# Alliance Portfolio

## “Alliance” Variable Tab in EuGene

The Expected Utility Generation and Data Management Program (EUGene) is designed primarily to generate values for variables pertaining to the so-called Expected Utility Theory of War developed by Bruce Bueno de Mesquita and colleagues (Bueno de Mesquita, 1981, 1985; Bueno de Mesquita and Lalman, 1992). In addition, EUGene serves as a data management tool for creating data sets for use in international relations with the country-year, directed-dyad-year, and directed-dispute-dyad-year as the unit of analysis.

Note: in the “Expected Utility” Variable Tab, Uncertainty, the output will include regional uncertainty as defined by Bueno de Mesquita and Lalman (1992), available in both Tau-b and S versions.

Alliance Type (Available for Dyad-Year and Dispute-Dyad Output Only): Output will contain the COW alliance type. As of version 3 of EUGene, the “Dyadic Alliance File” uses the COW v3.0 alliance data released in December, 2002. Options to use other versions of the data have been removed. The codes for various types of alliance are 1=defense pact, 2=neutrality, 3=entente, 4=no agreement.

Alliance Portfolio – unweighted (Available for Dyad-Year and Dispute-Dyad Output Only): Output variables are the cells of a 4×4 matrix representing the alliance portfolio between the two states, as seen initially in Bueno de Mesquita 1978 and 1980. Two separate matrices are output, one with membership including all states in the relevant region of conflict (corresponding to regional tau), and the second with membership including all states in the system (corresponding to global tau). Cell values are counts of the number of states falling into each combination of alliance types, e.g. variable “rportu11” refers to unweighted portfolio (based on states in relevant region) [1,1], and counts the number of states with whom both ccode1 and ccode2 share defense pacts. Variable “rportu12” then refers to regional portfolio[1,2] (row 1, column 2), and so on. Row and column 2 refers to neutrality pacts, 3 refers to entente agreements, and 4 refers to states where there is no alliance. So “rportu24” is portfolio[2,4], the count of states where ccode1 has neutrality agreements and ccode2 has no alliance. Variables “gportu11” through “gportu44” refer to the unweighted portfolio using all states around the globe. A variable “rportn” (and correspondingly “gportn”) is also output, representing the total number of states counted in the unweighted alliance portfolio table.

Alliance Portfolio – weighted (Available for Dyad-Year and Dispute-Dyad Output Only): Output variables are the cells of two 4×4 matrices representing the alliance portfolio between the two states, but with modifications for the weighted version of S as developed by Signorino and Ritter (1999). Here, cell values represent the sum of COW CINC scores for the states falling into each combination of alliance types, e.g. variable “gportw11” refers to the sum of capabilities falling into weighted portfolio cell [1,1] in the global alliance portfolio version. A variable “dmax” is also output, representing the total sum of all capabilities in the weighted alliance portfolio table.

Tau-b Scores (Available for Dyad-Year and Dispute-Dyad Output Only): Output will include the tau-b between the two states. Both global tau-values (calculated using every state in the system) and regional tau-values (calculated using only states in the relevant region for the dyad) will be reported. In directed dyads, the output will always be from CCode1 to CCode2. In non-directed dyads, EUGene provides the output in both directions.

S Scores (Available for Dyad-Year and Dispute-Dyad Output Only): (See Signorino and Ritter 1999) Output will include the unweighted or weighted S between the two states. Weighted S scores are weighted using system capabilities. Both global S-values (calculated using every state in the system) and regional S-values (calculated using only states in the relevant region for the dyad) will be reported. In directed dyads, the output will always be from CCode1 to CCode2. In non-directed dyads, EUGene provides the output in both directions.

Tau or S with System Leader: Output will include the tau or S between the state in question (country-year unit) or states in question (dyad-year unit) with the system leader, which is Britain up to 1945, and the US from 1946 forward.

Options: User may set whether the tau or S computed with the system leader is based on the alliances of states only involved in the relevant region of the ccode vs. the system leader dyad (regional option), or is based on all states in the international system (global option). For S, the user may specify whether to use the weighted or unweighted S with the system leader.

