Research ArticleSOCIAL SCIENCES

A three-degree horizon of peace in the military alliance network

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Science Advances  01 Mar 2017:
Vol. 3, no. 3, e1601895
DOI: 10.1126/sciadv.1601895
  • Fig. 1 Illustration of degrees of separation in the alliance network.

    Examples of alliances at one to four degrees of separation are presented, with the focal states embedded within the global alliance network. The paths linking the focal pair of states are in red, whereas the rest of the states in the network are in light yellow. Our research investigates the probability of conflict between states at different degrees of separation in the alliance network.

  • Fig. 2 The interplay between the international alliance and conflict networks.

    (Top) Networks in 1965, 1980, and 2000. States are plotted as nodes in the network, and the node color indicates the number of alliances of a given state, with darker nodes having more allies. Red ties represent conflicts in all plots, whereas alliance ties are in different colors across time. Names of communities are given by the multinational alliance to which most of the members in the community belong. On the world map of 1980, with the alliance network in light orange, we illustrate sample states in higher-order alliances. Spain and Italy, joined together by the United States, are at two degrees of separation. Central African Republic and Sudan, allies at three degrees of separation, are connected by France and Djibouti. CSTO, Collective Security Treaty Organization; ECOWAS, Economic Community of West African States; ECCAS, Economic Community of Central African States; ANAD, Agreement of Non-Aggression and Defense Assistance.

  • Fig. 3 Conflict onset by degree of separation for geographically contiguous states in the alliance network.

    Pairs of states that are not connected at any degree are denoted as infinite (“Inf”), and conflict onsets are observed between contiguous states at up to five degrees of separation. (Left) Rate of conflict onset from the raw data, with the pink horizontal line indicating the average rate for contiguous dyads. The first three degrees of separation see below-average conflict onset rates. (Right) Dyads at degrees of separation ranging from one to four are sampled, and their respective conflict probabilities conditional on the rest of the network are computed. The plot shows the probability of conflict when an alliance is present or absent between a contiguous pair of states with 95% confidence intervals. The probability of conflict drops substantially between contiguous states indirectly allied up to three degrees.

  • Fig. 4 Pairs of states at different degrees of separation can be categorized by the community structure of the alliance network.

    Within community counts the number of state pairs, where both states belong to the same alliance community. Neighboring communities are composed of pairs of states that are embedded within different communities while the two communities are themselves connected by some ties. The “Any tie” bars denote the number of ties that belong to either within community or neighboring communities. The horizontal axis shows the proportion of alliances that belong to a specific community structure. Because several states belong to more than one community, some alliances fall into both within community and neighboring communities at the same time.

  • Table 1 TERGMs of the conflict network with geographic contiguity interacted with alliances, 1965–2000.

    All models are estimated with bootstrap-corrected pseudolikelihood using 1000 replications. Ninety-five percent confidence intervals are presented in brackets. Coefficients and confidence intervals displayed in bold are statistically significant at the P = 0.05 level.

    VariableModel 1Model 2
    Edges−7.99 (−8.24 to −7.77)−8.06 (−8.28 to −7.85)
    Alternating k-stars (2)1.11 (0.98 to 1.22)1.11 (0.98 to 1.23)
    Four-cycle0.56 (0.44 to 1.16)0.55 (0.44 to 1.08)
    GWESP (0)−0.30 (−0.51 to −0.13)−0.31 (−0.52 to −0.13)
    Joint democracy−0.66 (−0.91 to −0.44)−0.69 (−0.94 to −0.49)
    Direct contiguity4.34 (4.10 to 4.64)4.39 (4.16 to 4.68)
    Capability ratio−0.17 (−0.22 to −0.12)−0.16 (−0.22 to −0.12)
    Trade dependence−0.18 (−0.52 to −0.05)−0.16 (−0.43 to −0.04)
    One-degree alliance0.96 (0.44 to 1.42)
    Two-degree alliance0.17 (−0.31 to 0.61)
    Three-degree alliance0.44 (−0.03 to 0.91)
    Four-degree alliance−0.26 (−1.02 to 0.26)
    Contiguity × One-degree alliance−1.49 (−1.92 to −0.99)
    Contiguity × Two-degree alliance−0.84 (−1.45 to −0.27)
    Contiguity × Three-degree alliance−1.28 (−2.10 to −0.54)
    Contiguity × Four-degree alliance0.13 (−0.85 to 1.15)
    Within community0.70 (0.26 to 1.10)
    Neighboring communities0.63 (0.27 to 0.99)
    Contiguity × Within community−1.16 (−1.54 to −0.73)
    Contiguity × Neighboring communities−1.43 (−2.02 to −0.87)

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/3/e1601895/DC1

    fig. S1. The number of dyads and contiguous dyads at different degrees of separation.

    fig. S2. Conflict onset by degree of separation in the alliance network.

    fig. S3. Interaction effect of degrees of separation and contiguity on the conditional probability of military conflict.

    fig. S4. Endogenous goodness of fit.

    fig. S5. Microlevel interpretations for pairs of states connected by higher-order alliances.

    fig. S6. The persistence of alliance paths.

    fig. S7. Modularity score of different community detection algorithms.

    fig. S8. Maps of the international system in 1965, 1990, and 2000.

    fig. S9. Hypothesized mediation model.

    table S1. Contiguous dyads in the defensive alliance network in 1965.

    table S2. Contiguous dyads in the defensive alliance network in 1980.

    table S3. Contiguous dyads in the defensive alliance network in 2000.

    table S4. Summary statistics for variables used in the TERGMs.

    table S5. TERGM model robustness checks.

    table S6. TERGMs using Maoz MID data as robustness tests.

    table S7. TERGMs using Gibler and Little’s nonprotest dispute data as robustness tests.

    table S8. Logistic models for mediation analysis using Baron and Kenny’s procedure.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. The number of dyads and contiguous dyads at different degrees of separation.
    • fig. S2. Conflict onset by degree of separation in the alliance network.
    • fig. S3. Interaction effect of degrees of separation and contiguity on the conditional probability of military conflict.
    • fig. S4. Endogenous goodness of fit.
    • fig. S5. Microlevel interpretations for pairs of states connected by higher-order alliances.
    • fig. S6. The persistence of alliance paths.
    • fig. S7. Modularity score of different community detection algorithms.
    • fig. S8. Maps of the international system in 1965, 1990, and 2000.
    • fig. S9. Hypothesized mediation model.
    • table S1. Contiguous dyads in the defensive alliance network in 1965.
    • table S2. Contiguous dyads in the defensive alliance network in 1980.
    • table S3. Contiguous dyads in the defensive alliance network in 2000.
    • table S4. Summary statistics for variables used in the TERGMs.
    • table S5. TERGM model robustness checks.
    • table S6. TERGMs using Maoz MID data as robustness tests.
    • table S7. TERGMs using Gibler and Little’s nonprotest dispute data as robustness tests.
    • table S8. Logistic models for mediation analysis using Baron and Kenny's procedure.

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