Research ArticleINTERNATIONAL COOPERATION

Detecting reciprocity at a global scale

See allHide authors and affiliations

Science Advances  03 Jan 2018:
Vol. 4, no. 1, eaao5348
DOI: 10.1126/sciadv.aao5348
  • Fig. 1 Mapping cooperation, influence, and reciprocity in the European Union (EU) and around the world.

    (A) The directed Goldstein time series for the United States (USA)–Russia (RUS) relationship. The time series have been smoothed using a 30-day moving average for visualization purposes. (B) A network representing overall attitude of EU countries, the amount of interaction between nations (darker edges indicate more actions), and how cooperative interactions are on average (edge width). (C) A network representation of influence among EU nations [that is, CCM(A, B) ≥ 0.25). ]. (D) Countries are colored according to their total imposed influence on others, and yellow lines connect pairs of countries exhibiting reciprocity. Gray countries had insufficient data for CCM analysis.

  • Fig. 2 Country pairs exhibiting reciprocity are cooperative on average but reciprocate conflict.

    Given an observation of cooperation (left) or conflict (right), reciprocating country pairs are more likely to cooperate (A and B) regardless of recent interaction, less likely to conflict given recent cooperation (C), but more likely to reciprocate conflict (D) in the cumulative interactions of the following day, 3 days, and 7 days (x axis). Each point represents the average rate of cooperation or conflict between countries A and B, denoted by PAB, for reciprocating country pairs (yellow) or nonreciprocating country pairs (purple), and error bars represent the standard error. Probabilities (y axis) have been shifted according to the aggregate probabilities of cooperation or conflict, respectively, across the entire Integrated Crisis Early Warning System (ICEWS) data set.

  • Fig. 3 CCM reciprocity indicates mirroring of specific interaction types.

    Given an observed interaction type (x axis, denoted by Q) between a country pair with (yellow) or without (purple) CCM reciprocity, we plot the probability (y axis) of (A) material cooperation, (B) material conflict, (C) verbal conflict, and (D) verbal cooperation in the day following the interaction (see section S3 for additional time windows).

  • Fig. 4 Generalizing reciprocity from country pairs in isolation.

    (A) The global influence network. Countries are represented by nodes. An arrow connects country A to country B if CCM(A, B) ≥ 0.25. Node size and color reflect the node’s out-degree. (B) The number of two and three cycles in the global influence network. (C) Country pairs with higher shared influence [that is, (CCM(A, B) + CCM(B, A))/2; x axis] have increasingly correlated attitudes toward each other (y axis). Marker colors indicate whether the country pair has reciprocity [that is, CCM(A, B) ≥ 0.25 and CCM(B, A) ≥ 0.25; yellow] or not (purple). The black dashed line represents a LOWESS (locally weighted scatterplot smoothing) regression fit.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/1/eaao5348/DC1

    section S1. Summarizing ICEWS

    section S2. Measuring influence using CCM

    section S3. Characterizing instances of reciprocity

    section S4. Varying thresholds for CCM reciprocity

    section S5. Country pairs with asymmetric influence

    fig. S1. The distributions of Goldstein scores by CAMEO event type occurring in the ICEWS data set.

    fig. S2. The distribution of CAMEO quad classes in the ICEWS data set.

    fig. S3. The number of events per day during the entire ICEWS data set.

    fig. S4. Gaps in interactions between country pairs are small.

    fig. S5. An example from dynamical systems.

    fig. S6. Examples of shadow manifolds.

    fig. S7. Using nearest neighbors of shadow manifolds to recover variable dynamics.

    fig. S8. Using CCM to infer causality between using United States (USA) treatment of Saudi Arabia (SAU) and Saudi Arabia’s treatment of the United States (E = 200, τ = 1).

    fig. S9. The number of pairs of countries exhibiting CCM reciprocity (y axis) during four 5-year time periods (x axis) as we vary the minimum influence threshold (that is, minimum Pearson correlation of CCM reconstruction, indicated by color).

    fig. S10. CCM causation decreases with increased artificial noise.

    fig. S11. The effects of biased news data (λ = 0.00).

    fig. S12. The effects of biased news data (λ = 0.10).

    fig. S13. The effects of biased news data (λ = 0.20).

    fig. S14. The effects of biased news data (λ = 0.30).

    fig. S15. The effects of biased news data (λ = 0.40).

    fig. S16. The effects of biased news data (λ = 0.50).

    fig. S17. The effects of biased news data (λ = 0.60).

    fig. S18. The effects of biased news data (λ = 0.70).

    fig. S19. The effects of biased news data (λ = 0.80).

    fig. S20. The effects of biased news data (λ = 0.90).

    fig. S21. Main results using CCM analysis with E = 200 and τ = 2.

    fig. S22. Main results using CCM analysis with E = 200 and τ = 3.

    fig. S23. Main results using CCM analysis with E = 200 and τ = 4.

    fig. S24. Main results using CCM analysis with E = 200 and τ = 5.

