Mutual Optimism as a Cause of Conflict - Secret Alliances and Conflict Onset - Supporting Information

Q: How is mutual optimism calculated in a dyad with a third-party state?

Mutual optimism is computed from the alliance status among states A, B, and the third party C using coding rules that distinguish secret alliances from public alliances with secret provisions.

Q: What is the baseline outcome variable reported in the summary statistics?

The baseline outcome variable is MID, with values ranging from 0 to 1 and a reported sample size of 24,886.

Q: What robustness checks are performed in the appendix?

Robustness tests include using an alternative outcome (use of force), dropping dyads with recent secret alliance signers, and restricting to dyads with only secret defensive allies (and other ally-related restrictions in subsequent tables).

Q: How are the regression models specified for these tests?

Logistic regression is used with non-directed politically relevant dyad-year observations, and standard errors are clustered on the dyad.

Aug 26, 2026

Uploaded by Jacob

This supporting appendix provides the operationalization and empirical results linking mutual optimism to conflict onset in dyadic state interactions, with a third-party state as context. It defines a coding logic for calculating mutual optimism based on secret versus public offensive/defensive alliances and reports regression-based evidence using MID as the baseline outcome. Robustness checks use alternative outcomes (use of force) and re-specified samples to address dyads with recent signers and different alliance restrictions, with logistic models and dyad-clustered standard errors.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

Table 1: Calculating Capabilities

Table 2: Summary statistics

Table 3: Alternative Outcome Variable: Use of Force

Table 4: Robustness Test: Drop Dyads with Recent Signers

Table 5: Robustness Test: Only Include Secret Defensive Allies

Table 6: Robustness Test: Only Dyads with Allies

Supporting Information for “Mutual Optimism as a Cause of Conﬂict: Secret Alliances and Conﬂict Onset” Table 1: Calculating Capabilities | C's capabilities | Conditions | | --- | --- | | A adds C to A | (1) A and C have public or secret offensive/defensive alliance AND
(2) B and C have no public alliance | | A adds C to B | (1) B and C have public offensive/defensive alliance AND
(2) A and C have no alliance | | A is uncertain about C | A and C have no alliance & B and C have no public alliance | | A excludes C | A and C have an alliance & B and C have a public alliance | Notes: Coding rules for calculating Mutual Optimism in a dyad involving states A and B where state C is a third party. Alliances are coded as secret only if the entirety of the alliance was secret as coded by ATOP. Public alliances with secret provisions are coded as public. Any bias from the latter coding choice would work against our results, suggesting our effect sizes may be understated. Table 2: Summary statistics | Variable | Mean | Std. Dev. | Min. | Max. | N | | --- | --- | --- | --- | --- | --- | | Outcome Variable | | | | | | | MID | 0.021 | 0.142 | 0 | 1 | 24,886 | | Explanatory Variables
Mutual Optimism | | | | | | | Continuous, no prior | 1.035 | 0.11 | 1 | 1.97 | 24,886 | | Binary, no prior | 0.390 | 0.488 | 0 | 1 | 24,886 | | Continuous, prior | 0.849 | 0.251 | 0.005 | 1.846 | 24,886 | | Binary, no prior | 0.081 | 0.273 | 0 | 1 | 24,886 | | Control Variables | | | | | | | Relative Capabilities | 0.106 | 0.126 | 0 | 0.5 | 24,886 | | Contiguity | 0.299 | 0.458 | 0 | 1 | 24,886 | | Joint Democracy | 0.031 | 0.172 | 0 | 1 | 24,886 | | Alliance | 0.094 | 0.292 | 0 | 1 | 24,886 | | Peace Years | 27.139 | 23.976 | 0 | 107 | 24,886 | Table 3: Alternative Outcome Variable: Use of Force | | No Prior
(1) (2) Continuous Dichotomous | | (3)
Continuou | Prior
(4) s Dichotomous | | --- | --- | --- | --- | --- | | Mutual Optimism | 1.29***
(0.44) | 0.45***
(0.14) | 0.20
(0.23) | 0.48**
(0.19) | | Relative Capabilities | 1.79***
(0.61) | 1.98***
(0.58) | 2.04***
(0.59) | 1.63***
(0.63) | | Contiguity | 0.91***
(0.20) | 0.97***
(0.20) | 0.95***
(0.21) | 0.93***
(0.20) | | Joint Democracy | -0.09
(0.29) | -0.19
(0.28) | -0.11
(0.29) | -0.13
(0.28) | | Alliance | -1.02*** | -0.99*** | -1.01*** | -1.00*** | | | (0.25) | (0.25) | (0.26) | (0.26) | | Peace Years | -0.18*** | -0.18*** | -0.18*** | -0.18*** | | | (0.02) | (0.02) | (0.02) | (0.02) | | Constant | -4.85*** | -3.73*** | -3.74*** | -3.55*** | | | (0.49) | (0.20) | (0.26) | (0.18) | | N | 24,886 | 24,886 | 24,886 | 24,886 | 􀀃 p < 0:1;􀀃􀀃 p < 0:05;􀀃􀀃􀀃 p < 0:01 Notes: Logistic regression with non-directed politically relevant dyad year as the unit of analysis. Outcome variable is the use of force indicated by a militarized dispute with a hostility level of either “use of force” or “war.” Standard errors in parentheses are clustered on the dyad. Results for higher order Peace Years are not shown. Additional analysis (not shown) indicates that Mutual Optimism has the strongest effect in Model 3 when moving from values just below one to values just above one. This is consistent with the theoretical expectation that increasing optimism is most problematic when the summed probabilities of victory are close to one. Table 4: Robustness Test: Drop Dyads with Recent Signers | | No Prior
(1) (2) Continuous Dichotomous | | (3)
Continuou | Prior
(4) s Dichotomous | | --- | --- | --- | --- | --- | | Mutual Optimism | 0.90**
(0.44) | 0.38***
(0.14) | 0.19
(0.24) | 0.38**
(0.19) | | Relative Capabilities | 2.35***
(0.62) | 2.44***
(0.62) | 2.50***
(0.61) | 2.25***
(0.62) | | Alliance | -1.03*** | -1.03*** | -1.03*** | -1.02*** | | | (0.28) | (0.28) | (0.28) | (0.28) | | Contiguity | 0.75***
(0.21) | 0.80***
(0.21) | 0.79***
(0.23) | 0.76***
(0.21) | | Joint Democracy | -0

FAQs

How is mutual optimism calculated in a dyad with a third-party state?

Mutual optimism is computed from the alliance status among states A, B, and the third party C using coding rules that distinguish secret alliances from public alliances with secret provisions.

What is the baseline outcome variable reported in the summary statistics?

The baseline outcome variable is MID, with values ranging from 0 to 1 and a reported sample size of 24,886.

What robustness checks are performed in the appendix?

Robustness tests include using an alternative outcome (use of force), dropping dyads with recent secret alliance signers, and restricting to dyads with only secret defensive allies (and other ally-related restrictions in subsequent tables).

How are the regression models specified for these tests?

Logistic regression is used with non-directed politically relevant dyad-year observations, and standard errors are clustered on the dyad.

Aug 26, 2026

Uploaded by Jacob