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page 1679 note 1 For a comparative instance of the word “κράτος” but without the prefix “εὔ,” see V, 105.2.
page 1680 note 2 Here compare the Athenians' typification of the Melians relative weakness (V, 97) with Thucydides' description of Mytilene as a relatively weakly controlled allied polis (III, 36.2). Neither Cleon (III, 39.2) nor the Athenians at Melos (V, 94 and 95) can consider independence or neutrality of the relatively weak polis in contention. Is this because of the relative weakness of the Melians and the Mytilenians or because of the relative weakness of the Athenians at Melos and of Cleon? I contend the former is only a threat because of the latter.
page 1680 note 3 It is also interesting to compare the reversals of conventional meanings in the Melian dialogue (e.g., V, 111.3 with the word “αἴσχρός”) with Thucydides' discussion of the conditions for and the process of perversion of normal language meanings (III, 82.4).
page 1680 note 1 Nor do the Athenians either at Sparta or Melos assert that “justice is only the advantage of the stronger.” (See I, 76.3 and V, 89, and cf. V, 105.4.) As for the latter, it is not absolutely clear that in their view, “the slaughter at Melos is required once the Melians refuse to submit,” that they would not, had the decision been theirs, rather have imposed banishment, for example. And their original terms, as they indicate in passing (V, 111.4), were moderate, so that one cannot fairly say that “there is no gentleness to their foreign policy.”
page 1681 note 1 It should be recognized that the Durbin-Watson test (DW), which Gray appears to have employed, is not valid for this case, primarily for reasons related to the distortion of the residuals, and detailed in the text above. In addition, however, DW tests only for the statistical significance of the coefficient of a first order auto-regressive process, which need not be the appropriate serial dependence model. Thus, it is generally preferable to examine the correlograms of the residuals in order to ascertain the model generating the serial correlation, as opposed to relying upon DW alone. Hibbs, Douglas A. Jr.,, “Problems of Statistical Estimation and Causal Inference in Time Series Regression Models,” in Costner, H. L., ed., Sociological Methodology 1973–74 (San Francisco: Jossey-Bass, 1974)Google Scholar, is an excellent reference on this point and related complexities.
page 1681 note 2 For example, if
A t = bA t-1, + c + e t, (1)
while e t is a first order auto-regressive process
e t, = ρe t-1 + v t, (2)
then, substituting in (1)
A t, = bA t-1, + c + ρe t-1, + v t, (3)
But, since A t-1 is a linear function of e t-1 and e t, is a linear function of e t-1, then A t-1, is correlated with the disturbance term e t. Similar results can be proved for et generated by alternate disturbance structures, as long as e t, is auto-correlated, (i.e., a function of e t-1).
page 1682 note 3 Indeed, Gray's Figure 1 strongly suggests thatc auto-correlation is present.
page 1682 note 4 More complete discussion of these complexities, plus an appended bibliography, can be found in Raisa Deber and Nazli Choucri, Appendix B (“Note on Methodology,”) and Raisa Deber, Appendix C (“The Results of an Experiment,”) in Choucri, Nazli and North, Robert, Nations in Conflict: Population, Expansion, and War (San Francisco: W. H. Freeman, 1974)Google Scholar.
page 1682 note 1 Christ, Carl F., Econometric Models and Methods (New York: John Wiley & Sons, 1966)Google Scholar.
page 1682 note 2 Gray, Virginia, “Innovation in the States: A Diffusion Study,” American Political Science Review, 67 (December, 1973), 1174–1185CrossRefGoogle Scholar.
page 1682 note 3 Wonnacott, Ronald J. and Wonnacott, Thomas H., Econometrics (New York: John Wiley & Sons, 1970), pp. 146–147Google Scholar.
page 1682 note 4 Johnston, J., Econometric Methods (New York: McGraw-Hill Book Co., 1972), p. 309Google Scholar.
page 1682 note 5 Ibid., pp. 311–312.