    fig. S25. Country pairs exhibiting CCM reciprocity are more likely to reciprocate cooperation or conflict.

    fig. S26. The patterns of behavior in the day following an interaction.

    fig. S27. The patterns of behavior in the three days following an interaction.

    fig. S28. The patterns of behavior in the week following an interaction.

    fig. S29. The patterns of behavior in the month following an interaction.

    fig. S30. The effects of varying the CCM threshold for causality.

    fig. S31. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.15] are connected using yellow edges.

    fig. S32. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.20] are connected using yellow edges.

    fig. S33. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.25] are connected using yellow edges.

    fig. S34. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.30] are connected using yellow edges.

    fig. S35. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.35] are connected using yellow edges.

    fig. S36. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.40] are connected using yellow edges.

    fig. S37. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.45] are connected using yellow edges.

    fig. S38. Pairs of countries exhibiting CCM reciprocity [that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.50] are connected using yellow edges.

    table S1. Nations ordered by total imposed influence.

    table S2. The Pearson correlation for proportion of interactions of each quad class between a pair of countries to the shared influence for that pair of countries.

    table S3. Country pairs ordered by increasing absolute difference in directed influence [that is, CCM(A, B) − CCM(B, A)].

  • Supplementary Materials

    This PDF file includes:

    • section S1. Summarizing ICEWS
    • section S2. Measuring influence using CCM
    • section S3. Characterizing instances of reciprocity
    • section S4. Varying thresholds for CCM reciprocity
    • section S5. Country pairs with asymmetric influence
    • fig. S1. The distributions of Goldstein scores by CAMEO event type occurring in the ICEWS data set.
    • fig. S2. The distribution of CAMEO quad classes in the ICEWS data set.
    • fig. S3. The number of events per day during the entire ICEWS data set.
    • fig. S4. Gaps in interactions between country pairs are small.
    • fig. S5. An example from dynamical systems.
    • fig. S6. Examples of shadow manifolds.
    • fig. S7. Using nearest neighbors of shadow manifolds to recover variable
      dynamics.
    • fig. S8. Using CCM to infer causality between using United States (USA) treatment of Saudi Arabia (SAU) and Saudi Arabia’s treatment of the United States (E = 200, τ = 1).
    • fig. S9. The number of pairs of countries exhibiting CCM reciprocity (y axis) during four 5-year time periods (x axis) as we vary the minimum influence threshold (that is, minimum Pearson correlation of CCM reconstruction, indicated by color).
    • fig. S10. CCM causation decreases with increased artificial noise.
    • fig. S11. The effects of biased news data (λ = 0.00).
    • fig. S12. The effects of biased news data (λ = 0.10).
    • fig. S13. The effects of biased news data (λ = 0.20).
    • fig. S14. The effects of biased news data (λ = 0.30).
    • fig. S15. The effects of biased news data (λ = 0.40).
    • fig. S16. The effects of biased news data (λ = 0.50).
    • fig. S17. The effects of biased news data (λ = 0.60).
    • fig. S18. The effects of biased news data (λ = 0.70).
    • fig. S19. The effects of biased news data (λ = 0.80).
    • fig. S20. The effects of biased news data (λ = 0.90).
    • fig. S21 . Main results using CCM analysis with E = 200 and τ = 2.
    • fig. S22. Main results using CCM analysis with E = 200 and τ = 3.
    • fig. S23. Main results using CCM analysis with E = 200 and τ = 4.
    • fig. S24. Main results using CCM analysis with E = 200 and τ = 5.
    • fig. S25. Country pairs exhibiting CCM reciprocity are more likely to reciprocate cooperation or conflict.
    • fig. S26. The patterns of behavior in the day following an interaction.
    • fig. S27. The patterns of behavior in the three days following an interaction.
    • fig. S28. The patterns of behavior in the week following an interaction.
    • fig. S29. The patterns of behavior in the month following an interaction.
    • fig. S30. The effects of varying the CCM threshold for causality.
    • fig. S31. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.15 are connected using yellow edges.
    • fig. S32. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.20 are connected using yellow edges.
    • fig. S33. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.25 are connected using yellow edges.
    • fig. S34. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.30 are connected using yellow edges.
    • fig. S35. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.35 are connected using yellow edges.
    • fig. S36. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.40 are connected using yellow edges.
    • fig. S37. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.45 are connected using yellow edges.
    • fig. S38. Pairs of countries exhibiting CCM reciprocity that is, CCM(A, B) ≥ 0.15 and CCM(B, A) ≥ 0.50 are connected using yellow edges.
    • table S1. Nations ordered by total imposed influence.
    • table S2. The Pearson correlation for proportion of interactions of each quad class between a pair of countries to the shared influence for that pair of countries.
    • table S3. Country pairs ordered by increasing absolute difference in directed influence that is, CCM(A, B) − CCM(B, A).

    Download PDF

    Files in this Data Supplement: