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that a nationalist would be elected in Russia is one event and the probability that such a
nationalist would disavow arms control agreements is an independent event.
Critics often considered these probabilities only in the conditional sense: given a
nationalist, what is the probability of Russia disavowing an arms control treaty? In formal
terms, the probability of Russia abrogating arms control agreements given nationalist
government could be represented as p(a|H), with a denoting the abrogation and H
denoting the condition, a nationalist government. We can stipulate the probability as
p(a|H)= .75. That is, there is a 75% chance that a nationalist government would abrogate
an arm control treaty. But the probability of the condition, a nationalist government
coming to power, needs to be estimated. Assume that the probability that a nationalist
government comes to power in response to NATO expansion is .60, or p(H)= .60. What
worried critics was the conjunction of these events: a nationalist government and the
abrogation of arms control agreements by such a government. The probability of the
conjunction, or p(a and H), would be p(a|H)*p(H).
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The product would be .45. In other
words, given NATO expansion, the likelihood of the adverse outcome was only about 1
in 2.
NATO backers made similar claims as NATO critics. Without NATO expansion, Central
European states would arm more with some probability, the critics argued, and such
arming would trigger a conflict with some probability. Backers focused on the probability
of conflict given the arming, not the fact that the conjunction of arming and conflict
would be less likely than either event. Since international politics is not an experimental
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For a brief summary of these principles, see Hastie and Dawes, p.343-44.
Convention