likely to be influenced by the MPR itself, a pattern that introduces survivor-treatment bias and complicates econometric identification strategies that do not account for it (Austin et al. 2006; Beyersmann et al. 2008).

We offer an approach that addresses these challenges. Empirically, we turn to a rich data source that allows the study of states’ cooperation behavior over time. We examine the MPR design variation in multilateral agreements deposited with the UN Secretary-General between 1945 and 2018, as well as the corresponding 21,830 individual ratification instances. To model the data, we introduce an estimator that relies on matching in a survival model context (Fredriksson and Johansson 2008). Comparing ratification behavior after satisfying the MPR with a counterfactual situation before satisfying the MPR, the estimator allows the identification of a causal treatment effect of MPRs over time.

Our study shows that MPRs have a measurable impact on states’ ratification behavior. They accelerate the ratification of agreements and lower the risk of states benefiting without contributing. As expected, MPRs are especially effective in treaties that provide public goods. However, our findings also reveal that provision point mechanisms encourage participation more broadly, including in issue areas where freeriding should be less pronounced. This suggests that the usefulness of MPRs extends beyond public goods and may apply across a wider range of international agreements.

We begin by developing a theoretical framework grounded in public choice theory. The following section discusses the conditions that should facilitate or hinder the attainment of entry-into-force thresholds and explores how MPRs shape ratification dynamics. We then introduce our dataset, highlighting both variation and recurring patterns in MPR design across treaties. The fourth section outlines our methodological approach, presenting a survival-model framework and explaining how matching techniques are employed to estimate the dynamic effects of MPRs. Finally, we turn to the empirical analysis, evaluating how MPRs influence treaty ratification and contribute to international cooperation. The conclusion draws out the broader implications of our findings.

Minimum Participation Rules in Multilateral Agreements

Multilateral treaty cooperation is inherently complex, as it involves numerous states that, in principle, are free to craft agreements in accordance with their individual interests. Typically, however, this process unfolds in two stages. First, states negotiate and formalize the terms of the agreement in writing. At this stage, states may sign the agreement, signaling their intention to cooperate. Ratification is the second step. Most treaties become legally binding only for states that have ratified them. ³

A treaty with an MPR only enters into force if a minimum coalition of countries has consented to be bound. Until this threshold is met, the treaty is not legally binding and does not require states to change their behavior. In its simplest form, a coalition is defined by a specific number of states. However, MPRs may also incorporate more elaborate criteria, such as weighting states' participation based on factors like export volume or share of global emissions. Additionally, MPRs may specify a waiting period after the threshold is reached before the treaty becomes legally binding.

The literature broadly agrees that the size of the minimum coalition matters for cooperation (e.g., Ostrom 2003; Snidal 1985). Both formal models and experimental studies show that MPRs can incentivize the provision of joint goods (e.g., Isaac et al. 1989; Marks and Croson 1999; Rondeau et al. 1999). Building on these foundational insights, scholars have applied these findings to the study of international environmental agreements. Most of this work examines the determinants of minimum coalition size, drawing on theoretical models (Carraro et al. 2009; Köke and Lange 2017; Rutz 2001; Weikard et al. 2015), experimental evidence (McEvoy et al. 2015), or surveys of treaty negotiators (Kesternich 2016). Other contributions develop theoretical expectations regarding the conditions under which the minimum coalition is likely to be achieved (Black et al. 1993; Courtois and Haeringer 2012). By contrast, in the international relations literature, MPRs receive scant attention (see Arnold 2017, 652; Cole 2009, 576–578; Milewicz and Snidal 2016, 825; von Stein 2018, 13–14; Laurens et al. 2023, 3). Although many agree that MPRs should matter in theory, few empirical studies examine how they affect international cooperation in practice. Do they accelerate or delay cooperation? And do they deliver the protection against freeriding that theorists and experimentalists expect?

In line with the existing literature, we argue that MPRs function as flexibility devices designed to facilitate cooperation by helping states manage uncertainty. Uncertainty is a central obstacle to international cooperation, and states have developed various mechanisms to introduce flexibility, thereby encouraging broader participation. Often located in the “final clauses” of treaties, such provisions provide ways to manage uncertainty about others’ preferences, anticipated behavior, and changing circumstances (Koremenos et al. 2001), thereby insulating states from potential contractual disappointments (Helfer 2013; Martin and Simmons 2013).

For example, reservations, understandings, and declarations (RUDs) can incentivize ratification by allowing states to clarify the scope of their obligations (McKibben and Western 2020; McLaughlin Mitchell and Powell 2009; Neumayer 2007; Simmons 2009; Zvobgo et al. 2020). Without some flexibility, states may hesitate to ratify newly negotiated agreements due to uncertainty about their eventual interpretation and reach (Cole 2009). Safeguard clauses similarly broaden participation by authorizing states to temporarily suspend treaty obligations without breaching the agreement (Baccini 2010; Kucik and Reinhardt 2008; Pelc 2009; Rosendorff and Milner 2001). Treaties may also include mechanisms to update or amend provisions in response to new information about “participants’ preferences, cooperation behavior, and the state of the environment” (Laurens et al. 2023, 5). Finally, exit clauses are expected to enhance cooperation by establishing clear procedures for lawful withdrawal from an agreement (Helfer 2005; Koremenos and Nau 2010; Schmidt 2025).