page 1682 note 6 Ibid., pp. 312–313.
page 1682 note 7 Durbin, J., “Testing for Serial Correlation in Leastsquares Regression When Some of the Regressors Are Lagged Dependent Variables,” Econometrica, 38 (May, 1970), 410–421CrossRefGoogle Scholar.
page 1683 note 8 Hibbs, Douglas A. Jr.,, “Problems of Statistical Estimation and Causal Inference in Time Series Regression Models,” in Costner, H. L., ed., Sociological Methodology 1973–74 (San Francisco: Jossey-Bass, 1974)Google Scholar.
page 1683 note 9 In answer to “how large is large?” Theil reports sampling experiments consisting of 20 observations where the true value of the lagged coefficient was underestimated 75% of the time, thus leading to a conservative bias: Theil, Henri, Principles of Econometrics (New York: John Wiley & Sons, 1971), pp. 425–427Google Scholar.
page 1683 note 10 The statement appears in the first edition of Johnston where he is discussing the solutions to multicollinearity: Johnston, J., Econometric Methods (New York: John Wiley & Sons, 1963), p. 207Google Scholar.
page 1683 note 11 For theory see: Coleman, James S., Introduction to Mathematical Sociology (London: Free Press of Glencoe, 1964)Google Scholar, chapter 17; Bartholomew, David J., Stochastic Models for Social Processes (London: John Wiley & Sons, 1967), p. 206Google Scholar.
page 1683 bote 12 Hamblin, Robert L., Jacobsen, R. Brooke, and Miller, Jerry L. L., A Mathematical Theory of Social Change (New York: John Wiley & Sons, 1973), p. 4Google Scholar. The universality of the S-curve is also supported by many studies reported in Rogers, Everett M. and Shoemaker, F. Floyd, Communication of Innovations (New York: The Free Press, 1971), pp. 161–164Google ScholarPubMed.
page 1687 note 1 American Political Science Review, 66 (December, 1973), 1235–1247Google Scholar.
page 1688 note 2 Cf. Buchanan, James M. and Tullock, Gordon, The Calculus of Consent (Ann Arbor: University of Michigan Press, 1962), pp. 126–130CrossRefGoogle Scholar.
page 1688 note 3 Riker, and Brams, , “Paradox of Vote Trading,” p. 1240Google Scholar.
page 1688 note 4 Gordon Tullock, “Entrepreneurial Politics,” Research Monogram #8, Thomas Jefferson Center for Political Economy, University of Virginia, 1964; Tullock, Gordon, “A Simple Algebraic Logrolling Model,” American Economic Review, 60 (June, 1970), 419–426Google Scholar.
page 1689 note 1 “The Paradox of Vote Trading,” American Political Science Review, 67 (December, 1973), 1235–1247CrossRefGoogle Scholar.
page 1689 note 2 Riker and Brams seem first to realize this: “We assume, however, that once a set of trades on particular issues is made, new trades cannot be made on these issues” (p. 1240). Later on, however, they state: “in the next section … we drop even this assumption and show that the paradox persists even with unrestricted trading” (p. 1241).
page 1691 note 3 Bernholz, Peter, “Logrolling, Arrow-Paradox and Decision Rules: A Generalization,” Kyklos (fasc. 1, 1974), 49–62Google Scholar, and the earlier paper by the same author: “Logrolling, Arrow-Paradox and Cyclical Majorities,” Public Choice, 15 (Summer, 1973), 87–95CrossRefGoogle Scholar.
page 1694 note 1 In my opinion, the probabilistic considerations described above clearly demonstrate the extreme weakness of player 1's bargaining position. However, Howard is right in pointing out that the concept of “risk-dominance” as defined in an earlier paper of mine (in Advances in Game Theory, Princeton: Princeton University Press, 1964)Google Scholar is not sensitive enough to bring out this asymmetry in the two players' bargaining positions.
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