¹ For example, the distance between two jobs in a hierarchical organizational structure can be regarded as the number of layers of the organization that have to be ascended to reach a common boss. See p. 232 below.

² The symmetry of propensities guarantees that if one nation reduces its frustration by switching sides then the energy for the whole system will be reduced. Here is the proof. Without loss of generality, let X = A′ versus B where A′ = A∪{k}, and let Y = A versus B′ where B′ = B∪{k}. To shorten the notation let K = {k} and r _ij = s_ts_jp_ij. E(X) = Σ_A′Σ_Br_ij + Σ_BΣ_A′r_ij since d _ij(X) = 0 for i∈A′, j∈A′ or i∈B, j∈B; and d _ij = 1 for i∈A, j∈B′ or i∈B, j∈A′. Likewise E(Y) = Σ_AΣ_B′r_ij + Σ_B′Σ_Ar_ij. So E(X) − E(Y) = Σ_A′Σ_Br_ij − Σ_AΣ_B′r_ij + Σ_BΣ_A′r_ij − Σ_B′Σ_Ar_ij = Σ_KΣ_Br_ij − Σ_AΣ_Kr_ij + Σ_BΣ_Kr_ij − Σ_KΣ_Ar_ij since Σ_A′Σ_Br_ij = Σ_AΣ_Br_ij + Σ_KΣ_Br_ij. But Σ_KΣ_Br_ij = Σ_BΣ_Kr_ij and Σ_AΣ_Kr_ij = Σ_KΣ_Ar_ij since p_ij = p_ij. So E(X) − E(Y) = 2(Σ_KΣ_Br_ij − Σ_KΣ_A′r_ij) = 2(S_kΣ_BS_jp_kj − S_kΣ_AS_jp_kj) = 2S _k(F _k{X) − F _k(Y)), since d _kj(X) = 0 for jΣA, d_kj(X) = 1 for jΣB, d_kj(Y) = 0 for jΣB, and d_kj(Y) = 1 for jΣA. But S_k > 0. So for adjacent configurations, X and Y, differing only by nation k, if F _k(X) − F _k(Y) > 0 then E(X) − E(Y) > 0.

³ Since every allowable change lowers the energy of the system, the system can never return to a previous configuration.

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²³ For example, Altfield, Michael F. and de Mesquita, Bruce Bueno, ‘Choosing Sides in War’, International Studies Quarterly, 23 (1979), 87–112CrossRefGoogle Scholar; Altfield, Michael F., ‘The Decision to Ally: A Theory and Test’, Western Political Quarterly, 37 (1984), 523–44Google Scholar; Morrow, James D., ‘On the Theoretical Basis of a Measure of National Risk Attitudes’, International Studies Quarterly, 31 (1987), 423–38CrossRefGoogle Scholar; Walt, Stephen M., ‘Testing Theories of Alliance Formation: The Case of Southwest Asia’, International Organization, 42 (1988), 275–316CrossRefGoogle Scholar; and The Origins of Alliances.

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²⁵ Specifically, the countries selected are the five major ropean powers (Britain, France, Germany, Italy and the Soviet Union) and the twelve countries which had a formal defence or neutrality pact with any of them. Turkey was not considered to be in Europe. Two European countries were excluded: Albania because it was not independent of Italy, and Belgium because it withdrew from its defence agreement with France in 1936. Information about which was allied with which was not used in the analysis. The sources of alliance data are Singer, J. David and Small, Melvin, ‘Formal Alliances, 1815–1939’, Journal of Peace Research, 3 (1966), 1–31CrossRefGoogle Scholar and Small, Melvin and Singer, J. David, ‘Formal Alliances, 1815–1965: An Extension of the Basic Data’, Journal of Peace Research, 6 (1969), 257–82.CrossRefGoogle Scholar

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²⁷ Due to the limitations of available data, we have not been able to operationalize economic issues and the level of economic interdependence in all dyads. Hence, we have simply omitted this category when calculating propensity.

²⁸ With n countries, there are n(n - 1)/2 pairwise propensities. For n = 17, there are 136 pairwise propensities. Propensities are estimated as follows: ethnic conflict, a border disagreement or a recent history of war between two nations counted as -1 each for their propensity. Similarity of religion was counted as +1 within categories (Catholic, Protestant, Orthodox, Muslim and Atheist), and – 1 across major categories (Christian, Muslim, Atheist), all calculated according to proportions of each religion in each country. Similarity or difference of government type was considered for two countries with democratic, fascist or communist governments: +1 if they were the same type and – 1 if they were of different types. The source for ethnic conflict, border disagreement, history of war, and government type is Kinder, Hermann and Hilgemann, Werner, The Anchor Alias of World History, vol. II (New York: Anchor Press, 1978).Google Scholar Religion is given in the Correlates of War Project's Cultural Data Set for 1930 (version of 7/90 prepared by Phil Schaefer). Selecting equal weights for the five propensity factors is the least arbitrary way of combining them.

²⁹ This is 2¹⁷/2. Each country can be in one of two possible sides, but which side is listed first is arbitrary.

³⁰ For example, Britain declared war on Germany in 1939. Poland was first invaded by Germany and hence is counted as being aligned opposite to Germany. Hungary and Romania were allied with Germany and in 1941 assisted in the invasion of the Soviet Union.

³¹ In Configuration 2, Greece and Yugoslavia join the Soviet Union largely to avoid aligning with Germany, with whom both have a history of war.

³² There are 154 configurations that are as accurate or more so than the configuration that had two mistakes among the seventeen predicted nations. Since two different predictions are made and there are 2¹⁷/2 = 65,536 configurations, the chance that one of them would be this good is 2 x (154/65,536) = 0.0047.

³³ Steepest descent in the energy landscape is used to calculate basin size.

³⁴ For example, as late as 1939 when the Soviet Union invaded Finland, there were some active voices in Britain and France calling for intervention against the Soviet Union, despite the growing consensus that Germany was the major threat. Had Germany not blocked access by invading Norway, such action against the Soviets would not have been out of the question. Incidentally, the main reason that Yugoslavia and Greece side with the Soviet Union in Configuration 2 is that they both have a war history with Germany, but no serious problems with the Soviet Union.

³⁵ The error of placing Poland on the anti-German side occurred because Poland disliked the Soviet Union even more than it disliked Germany. This in turn was largely due to the Soviet Union's greater size (national capabilities) in 1936. As discussed below, this error was eliminated by 1939 as Germany mobilized its strength faster than the Soviet Union did. Portugal, which was actually neutral, was incorrectly placed on the German side because that side was more favourable for Portugal's Catholic religious propensity.

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³⁵ The only change in the factors that went into the propensities from 1936 to 1939 was that Romania switched from a democratic government to an authoritarian government in 1938. Thus the changes in the landscape from 1936 to 1939 were almost entirely due to changes in the national capabilities of the various countries as they mobilized for war.

³⁸ Note that six of these countries were not destined to enter the war on either side for another year or two. In 1940 Hungary and Romania allied with Germany, and Denmark and Greece were invaded. In 1941, Yugoslavia and the Soviet Union were invaded.

³⁹ Since there are 65,536 different configurations, and only eighteen of them are off by zero or one country, the probability of a result this good happening by chance is 18/65,536 = 0.00027.

⁴⁰ Altfeld, and de Mesquita, Bueno, ‘Choosing Sides in War’.Google Scholar

⁴¹ Thus mutual membership in the EEC added one point to the propensities of a pair of such countries. Because of limited data availability from the former Eastern bloc countries, a more precise measure of economic interdependence is unavailable. War history was based on the Second World War; Italy was considered to have a war history with no one since it fought on both sides. An additional source for coding ethnic conflicts is Larrabee, Stephen F., ‘Long Memories and Short Fuses, Change and Instability in the Balkans’, International Security, 15 (1990/1991), 58–91.CrossRefGoogle Scholar Size data was available as of 1985. To simplify the calculations Benelux was treated as one country and Spain/Portugal as another.

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⁴⁶ Here is another derivation of the same propensity values. Firms prefer to be aligned with each other to increase the size of their alliance, but they prefer not to align with rivals. For distant rivals, these two considerations counterbalance, making p _ij= 0. For close rivals, the rivalry consideration dominates, makingp _ij = – 1.

⁴⁷ As in the international cases, it was assumed that there would be at most two groupings.

⁴⁸ There are 2⁷= 128 ways of assigning the remaining seven firms to two alliances. Of these, one is completely correct and seven are off by one firm. Therefore, the probability of getting six or more of seven right by chance is (7 + 1)/128 = 1/16.

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