Provision-point mechanisms differ from these other flexibility devices in that they primarily allow states to hedge against uncertainty about the actions of others, particularly their willingness to accept an agreement as legally binding. Because thresholds are set during the negotiation phase, provision-point mechanisms are likely to influence state behavior differently before and after an agreement enters into force. As a result, the effects of MPRs are dynamic and difficult to capture in observational data. In the sections that follow, we first set out our hypotheses on how MPRs structure the ratification process and then introduce our empirical strategy.

How MPRs Differ Across Treaties

We begin by asking whether MPRs accelerate or delay the ratification process. To answer this question, we examine how MPRs shape states’ ratification behavior, focusing on whether these patterns differ before and after a treaty enters into force.

The existing literature provides mixed expectations. Scholars emphasizing the distributive dynamics of ratification argue that states are often less willing to ratify before the MPR threshold is reached than afterward. The inclusion of an MPR can raise the risk of strategic holdout, as states may withhold consent to extract concessions or side payments \citep{barrett2003environment, benedick1998ozone, Kesternich2016}. Although repeated treaty negotiations may reduce this risk through reputation effects (Courtois and Haeringer 2012), evidence suggests that entry-into-force rules can still empower holdouts. A notable example is the U.S. decision not to ratify the Kyoto Protocol, which effectively gave Russia a veto over the treaty’s entry into force and prompted the European Union to drop its opposition to Russia’s World Trade Organization accession (Walsh 2004, 22 May).

Yet there are also reasons to expect that MPRs may have the opposite effect. We contend that MPRs shape states’ cost-benefit calculations in two principal ways. First, thresholds operate as a “money-back guarantee,” mitigating the risk of wasted investment if the threshold is not met. Second, by requiring a minimum coalition for entry into force, MPRs ensure that once the treaty becomes legally binding, a baseline level of the public good will be provided. This assurance, in turn, signals to ratifying states that they can expect an adequate return on their investment.

The effect of MPRs on the probability of ratification is endogenous to the treaty-making process and exerts a dynamic influence on ratification outcomes. Information about each state’s willingness to contribute shapes both the decision to include an MPR and the type of MPR chosen during negotiations. Likewise, states’ ratification decisions are informed by observations of others’ behavior. ⁴ States are aware that each ratification moves the agreement closer to entering into force, which ultimately serves their interests by ensuring access to the treaty’s benefits once it becomes operational. In addition, states may feel normatively bound to honour their commitment to cooperate (Schulz and Levick 2023; Van de Kragt et al. 1983). Holdouts, those whose ratification is indispensable for an agreement’s entry into force, can also be subject to considerable pressure to act (Milewicz and Snidal 2016). Naming-and-shaming campaigns frequently target such states. For example, Article 14 of the Comprehensive Nuclear-Test-Ban Treaty (1996) lists 44 states whose ratification is required to meet the MPR and mandates periodic conferences of the parties to consider measures for accelerating the process. In recent years, the United Nations and civil society groups have invoked this provision to single out non-ratifiers such as India and the United States. Taken together, these dynamics suggest that ratification tends to proceed more quickly before a treaty enters into force than after. We therefore hypothesize that the probability of ratification is higher prior to a treaty becoming active and that, once the minimum coalition has been achieved, the probability of ratification declines. This leads to our first hypothesis:

Hypothesis 1

States are more likely to ratify before a treaty enters into force. Once a treaty has entered into force, the probability of subsequent ratifications decreases.

MPRs and the Mitigation of Freeriding

Beyond shaping when and how likely an agreement is to enter into force, MPRs may also play a role in coordinating joint action, and their effects may vary depending on the type of good involved. In principle, the impact of threshold provisions should differ between treaties that allow freeriding and those that do not. Freeriding may occur when the goods provided under an agreement are non-excludable, meaning that even those who do not contribute cannot be prevented from benefiting, as is the case with public or common goods. A minimum coalition can help to limit freeriding by changing how the joint good is produced (Hale 2020; Snidal 1985). ⁵

A treaty does not become binding until the threshold set by the MPR is reached, and until that point participating states are not required to change their behavior. Because no joint good is produced before entry into force, there is no scope for freeriding. For example, before the Treaty on the Prohibition of Nuclear Weapons (TPNW) entered into force in 2021, ratifying states could not yet draw on its institutional and support mechanisms. Once the threshold was met, the treaty became active, and even non-ratifying states could benefit indirectly. In such cases, a state may avoid the political or strategic costs of joining while still enjoying the security gains created by others’ cooperation. We therefore hypothesize that the type of public good governed by the treaty does not influence when the threshold is reached, since freeriding is not possible beforehand.