Source: EUGene documentation, by D. Scott Bennett and Allan C. Stam

## Tau-b Calculation

The Kendall Tau-b correlation calculation performed by EUGene is based on the calculation used in Bueno de Mesquita (1975, 1981). Here, the Kendall tau-b is a rank order correlation for two states’ alliance portfolios. The alliances of each state are combined into a 4 x 4 table where alliances are ranked as 1 (defense pact), 2 (neutrality pact), 3 (entente) and 4 (no alliance). Note that all states in the international system are included, even if they do not engage in any alliance behavior (these states contribute to the “no alliance” cells of the table). This is different from some of the earlier work by Bueno de Mesquita, where states were included for purposes of calculation only if they engaged in at least 1 international alliance. Tau-b is calculated from this 4×4 table, and ranges from -1 to +1, representing totally opposite alliance agreements to complete agreement in the alliances formed. The actual algorithm used to calculate tau-b within EUGene was obtained from Hays, 1981: 603-604.

When generating Taus, EUGENE generates both regional and global taus. The global tau is the tau-b score when all states in the international system are included. The regional tau between states A and B is calculated from the 4 x 4 table with only states in the relevant region of A vs. B are included. Bueno de Mesquita in his calculations uses only the regional taus; that is, tau includes only states in a sub-region. Thus while EUGene calculated global taus, they are for information only, as subsequent calculations such as those for expected utility and risk use the regional conception. Also note that in War and Reason, Bueno de Mesquita and Lalman modify taus of 1.0 to be 0.999 (see p. 291) in expected utility calculations. We make the same modification when we compute utility and equilibria values. However, when just tau scores are selected as an individual output variable, we present the calculated values without this modification.

Tau-b can be computed from 1816-2000 using the COW v3.0 alliance data.

Source: EUGene documentation, by D. Scott Bennett and Allan C. Stam

## S Calculation

The S correlation calculation performed by EUGene is based on the calculation used by Signorino and Ritter (1999). Like the Kendall tau-b, S evaluates the rank order correlation for two states’ alliance portfolios. Unlike tau-b, S also takes into account both the presence and absence of an alliance in the correlation calculation. For example, the fact that a state has identical alliances with some states as well as no alliances with identical sets of other states is accounted for in the S calculation, but not in tau-b. Signorino and Ritter note that while tau-b is an excellent measure of rank order similarity, it has inherent flaws that allow a variety of alliance portfolio tables to have identical tau-b results which impact studies looking beyond rank order similarity.

Like tau-b, EUGene calculates S on both regional and global levels, with the same country inclusion criteria as with the tau-b calculation (see above). In addition, S is calculated in both weighted and unweighted forms, taking into account country capabilities and Signorino and Ritter’s discussions about the differences in weighted and unweighted S values. For use in expected utility calculations, the regional s score is used, and like taus, S scores are modified from 1.0 to 0.999 between states. When s scores are selected as an individual output variable, we present the calculated values without this modification. Also, like tau-b, all states in the international system are included, even if they do not engage in any alliance behavior (these states contribute to the “no alliance” cells of the table). This is different from some of the earlier work by Bueno de Mesquita, where states were included for purposes of calculation only if they engaged in at least 1 international alliance.

Source: EUGene documentation, by D. Scott Bennett and Allan C. Stam

## Alliances and Alliance Patterns variable: Tau-b with system leader (regional subsystem or global system)

## Alliances and Alliance Patterns variable: Weighted or unweighted S with system leader (regional subsystem or global system)

### Further Reading

Curtis Signorino et al., Tau-b or Not Tau-b: Measuring Alliance Portfolio Similarity

Leeds, Brett, et al., “Alliance Treaty Obligations and Provisions, 1815-1944.” International Interactions 28.3 (2002): 237-260.

Gibler, Douglas M. 2009. International military alliances, 1648-2008. CQ Press.

Bueno de Mesquita (1975); Bueno de Mesquita. (1981)

Lemke and Reed (1998).