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Review Article: Mathematical Political Theory

Published online by Cambridge University Press:  27 January 2009

Michael Taylor
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This paper attempts to survey the present state of what I have called ‘mathematical political theory’. In a strict sense of theory’, this happens to be roughly coextensive with ‘political theory’, but the addition of the word ‘mathematical’ seems necessary (for the time being) to avoid confusion with the other usages of ‘political theory’: the exegesis of the outstanding political philosophers of the past is certainly not political theory; nor is most of what is now called ‘empirical political theory’. However, the scope of the survey is widened in a few places to include some related studies which, although they are not mathematical, are nevertheless ‘analytical’.

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Review Article
Information
British Journal of Political Science , Volume 1 , Issue 3 , July 1971 , pp. 339 - 382
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Copyright © Cambridge University Press 1971

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References

BIBLIOGRAPHY

Abelson, Robert P. (1963), ‘A “Derivation” of Richardsons Equations’. Journal of Conflict Resolution, VII, 13–15.CrossRefGoogle Scholar
Armstrong, W. E. (1951), ‘Utility and the Theory of Welfare’, Oxford Economic Papers, New series, III, 259–71.CrossRefGoogle Scholar
Arrow, Kenneth J. (1950), ‘A Difficulty in the Concept of Social Welfare’. The Journal of Political Economy, LVIII, 328–46.CrossRefGoogle Scholar
Arrow, Kenneth J. (1951, 1963), Social Choice and Individual Values. New York: John Wiley. First Edition, 1951; Second Edition, 1963.Google Scholar
Arrow, Kenneth J. (1967), ‘Values and Collective Decision-Making’. Chapter 10 in Laslett, P. and Runciman, W. G., eds., Philosophy, Politics and Society, Third Series. Oxford: Basil Blackwell.Google Scholar
Arrow, Kenneth J.(1969), ‘Tullock and an Existence Theorem’. Public Choice, VI, 105–11.CrossRefGoogle Scholar
Ashenfelter, Orley, and Johnson, George E. (1969), ‘Bargaining Theory, Trade Unions, and Industrial Strike Activity’. American Economic Review, LIX, 35–49.Google Scholar
Aumann, Robert J. (1967), ‘A Survey of Cooperative Games Without Side Payments’. Chapter I in Shubik, M., ed., Essays in Mathematical Economics in Honour of Oskar Morgenstern. Princeton, N.J.: Princeton University Press.Google Scholar
Aumann, Robert J., and Maschler, Michael (1964), ‘The Bargaining Set for Cooperative Games’. In Dresher, M. et al. , eds., Advances in Game Theory (Annals of Mathematics Studies, No. 52). Princeton, N.J.: Princeton University Press, pp. 443–76.CrossRefGoogle Scholar
Axelrod, Robert (1970), Conflict of Interest. Chicago: Markham.Google Scholar
Bailey, N. T. J. (1957), The Mathematical Theory of Epidemics. London: Griffin.Google Scholar
Barry, Brian (1965), Political Argument. London: Routledge and Kegan Paul.Google Scholar
Barry, Brian (1970), Sociologists, Economists and Democracy. London: Collier-Macmillan.Google Scholar
Bartholomew, David J. (1967), Stochastic Models for Social Processes. London and New York: John Wiley.Google Scholar
Bartos, Otomar J. (1965), ‘A Model of Negotiation and Some Experimental Evidence’. In Massarik, F. and Ratoosh, P., eds., Mathematical Explorations in the Behavioral Sciences. Homewood, III.: Richard D. Irwin and the Dorsey Press, pp. 140–58.Google Scholar
Bartos, Otomar J. (1967), Simple Models of Group Behavior. New York: Columbia University Press.Google Scholar
Baumol, William J. (1952, 1965), Welfare Economics and the Theory of the State. London: G. Bell & Sons. First Edition, 1952; Second Edition, 1965.Google Scholar
Bishop, R. L. (1964), ‘A Zuethen-Hicks Theory of Bargaining’. Econometrica, XXXII, 410–17.CrossRefGoogle Scholar
Black, Duncan (1948), ‘The Decisions of a Committee Using a Special Majority’. Econometrica, XVI, 245–61.CrossRefGoogle Scholar
Black, Duncan (1958), The Theory of Committees and Elections. Cambridge: The University Press.Google Scholar
Black, Duncan, and Newing, R. A. (1951), Committee Decisions with Complementary Valuation. London: William Hodge.Google Scholar