Hypothesis 2a

The type of good regulated by the treaty (excludable vs. non-excludable) does not influence the time required to meet the Minimum Participation Rule threshold.

Concerns about expected benefits, the distribution of burdens, and the risk that others might freeride on collective efforts feature prominently in political debates over treaty participation. As noted, freeriding is not technically possible before an agreement has entered into force, yet such concerns nonetheless shape states’ choices in practice. A prominent example is the Kyoto Protocol again. Although the Protocol ultimately achieved near-universal ratification, U.S. policymakers argued during negotiations that major developing emitters, such as China and India, were exempt from binding emissions targets. The United States chose not to ratify and, once the Protocol entered into force, effectively benefited from the (modest) emission-reduction measures undertaken by others, enjoying these non-excludable climate gains without assuming the treaty’s obligations throughout its period in force (2005–2020).

In some countries, however, the question of ratification remains open after a treaty has entered into force. States may delay ratification until the scope and effectiveness of a treaty regime become clearer, or they may deliberately abstain from joining because they can benefit regardless. Although real-world dynamics are often more intricate, we expect the ratification patterns of treaties with an MPR to diverge once the threshold is met. When a treaty governs a non-excludable good, incentives to freeride can emerge: some states may postpone ratification while benefiting from the externalities created by others’ cooperation, slowing the overall pace of ratification. By contrast, when a treaty regulates an excludable good, states can only benefit by joining, which is likely to lead to faster individual ratification.

Hypothesis 2b

Once a treaty enters into force, states’ ratification is slower in treaties that regulate non-excludable goods than in treaties that regulate excludable goods.

Put differently, we expect MPRs to act as coordination tools before a treaty enters into force, helping states align their actions and build a shared basis for cooperation. Once the threshold is reached and the treaty becomes legally binding, MPRs are likely to matter most in domains where the good in question is non-excludable and where the potential for freeriding shapes states’ strategic choices.

Describing the Variation of Minimum Participation Rules

To study the effect of MPRs on international cooperation, we first introduce and describe a dataset of multilateral agreements deposited with the United Nations Secretary-General (UNSG) between 1945 and 2018 (MTDSG). While the overall number of international treaties is much higher—the more comprehensive United Nations Treaties Series includes over 72,000 entries in our last year of observation, including 8,428 multilateral agreements—the MTDSG offers several advantages for our purposes. First, the MTDSG contains only open agreements negotiated under the UN framework or that the UNSG considers to be of “worldwide interest” (United Nations 1999, 7), which means that all states in the international system could potentially join. Second, agreements included in the MTDSG were adopted under similar procedural rules, which reduce the complexity of treaty law and clarify the meaning of state actions. Third, the MTDSG encompasses treaties across a wide range of issue areas, allowing for an analysis of differences in ratification patterns among them. Lastly and crucially, the MTSDG includes information independent of the agreements’ entry-into-force status. This feature is relevant for our analysis since we expect states to ratify treaties at different rates, depending on whether the agreements have entered into force. ⁶

We build on the dataset from Schulz and Levick (2023), which contains information from the UN for all treaties adopted since 1945 (as of 28 August 2018). The UNSG organizes treaties by issue area (chapter title) and provides details such as the agreement’s title, place and date of adoption, and date of entry into force (EIF). It also includes country-level information, including the type and date of each state’s action. We complement this data with manually coded information on threshold inclusion and design, as well as the type of good the treaty seeks to regulate, distinguishing between public goods (non-rivalrous and non-excludable), common goods (rivalrous and non-excludable), and others. Our data begins in 1945; the last agreement in the series, the “Treaty on the Prohibition of Nuclear Weapons,” was adopted in 2017.

The data show that MPRs are exceedingly common. Approximately 63 percent of all multilateral agreements in our sample include a threshold provision (330 out of 522). Moreover, MPRs have been a consistent element of treaty design, with their adoption rate remaining stable over time (see Appendix).

As evident in Figure 1, most MPRs include combinations of the following three elements: numerical thresholds that specify the number of ratifiers required for an agreement to enter into force; qualified thresholds that establish the characteristics of the minimum coalition; and the time that must elapse for an agreement to enter into force once all criteria are met (EIF time). Numerical thresholds are by far the most common design feature. For example, Art. 17(1) of the Convention on Cluster Munition (2006) establishes that the agreement “shall enter into force on the first day of the sixth month after the month in which the thirtieth instrument of ratification, acceptance, approval or accession has been deposited.” The Convention on Transit Trade of Land-locked States (1965) defines a more complex threshold. Art. 20(1) states that the convention “shall enter into force on the thirtieth day following the date of deposit of the instruments of ratification or accession of at least two land-locked States and two transit States having a sea coast.”

Figure 1.

Venn diagram of MPR combinations.

