Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-17T09:56:28.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple probability models of peacetime and wartime alliance formation

Published online by Cambridge University Press:  26 October 2009

Yoshinobu Yamamoto
Get access Rights & Permissions [Opens in a new window]

Extract

The aims of this paper are (a) to construct probability models for peacetime and wartime alliance formation, (b) to provide international political interpretations of the probability models, and (c) to obtain some policy implications from these models.

Since Horvath and Foster published their seminal work in 1963 on probability models of wartime alliance sizes, no further research has been undertaken to elaborate their ideas (except for Yamamoto, 1974; and Yamamoto and Bremer, 1980), even though varied probability models have been applied to the analysis of war occurrences (see Richardson; Singer and Small, 1972; and Wilkinson) and of peacetime alliance formation (see McGowan and Rood, and Siverson and Duncan). Horvath and Foster found that the frequency distribution of wartime alliance sizes is accounted for by a Yule distribution which has a long tail (meaning that large alliances are likely to form in war) and that a Yule distribution can be derived from a process in which a war alliance will acquire new members with.a probability directly proportional to its current size (i.e., the number of participating nations in the alliance) and in which the members of alliances are not allowed to leave until war ends.

Type
Research Article
Information
Review of International Studies , Volume 8 , Issue 3 , July 1982 , pp. 139 - 157
Copyright
Copyright © British International Studies Association 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Claude, Inis L., Jr., Power and International Relations (New York, 1962).Google Scholar

2. Coleman, James S., Introduction to Mathematical Sociology (New York, 1964).Google Scholar

3. Feller, William, An Introduction to Probability Theory and its Application, Vol. 1 (New York, 1968).Google Scholar

4. Goodman, Leo A., ‘Mathematical Methods for the Study of Systems of Groups’, American Journal of Sociology, 70 (1964) pp. 170–192.CrossRefGoogle Scholar

5. Gulick, Edward Vose, Europe's Classical Balance of Power (New York, 1955).Google Scholar

6. Horvath, William J., and Foster, Caxton C., ‘Stochastic Models of War Alliances’. Journal of Conflict Resolution, 7 (1963) pp. 110–116.CrossRefGoogle Scholar

7. Ijiri, Yuji and Simon, Herbert A., Skew Distributions and the Sizes of Business Firms (Amsterdam, 1977).Google Scholar

8. Irwin, I. O., ‘Inverse Factorial Series as Frequency Distribution’, in: Patil, Ganapati P., (ed.), Classical and Contagious Discrete Distributions (Calcutta, 1965) pp. 159–174.Google Scholar

9. Kaplan, Morton A., System and Process in International Politics (New York, 1957).Google Scholar

10. McGowan, Patrick J. and Rood, Robert M., ‘Alliance Behavior in Balance of Power Systems: Applying a Poisson Model to Nineteenth-Century Europe’. American Political Science Review, 69 (1975) pp. 859–870.CrossRefGoogle Scholar

11. Morgenthau, Hans J., Politics among Nations (New York, 1960).Google Scholar

12. Richardson, Lewis F., Statistics of Deadly Quarrels (Chicago, 1960).Google Scholar

13. Rothstein, Robert L., Alliances and Small Powers (New York, 1968).Google Scholar

14. Sabrosky, Alan N., ‘Interstate Alliances: Their Reliability and the Expansion of War’, in: Singer, J. David, (ed.), The Correlates of War: II (New York, 1980) pp. 161–198.Google Scholar

15. Singer, J. David and Small, Melvin, ‘Formal Alliances, 1815–1939: A Quantitative Description’, Journal of Peace Research, 3 (1966) pp. 1–32CrossRefGoogle Scholar; The Wages of War: 1816–1965 (New York, 1972).Google Scholar

16. Siverson, Randolph M. and Duncan, George T., ‘Stochastic Models of International Alliance Initiation, 1885–1965’, in: Zinnes, Dina A. and Gillespie, John V., (eds.), Mathematical Models in International Relations (New York, 1976) pp. 110–131.Google Scholar

17. Small, Melvin and Singer, J. David, ‘Formal AEiances, 1816–1965: An Extension of the Basic Data’. Journal ofPeace Research, 6 (1969) pp. 257–282.CrossRefGoogle Scholar

18. Yamamoto, Yoshinobu, ‘Probability Models of War Expansion and Peacetime Alliance Formation’, Ph.D. thesis, Univ. of Michigan, 1974Google Scholar; ‘ Role of Interstate Alliances in the International System’. The Annals ofSaitama University: School of Liberal Arts, 11 (1975) pp. 35–55Google Scholar (in Japanese); ‘ Mathematical Models of the International System’. The Annals of Saitama University: School of Liberal Arts, 15 (1979) pp. 53–103Google Scholar (in Japanese); Yamamoto, and Bremer, Stuart A., ‘Wider Wars and Restless Nights: Major Power Intervention in Ongoing War’, in : Singer, J. David, (ed.), The Correlates of War: II (New York, 1980) pp. 199–229.Google Scholar

19. White, Harrison, ‘Chance Models of Systems of Casual Groups’. Sociometry, 25 (1962) pp. 153–172.CrossRefGoogle Scholar

20. Wilkinson, David, Deadly Quarrels: Lewis F. Richardson and the Statistical Study of War. (Berkeley, 1980).Google Scholar