Boulding, Kenneth E. (1962), Conflict and Defense: A General Theory. New York: Harper and Brothers.Google Scholar
Blau, Julian H. (1957), ‘The Existence of Social Welfare Functions’. Econometrica, XXV, 302–13.CrossRefGoogle Scholar
Braithwaite, R. B. (1955), Theory of Games as a Tool for the Moral Philosopher. Cambridge: The University Press.Google Scholar
Braybrook, David, and Lindblom, Charles (1964), A Strategy of Decision. New York: The Free Press.Google Scholar
Buchanan, James M. (1954), ‘Social Choice, Democracy and Free Markets’. Journal of Political Economy, LXII, 114–23.CrossRefGoogle Scholar
Buchanan, James M., and Tullock, Gordon (1962), The Calculus of Consent. Ann Arbor: University of Michigan Press.Google Scholar
Caplow, Theodore (1956), ‘A Theory of Coalitions in the Triad’. American Sociological Review, XXI, 489–93.CrossRefGoogle Scholar
Caplow, Theodore (1968), Two Against One: Coalitions in Triads. Englewood Cliffs, NJ.: Prentice-Hall.Google Scholar
Caspary, William R (1967), ‘Richardson's Model of Arms Races: Description, Critique, and an Alternative Model’. International Studies Quarterly, XI, 63–88.CrossRefGoogle Scholar
Chase, P. E. (1969), ‘Feedback Control Theory and Arms Races’. General Systems, XIV, 137–49.Google Scholar
Coddington, Alan (1968), Theories of the Bargaining Process. London: George Allen and Unwin.Google Scholar
Coleman, James S. (1966a), ‘Foundations for a Theory of Collective Decisions’. American Journal of Sociology, LXXI, 615–27.CrossRefGoogle Scholar
Coleman, James S. (1966b), ‘The Possibility of a Social Welfare Function’. American Economic Review, LXI, 1105–22.Google Scholar
Coleman, James S. (1971), ‘Control of Collectivities and the Power of a Collectivity to Act’. In Liebermann, B., ed., Social Choice (Proceedings of a Conference at the University of Pittsburgh, 09 1968). New York: Gordon and Breach.Google Scholar
Condorcet, Marquis de (1785), ‘Essai sur l'Application de I’Analyse à la Probabilité des Décisions Rendues à la Pluralité des Voix’. ParisGoogle Scholar
Contini, Bruno (1967), ‘Threats and Organisational Design’. Behavioral Science, XII, 453–62.CrossRefGoogle Scholar
Contini, Bruno, and Zionts, Stanley (1968), ‘Restricted Bargaining with Multiple Objectives’. Econometrica, XXXVI, 397–414.CrossRefGoogle Scholar
Converse, Phillip E. (1966), ‘The Problem of Party Distances in Models of Voting Change’. In Jennings, M. K. and Zeigler, H., eds., The Electoral Process. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Cross, J. G. (1965), ‘A Theory of the Bargaining Process’. American Economic Review, LVI, 522–30.Google Scholar
Cross, J. G. (1967), ‘Some Theoretic Characterisations of Economic and Political Coalitions’. Journal of Conflict Resolution, XI, 184–95.CrossRefGoogle Scholar
Cross, J. G. (1969), The Economics of Bargaining. New York: Basic Books.Google Scholar
Curtis, Richard M. (forthcoming), ‘Decision Rules and Collective Values in Constitutional Choice’. In Niemi, R. and Weisberg, H., eds., Probability Models of Voting Bodies. Columbus, Ohio: Charles E. Merrill.Google Scholar
Dahl, Robert A. (1956), A Preface to Democratic Theory. Chicago: University of Chicago Press.Google Scholar
Davis, John M. (1958), ‘The Transitivity of Preferences’. Behavioral Science, III, 26–33.Google Scholar
Davis, Otto M., Dempster, M. A. H., and Wildavsky, Aaron (1966a), ‘On the Process of Budgeting: An Empirical Study of Congressional Appropriation’. In Tullock, G., ed., Papers on Non-Market Decision Making. Charlottesville: The Thomas Jefferson Center for Political Economy, University of Virginia, pp. 63–132.Google Scholar
Davis, Otto M., Dempster, M. A. H., and Wildavsky, Aaron (1966b), ‘A Theory of the Budgetary Process.’ American Political Science Review, LX, 529–47.CrossRefGoogle Scholar
Davis, Otto M., and Hinich, Melvin (1966.), ‘A Mathematical Model of Policy Formation in a Democratic Society’. In Bernd, J. L., ed., Mathematical Applications in Political Science, II. Dallas: Southern Methodist University Press, pp. 175–208.Google Scholar
Davis, Otto M., and Hinich, Melvin (1967), ‘Some Results Related to a Mathematical: Model of Policy Formation in a Democratic Society’. In Bernd, J. L., ed., Mathematical Applications in Political Science, III. Charlottesville: University Press of Virginia, pp. 14–38.Google Scholar