While MPRs are a longstanding and pervasive feature of multilateral treaties, threshold provisions are not distributed evenly across issue areas (Figure 2). An analysis of the chapters used by the UN Secretary-General to classify agreements shows that treaties without thresholds are concentrated in only a few subject areas, such as consular affairs or traffic regulations. In contrast, thresholds appear almost universally in areas concerned with “high politics,” such as peace and security (disarmament, conflict resolution) or state sovereignty (law of the sea). This pattern is consistent with studies suggesting that flexibility mechanisms are more likely to be adopted in domains where states are especially attentive to how costs and benefits are distributed (Copelovitch and Putnam 2014; Koremenos 2016).

Figure 2.

MPRs per UN Charter chapter (as proxy of issue area). The left figure plots relative frequencies within each chapter. The figure on the right plots absolute numbers. Treaties with an MPR are in dark blue, treaties without an MPR are in ocher.

Next, we examine whether the prevalence and type of MPRs depend on the number of states participating in an agreement. Specifically, we ask whether the size of the threshold reflects the number of states involved in negotiating the treaty. Figure 3 plots the number of signatures and ratifications (or their equivalents) against the numerical MPR thresholds across different domains. The figure shows that the relationship between the threshold level and ratifications is not always straightforward. In some areas, such as navigation and health, ratifications appear to correlate with the number required for an agreement to enter into force. In others, particularly human rights and environmental agreements, this pattern is less apparent. Notably, human rights treaties often include numerical MPRs despite binding only state parties. This pattern reinforces the view that MPRs serve at least two purposes: they help address freeriding concerns and, importantly, act as coordination devices that encourage broader participation.

Figure 3.

The value of the numerical threshold, and signatures (blue circle) and ratifications (red cross) in each treaty. Chapters are ordered alphabetically.

The relationship between signature patterns and MPR design is similarly revealing. Treaties typically remain open to signature for a limited time after adoption, making signatories a proxy for the states most closely associated with the negotiations. However, the number of signatures does not readily translate into threshold requirements. States appear to opt for similar threshold levels, evident in signatures clustering in vertical columns (e.g., penal matters, human rights, or environmental agreements categories). Figure 2 demonstrated that MPRs are relatively rare in the diplomatic and consular relations category. Figure 3 further shows that MPRs in this domain tend to follow a similar formula.

Finally, Figure 4 describes the variation in MPRs and plots the frequency of time-lapse and numerical threshold provisions. As indicated above, some formulas are more common than others. As Figure 4(a) on the left illustrates, treaties often specify a lag of zero days (71 cases), 30 days (72 cases), 90 days (124 cases), 180 days (24 cases), or 365 days (27 cases). Other values are less frequent. Figure 4(b) on the right displays the occurrence of numerical thresholds. The median value is 15, while the modal value is five. Again, we find that some values are particularly common. The numerical thresholds that occur at least ten times are two countries, three countries, five countries, six countries, ten countries, 16 countries, 20 countries, 22 countries, and 40 countries. Overall, the descriptive analysis shows that MPRs vary considerably in their design, yet it also provides prima facie evidence for recurrent institutional choices that are not readily explained by the number of states involved. Boilerplating, whereby existing formulas are adopted for efficiency gains, may also play a role in MPR design (Allee and Elsig 2019; Peacock et al. 2019).

Figure 4.

Frequency of different thresholds.

Modeling the Effects of MPRs

We now turn to our survival analysis to examine how MPRs influence treaty ratification and assess their effectiveness as mechanisms for mitigating freeriding. Following established practice in the quantitative study of treaty ratification, we employ survival models, which estimate the risk of a discrete event occurring over time (e.g., Mastenbroek 2003; Simmons 2000; von Stein 2005). Survival models allow us to assess the likelihood of an event while accounting for factors that may influence the time until ratification, such as a treaty’s entry into force or the type of good it governs. ⁷ To analyze this treaty-level data (hypothesis 2a) without making assumptions about the distribution of failure times (i.e., ratification), we employ a Cox proportional hazards model (Cox 1972).

Modeling each country’s ratification behavior after a treaty enters into force (hypotheses 1 and 2b) involves addressing three key challenges. First, it is crucial to recognize the dynamic effect of treaty activation on the timing of individual ratification decisions. Before a treaty enters into force, it influences ratification behavior in one way. After a treaty takes effect, it impacts states that have not yet ratified it differently. Modeling this effect using a simple covariate or strata to represent the presence or absence of an active treaty would be inadequate. It would assume that the treaty affects ratification behavior from the first day of its signing. However, our goal is to assess whether activating a treaty alters individual ratification behaviors from that day onward. Any model treating the effect as constant would likely underestimate the causal effect of interest.

Second, MPRs are similar to time-varying covariates in that they change their value over time (Bennett 1999). In our application, however, a time-varying covariate would not be an appropriate choice, either. By definition, those states that ratify before fulfilling the MPR cannot receive the treatment from an active treaty. In contrast, those countries that take longer to ratify have a much higher chance of being treated. A time-varying covariate would overestimate the MPR’s effect, leading to survivor treatment bias (Austin et al. 2006; Beyersmann et al. 2008).

