(Page 40 of 40) - Needing an Arm to Twist: Conquest vs. Commerce in Asymmetric Dyads, the Role of Institutions authored by Leo, Blanken. and Gartner, Scott.

End Notes

The discussion treats “large W” and “small W” states as theoretically derived monothetic types, rather than

empirically derived modal or “typical” values. In reality, the size of the coalitions across states is a continuum, but
for conceptual clarity only two extreme values modeled. See Bailey, Kenneth D. 1973. Monothetic and Polythetic
Typologies and their Relation to Conceptualization, Measurement and Scaling. American Sociological Review 38
(1):18-33..

Analytic uncertainty (or “model uncertainty”) involves uncertainty about some state of the world distributed by

nature (which may be modeled as a disinterested player). Conceptually, this may include (as it does in this case)
uncertainty regarding one’s own payoffs. At face value, this may seem problematic to the basic assumption of
rationality. Aumann and Brandenburger argue that “knowledge of one’s own payoff function may be considered
tautologous” Aumann, Robert J., and Adam Brandenburger. 1995. Epistemic Conditions for Nash Equilibrium.
Econometrica 63 (5):1161-1180. To clear up this seeming confusion, however, analytic uncertainty does not include
uncertainty regarding what one prefers, it merely involves uncertainty as to how strategies map to payoffs. For
example, if one decides to carry an umbrella to work, one receives a positive payoff if it is raining by staying dry,
but a negative one if it is not raining (for the annoyance and extra weight of the umbrella). Mathematically this is
trivial; the uncertainty regarding an act of nature is merely folded into the payoffs as a lottery (as is done in these
models). It is theoretically valuable to make this uncertainty explicit, however, to represent the type of uncertainty
actors may face when they are unclear as to which outcomes are associated with which payoffs (similar to what
Goldstein and Keohane refer to as “roadmap beliefs” Goldstein, Judith, and Robert Keohane, eds. 1993. Ideas and
Foreign Policy: Beliefs, Institutions, and Political Change. Ithaca: Cornell University Press.) Actors know what
they prefer (chocolate over vanilla ice cream) but their choice is conditioned on a probability distribution as to
which flavor is in which unmarked tub.

iii

As per the model’s assumptions, b being greater than c is the ex ante belief of the state (the additional revenue of

increased economic activity outweighs the fiscal drag of the colony). Whether this, ex post, turned out to be true for
the European empires or not is an empirical question which is still open to debate. See Kennedy, Paul. 1989. The
Costs and Benefits of British Imperialism, 1846-1914. Past and Present 125:186-192, O'Brien, Patrick K. 1988. The
Costs and Benefits of British Imperialism 1846-1914. Past and Present 120:163-200, O'Brien, Patrick K. 1989. The
Costs and Benefits of British Imperialism, 1846-1914: Reply. Past and Present 125:192-199, Offer, Avner. 1999.
Costs and Benefits, Prosperity and Security, 1870-1914. In Oxford History of the British Empire: The Nineteenth
Century, edited by A. Porter. New York: Oxford University Press.

That the mutual payoff is zero derives from the following logic. Assume the result of a militarized conflict

between the actors is a flat distribution lottery for each player. The maximum benefit available in the lottery is c
(winning the right to take the colony on the cheapest possible victory over the rival) and extends out to negative c
(the costliest rival-rival conflict). Because we assert that the actors will only expend as many resources in the
conflict as they would through a victory, the paradox of all pay auctions is assumed away Dixit, Avinash, and Susan
Skeath. 2004. Games of Strategy. 2nd ed. New York: W.W. Norton..

In terms of the spatial range, the case of Africa covers the continent with the excepted territories of South Africa

and Egypt, which are excluded due to the problem of over determination and the difficulty in sorting out the relative
independent effects. The Cape of Good Hope occupied a strategic position along the primary route to the Indian
Ocean spice trade. The location was originally taken and held for its strategic value; as The Imperialism Game is a
sufficient conditions argument, this issue of equifinality does not hamper the predictive success of the theory. See
Saunders, Christopher, and Iain R. Smith. 1999. Southern Africa, 1795-1910. In Oxford History of the British
Empire: The Nineteenth Century, edited by A. Porter. New York: Oxford University Press. Egypt is likewise
excluded due to the Suez Canal. See Clayton, G.D. 1971. Britain and the Eastern Question: Missolonghi to
Gallipoli. London: University of London Press.

Another work rigorously tests this model in the cases of Q’ing Dynasty China and tropical Africa. See Blanken,

Leo. 2005. No Arm to Twist? Local Institutions and Formal Imperial Expansion. Paper read at Annual Meeting of
the Western Political Science Association.