Lastly, there is no single causal effect of ratifying after the MPR has been met. Instead, achieving the MPR at a particular moment has an evolving and variable impact over time. Meeting the MPR today may affect ratification tomorrow differently than ratification next month. Imai et al. (2023) refer to such processes as “cumulative” or “long-term” effects for their estimator in the context of time-series cross-sectional data.

We use a matching approach proposed by Fredriksson and Johansson (2008) to identify the dynamic effect of activating a treaty on individual ratification behavior over time. ⁸ We compare the ratification behavior of states where the treaty has entered into force with control cases where the treaty has not yet entered into force. Rooted in the causal inference framework, this model identifies the effect of a treatment at a specific time point on an ongoing duration process.

In causal inference, a treatment effect is defined as the difference in outcomes between units exposed to the treatment and those that are not. However, this difference cannot be directly measured in real-world settings, as a case can only be observed in either the control or treated state. To address this issue, Fredriksson and Johansson (2008) create counterfactual scenarios using matching techniques (Ho et al. 2007; Imbens 2004). Matching pairs treated cases with similar control cases, providing a plausible estimate of how the treated case would behave in the absence of the treatment. By controlling for potential confounding factors, matching allows researchers to attribute outcome differences to the treatment with greater confidence. ⁹

Once matched, the treatment effect of the MPR can be calculated using the Kaplan-Meier estimator. This method reflects the proportion of countries that have not ratified at a given point in time (Kaplan and Meier 1958). The causal effect of the MPR is determined by the observation-weighted difference between the survival curves of the treatment group, where the MPR has already been satisfied, and the control group, where the MPR has not been satisfied. A positive difference indicates that the proportion of countries that have not ratified is larger after satisfying the MPR compared to the counterfactual scenario where they ratify before meeting the MPR. In this case, the MPR leads to swifter ratification in the period leading up to its fulfillment than afterwards. Conversely, a negative difference suggests that fewer countries ratify before satisfying the MPR, implying that satisfying the MPR speeds up the ratification process. The causal effect of the MPR is not a single value; even after a treaty enters into force, ratification remains an ongoing process for some countries. Consequently, the MPR has a time-varying causal effect that evolves after it has come into force.

We do not pool the data over all treaties to calculate the average time-varying treatment effect. Instead, we first calculate the time-varying treatment effects for each treaty. We split our data set into those ratification cases that belong to the respective treaty (treatment group) and then match these observations with corresponding control cases from all other treaties. We perform this analysis separately for each of the 330 treaties with an MPR and then average over all observations to calculate the day-wise mean, thereby determining the average time-varying treatment effect over the 8 years following the respective treaty’s entry into force. If ratification is right-censored, we end the calculation of the treatment effect early.

As in other matching approaches, identifying the treatment effect critically depends on pairing the treatment cases with appropriate control cases. There are two aspects to this matching when analyzing how MPRs change states’ ratification behavior. First, it is necessary to match most similar cases, given their covariate values. The model in Fredriksson and Johansson (2008) relies on exact matching, that is, all observations are paired based on pre-defined and theoretically relevant covariates. Like other approaches from the family of monotonic imbalance bounding matching methods (e.g., Iacus et al. 2011; Ripollone et al. 2019), exact matching runs the risk of reducing the sample size of matched pairs because there may not be enough control cases. Yet the advantage of this approach is its transparency about what makes cases similar (Iacus et al. 2012). In addition, monotonic imbalance bounding matching does not require analyzing sample balance after matching—an unrealistic endeavor in the light of 330 individual treaties we study.

In our application, there is an additional aspect to matching due to the dynamic nature of the MPR’s effect over time. Identifying appropriate treated and control cases involves considering three distinct moments: (a) when individual states ratify, (b) when the MPR is fulfilled for the treaty in the treatment group, and (c) when the MPRs are fulfilled for the treaties in the control group. Selecting the treated cases is straightforward: they are all cases where ratification occurs after a treaty’s threshold has been met. To identify control cases, the model proposed by Fredriksson and Johansson (2008) suggests two conditions. First, any control case must not be influenced by its respective MPR, meaning ratification must occur before satisfying the corresponding MPR. Otherwise, the control cases would already have been treated by their respective MPR. Second, it is necessary to observe the control case for a period longer than the time it takes to satisfy the MPR in the treatment group. Since treatment cases require more time for ratification than the period necessary to satisfy their MPR, the control cases must meet this same condition.

How MPRs Foster International Cooperation

We construct several variables for our multivariate analyses. To account for threshold design, we distinguish between temporal lags, numerical thresholds, and qualified thresholds. We also record the number of states required to meet a numerical threshold. Potential boilerplating of threshold designs appears to be another variable that needs to be accounted for. As we saw from the Venn diagram in Figure 1, almost all treaties containing an MPR also feature a numerical threshold. Figure 4(b) indicates that certain numbers are particularly frequent. We define a boilerplate threshold as a numerical threshold observed at least 10 times.

Another design feature that may influence ratification patterns is the inclusion of dispute settlement mechanisms (Allee and Elsig 2016; Jo and Namgung 2012; Koremenos 2016). While not themselves flexibility devices, these mechanisms can alter the expected costs and benefits of participation by reducing uncertainty about enforcement while raising potential sovereignty costs. To capture this feature, we compiled the complete corpus of MTDSG treaty texts and used a Large Language Model to identify whether each agreement contains a dispute settlement mechanism. To ensure reliability, we manually validated the annotations by hand-checking a sample and comparing the outputs with Koremenos’s (2016) COIL dataset for the subset of treaties included in both sources. ¹⁰

We also take into account the type of good a treaty regulates, using the standard distinction based on excludability and rivalry in consumption (Ostrom 1990). Goods from which non-contributors can be excluded, such as private or club goods, generally do not create serious free-rider problems. The European Convention on International Commercial Arbitration (1961) is one example: only actors domiciled in a contracting state can make use of its provisions. The situation is different for common and public goods, both of which are non-excludable. Public goods are also non-rival, meaning one actor’s use does not reduce their availability to others. Common goods, by contrast, are rivalrous—each use diminishes what remains and can lead to overuse or underproduction. Because purely public or purely common goods are rare in practice, ¹¹ we code any treaty that regulates a good that is at least partly non-excludable as non-excludable, and any treaty that involves even some degree of rivalry as rivalrous. ¹²

Furthermore, we count the number of countries that expressed interest in the treaty through signatures or similar formal indications of intent to join, using this as a proxy for states’ involvement in the deliberation and negotiation of the agreement. Next, we identify whether a treaty was adopted before or after the end of the Cold War. To control for great power involvement, we annotate the signature of any of the five permanent members of the UN Security Council and explicitly account for whether the US has expressed its intent to cooperate via signature. ¹³ The participation of well-resourced states in treaty cooperation may affect the expected provision of goods and, consequently, states’ decisions to ratify. Additionally, powerful states may pressure smaller ones to join collective efforts (Milewicz and Snidal 2016; Schneider and Urpelainen 2013). To capture political dynamics beyond differences in material resources and influence, we also control for ideological differences among signatories. Building on a spatial understanding of political preferences in international politics, we draw on states’ yearly ideal points estimated from UN General Assembly voting records (Bailey et al. 2017). We then calculate the political alignment of signatories as the standard deviation of these ideal points in the year the treaty was signed. The literature further suggests that ratification depends on the importance or political salience of an agreement. We create a dummy variable based on Milewicz and Snidal (2016) to identify especially important multilateral treaties in our sample. Finally, we define dummy variables for each chapter as a proxy for the treaty issue area. ¹⁴

Our first hypothesis concerns the effect of MPRs once a threshold has been met. How does entry into force affect ratification in individual states? Some argue that it is plausible for states to engage in strategic holdouts and seek to delay an agreement’s entry into force. By contrast, we expect the likelihood of ratification to be higher before the MPR is satisfied, leading to swifter entry into force and slower ratification after the fact (Hypothesis 1).

The foundation of our research design is the exact matching estimator, as described in Fredriksson and Johansson (2008). We rely on four criteria for the matching. First, we use the fact that we observe the same country in multiple treaties. Matching on countries effectively eliminates idiosyncratic country characteristics, including differences in regime type or formal and informal decision-making procedures (on domestic constraints’ influence on treaty ratification, see Haftel and Thompson 2013). Second, to reflect the fundamental change in the international system following the fall of the Iron Curtain, we compare only treaties adopted before the end of the Cold War with those adopted after the end of the Cold War. Third, we examine the distinction between the acceptance, accession, and ratification of a treaty. While these actions have the same legal consequences, they imply different procedural rules and may differ in terms of the time required to express formal consent to be bound. Fourth and lastly, we also match observations depending on whether the treaty regulates an excludable or non-excludable good. In the Appendix, we report the results of robustness checks for additional matching on the depth of cooperation and issue area. In short, although the treated cases come from different treaties than the control cases, they originate from the same country and time period, rely on the same legal process for incorporation into domestic law, and regulate either excludable or non-excludable goods.

Exact matching based on the four covariates provides a sample of 250 treaties where the MPR has been activated and where we found control cases. Following Fredriksson and Johansson (2008), we calculate the treatment effect in each treaty as the weighted, day-wise difference between the Kaplan-Meier curve for treated cases where the treaty has entered into force and the Kaplan-Meier curve for the control cases where the treaty has not yet entered into force. Figure 5 plots this time-varying treatment effect for each treaty over 8 years after satisfying the MPR. In line with hypothesis 1, ratification rates decrease in most cases once the threshold has been met compared to the counterfactual scenario where the MPR has not been satisfied yet. Only a few exceptional cases follow the opposite trend, where entry-into-force expedites ratification. We rely on the logrank-test (Mantel 1966) to study the statistical significance of the difference between the treatment and the control group in each treaty. The data indicates a statistically significant difference in 187 (75 percent) of the 250 cases.

Figure 5.

Causal effect of the MPR on individual country ratification over 2,500 days after satisfying the MPR: Difference between Kaplan-Meier curve for treated cases (treaty has entered into force) and Kaplan-Meier curve for control cases (treaty has not yet entered into force). Daily, with random effects aggregated values across all treaties displayed with thick line. Uncertainty bounds represent 95 percent confidence interval. Matching model controls for country, Cold War period, legal form of consent to be bound, and whether a treaty generates excludable goods.

To visualize the findings from our study, we aggregate the treatment effect of the MPR from individual treaties with a random effects model for each day (Harrer et al. 2021) and visualize results in Figure 5. ¹⁵ The bold line shows the weighted average of the treatment effects for each day after the MPR is reached, while the dashed lines indicate the 95 percent confidence interval around this aggregate effect. Over the 4 years following a treaty’s entry into force, the daily average difference between the Kaplan-Meier curves of treaties with an MPR and their control group, where the MPR has not been satisfied, increases to approximately 0.45. After that, the effect plateaus. To illustrate the interpretation of the causal effect: Assume the treatment effect is 0.45 on a particular day, and that the value of the Kaplan-Meier curve for a treaty is 0.65 at that moment. The value of the control group would then be 0.65−0.45 = 0.20, which means that the matched cases from the control group, where the MPR has not been satisfied, show a non-ratification rate of 20 percent. These findings demonstrate the dynamic effect of MPRs: the rate at which states ratify agreements declines once the threshold has been met.

To test hypothesis 2a, we analyze when treaties satisfy the MPR using a conventional Cox proportional hazards model. ¹⁶ Figure 6 plots the results of the event history model (Box-Steffensmeier and Jones 2004, 60). ¹⁷ The horizontal axis shows how the hazard ratio changes when each covariate shifts from a low value to a high value—from the 25 percent quantile to the 75 percent quantile for continuous variables (e.g., number of countries required to ratify, number of signatory states, signatories’ alignment) and from 0 to 1 for all other dummy variables. A value below 0 on the x-axis indicates that the risk of satisfying the MPR declines, that is, the ratification process slows down, and it takes more time to reach the MPR threshold.

Figure 6.

Change in the risk of satisfying the MPR in a Cox Proportional Hazard Model. Results show the effect of an increase from the 25 percent quantile to the 75 percent quantile (continuous variables) or the shift from the absence to the presence of a variable (dummy variables). Controls include fixed effects for UN Charter chapters. Points indicate the mean; bars represent the 95 percent confidence interval. Effects not significantly different from 0 use a pale color.

Hypothesis 2a proposes that MPRs function as coordination devices regardless of the type of good at stake. While public goods and common goods create incentives to freeride due to their non-excludable benefits, these incentives should not delay when the MPR conditions are satisfied. The results shown in Figure 6 support this expectation. While treaties regulating common goods have a 23.52 percent higher risk and treaties regulating public goods have a 7.44 percent higher risk of entering into force than treaties with excludable goods, the uncertainty is considerable in both cases. Despite our sample’s sufficient statistical power, the 95 percent confidence intervals include 0 in both instances.

The effects reported above take into account a series of controls. Three of the variables are statistically significant at the 95 percent level. For one, the size of the minimum coalition, as defined in the MPR, is an important challenge to ratification—an intuitive finding. Increasing the minimum coalition from five countries (lower quartile) to 25 countries (upper quartile) reduces the likelihood of satisfying the MPR by 70.60 percent points. For another, the number of signatory states to a treaty matters. All else being equal, the more states participate in the negotiation of a treaty, the more likely it is that enough parties will ratify it. Increasing the number of signatory states from the lower quartile (24 countries) to the upper quartile (106 countries) increases the likelihood of meeting the threshold substantially by 288.43 percent. Lastly, signatories’ political alignment also matters. Treaties whose signatories are politically more cohesive reach the MPR sooner, controlling for all other factors. For example, reducing the standard deviation of signatories’ ideal points from 1.27 to 0.73 increases the hazard ratio by 34.84 percent. All other control variables remain insignificant.

To test Hypothesis 2b, we extend our analysis using the matching estimator to study the effects of non-excludable goods on individual ratification behavior. ¹⁸ As before, we aggregate the treatment effects from the treaties with daily random effects. ¹⁹ The variance in the random effect models allows for testing the statistical significance of the difference between the two groups of treaties. Figure 7 presents results and distinguishes the aggregated causal effects of the MPR in treaties that regulate a public or common good (red) from all other goods (blue). ²⁰ Bold lines indicate when the aggregate treatment effect of the two groups is significantly different from one another at p ≤ .05.

Figure 7.

Causal effect of the MPR on individual country ratification over 8 years after satisfying the MPR: Difference between Kaplan-Meier curve for treated cases (treaty has entered into force) and Kaplan-Meier curve for control cases (treaty has not yet entered into force). Distinction between public or common goods (red) and all other goods (blue). Results aggregated with daily random effect models for both groups. Bold lines indicate days when the aggregate treatment effect of the two groups is significantly different at p ≤ .05. Matching model controls for country, Cold War period, legal form of consent to be bound and whether a treaty generates excludable goods.

The trend in both cases is similar and largely follows the aggregated treatment effect in Figure 5. Throughout, non-ratification is higher for public or common goods than for all others (mean difference over the first 2,500 days is 0.10). Thanks to the estimator, it is also possible to appreciate the stability of the aggregated treatment effects over time. With our statistically conservative random effect approach for aggregating treaty effects, we find that the two curves are significantly different from one another very early on, after about 2 years, and again between years 3 and 4. In line with our theoretical expectations, where incentives for freeriding exist, the difference between ratifying before and after an MPR is higher.

Our analysis shows that MPRs facilitate treaty ratification. While strategic holdouts may occur, the broader pattern is clear: provision-point mechanisms consistently accelerate ratification. MPRs are especially effective in domains where freeriding is a concern. Before the threshold is met, ratification rates do not differ significantly between treaties regulating excludable and non-excludable goods. After entry into force, however, the pattern shifts—ratification slows for treaties involving non-excludable goods, consistent with emerging incentives to freeride.

Conclusion

This study demonstrates that MPRs function as effective provision point mechanisms in international cooperation. By making treaty commitments legally binding only after a predefined threshold is reached, threshold provisions create incentives for early ratification under conditions of uncertainty. Although MPRs are a common feature of multilateral treaties, they have received limited attention in institutional choice debates. Our analysis contributes to filling this gap by systematically examining how MPRs influence ratification dynamics across a wide range of treaties deposited with the UN Secretary-General between 1945 and 2018.

Our empirical strategy proceeded in two steps. First, we examined individual state behavior using a survival matching estimator developed by Fredriksson and Johansson (2008). We find that MPRs significantly shape ratification timing: states are more likely to ratify before the threshold is met than afterward. The average treatment effect increases over time and plateaus at approximately 0.45 after 4 years, indicating that MPRs accelerate early ratification but are followed by slower uptake once the threshold is reached.

Second, we investigated whether MPRs mitigate freeriding, particularly in treaties governing non-excludable goods. A first analysis comparing the time to entry into force for treaties with different types of goods revealed no systematic difference. However, when examining post-entry-into-force ratification behavior, we find that MPRs continue to exert a positive, albeit smaller, effect on cooperation. The average treatment effect remains relatively stable at around 0.075 over 8 years. These results suggest that while MPRs help reduce freeriding incentives, their primary contribution lies in promoting early coordination.

Our study offers several broader insights. Methodologically, we extend survival matching approaches to the analysis of dynamic, time-varying treatments, enabling counterfactual inference in the context of treaty ratification. Substantively, we provide new evidence that MPRs serve a dual function: they not only mitigate the risks of freeriding but also facilitate coordination among potential contributors, even in contexts where freeriding is not the dominant concern. This dual role distinguishes MPRs from other institutional design features and helps explain their widespread use.

We also find that the effect of MPRs is robust across issue areas and threshold designs. This suggests that concerns about boilerplating—that is, the inclusion of generic MPR clauses not tailored to the specific cooperation problem—may be overstated, at least in the case of numerical thresholds. Rather than functioning as mere formalities, MPRs appear to exert consistent and meaningful influence on the timing of cooperation.

Given the simplicity of these instruments, often no more than a clause specifying the number of required ratifications, it is striking that some treaties omit them entirely, a pattern that merits further analysis. Future research could usefully explore variation in the frequency and design of MPRs across issue areas. Although their effects appear broadly consistent, it remains unclear why MPRs are more prevalent in some domains than others. Notwithstanding this, our findings underscore the value of provision point mechanisms in international agreements. While they are no substitute for political will and cannot compel reluctant actors to cooperate, MPRs help reduce uncertainty and encourage early participation. Practitioners should therefore consider incorporating them into treaty design, not only where freeriding is a concern but more broadly as tools to facilitate timely ratification.

Supplemental Material

Supplemental Material - Reaching for the Threshold: How Minimum Participation Rules Facilitate Multilateral Treaty Ratification

Supplemental Material for Reaching for the Threshold: How Minimum Participation Rules Facilitate Multilateral Treaty Ratification by Christian Arnold and Carsten-Andreas Schulz in Journal of Conflict Resolution

Supplemental Material

Supplemental Material - Reaching for the Threshold: How Minimum Participation Rules Facilitate Multilateral Treaty Ratification

Supplemental Material for Reaching for the Threshold: How Minimum Participation Rules Facilitate Multilateral Treaty Ratification by Christian Arnold and Carsten-Andreas Schulz in Journal of Conflict Resolution