Davis, Otto M., and Hinich, Melvin (1968), ‘On the Power and Importance of the Mean Preference in a Mathematical Model of Democratic Choice’. Public Choice, v, 59–72.CrossRefGoogle Scholar
Davis, Otto M., Hinich, Melvin, and Ordeshook, Peter C. (1970), ‘An Expository Development of a Mathematical Model of the Electoral Process’. American Political Science Review, LXIV, 426–48.CrossRefGoogle Scholar
Davis, Morton, and Maschler, Michael (1965), ‘The Kernel of a Cooperative Game’. Naval Research Logistics Quarterly, XII, 223–59.CrossRefGoogle Scholar
Davis, Morton, and Maschler, Michael (1967), ‘Existence of Stable Configurations for Cooperative Games’. Chapter 3 in Shubik, M., ed., Studies in Mathematical Economics; Essays in Honour of Oskar Morgenstern. Princeton, N.J.: Princeton University Press.Google Scholar
Demeyer, Frank, and Plott, Charles R. (1970), ‘The Probability of a Cyclical Majority’. Econometrica, XXXVIII, 345–54.CrossRefGoogle Scholar
Dolanský, Ladislav (1964), ‘Present State of the Lanchester Theory of Combat’. Operations Research, XII, 344–58.CrossRefGoogle Scholar
Downs, Anthony (1957), An Economic Theory of Democracy. New York: Harper and Brothers.Google Scholar
Dresher, Melvin (1961), Games of Strategy: Theory and Applications. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Dummett, Michael, and Farquharson, Robin (1961), ‘Stability in Voting’. Econometrica, XXIX, 33–43.CrossRefGoogle Scholar
Edwards, Ward (1954), ‘The Theory of Decision Making’. Psychological Bulletin, LI, 380–417. Reprinted in Edwards, W. and Tversky, A., eds., Decision Making. Harmondsworth, Middlesex: Penguin Books (1967).Google Scholar
Ward, Edwards (1961), ‘Behavioral Decision Theory’. Annual Review of Psychology, XII, 473–98. Reprinted in Edwards, W. and Tversky, A., eds., Decision Making. Harmondsworth, Middlesex: Penguin Books (1967).Google Scholar
Farquharson, Robin (1956), ‘Straightforwardness in Voting Procedures’. Oxford Economic Papers, New Series, VIII, 80–9.CrossRefGoogle Scholar
Farquharson, Robin (1969), Theory of Voting. New Haven: Yale University Press; Oxford: Basil Blackwell.Google Scholar
Fishburn, Peter C. (1970a), ‘The Irrationality of Intransitivity’. Behavioral Science, xv, 119–23.CrossRefGoogle Scholar
Fishburn, Peter C. (1970b), ‘Intransitive Individual Indifference and Transitive Majorities’. Econometrica, XXXVIII, 482–9.CrossRefGoogle Scholar
Fishburn, Peter C. (1970c), ‘Arrow's Impossibility Theorem: Concise Proof and Infinite. Voters’. Journal of Economic Theory, 11, 103–6.CrossRefGoogle Scholar
Fishburn, Peter C. (1970d), ‘Intransitive Indifference in Preference Theory: A Survey’. Operations Research, XVIII, 207–28.CrossRefGoogle Scholar
Fishburn, Peter C. (1970e), Utility Theory for Decision Making. New York: John Wiley.CrossRefGoogle Scholar
Fishburn, Peter C. (1971a), ‘The Theory of Representative Majority Decision’. Econometrica, XXXIX.Google Scholar
Fishburn, Peter C. (1971b), ‘Comments on Hansson's “Group Preferences"’. Econometrica, XXXIX.Google Scholar
Foldes, L. (1964), ‘A Determinate Model of Bilateral Monopoly’. Economica, CXXII, 117–31.CrossRefGoogle Scholar
Fouraker, Lawrence E. and Siegel, Sidney (1963), Bargaining Behavior. New York: McGraw-Hill.Google Scholar
Gamson, William A. (1961), ‘A Theory of Coalition Formation’. American Sociological Review, XXVI, 273–82.Google Scholar
Goodhart, C. A. E., and Bhansali, R. J. (1970), ‘Political Economy’. Political Studies, XVIII, 43–106.CrossRefGoogle Scholar
Goodman, L. A. and Markowitz, Harry (1952), ‘Social Welfare Functions Based on Individual Rankings’. American Journal of Sociology, LVIII, 257–62.CrossRefGoogle Scholar
Guilbaud, G. Th. (1952), ‘Les Théories de I'Intérêt Général et le Problème Logique de I'Aggregation’. Economique Apliquee, v, 501–84. An English translation of parts of this appears in P. F.Lazarsfeld and N. W.Henry, eds.,Readings in Mathematical Social Science. Cambridge, Mass.: The M.I.T. Press (1966), pp. 262–307.Google Scholar
Hansson, Bengt (1969), ‘Group Preferences’. Econometrica, XXXVII, 50–4.CrossRefGoogle Scholar
Harsanyi, John C. (1955), ‘Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility’. Journal of Political Economy, LXIII, 309–21.Google Scholar
Harsanyi, John C. (1956), ‘Approaches to the Bargaining Problem before and after the Theory of Games: A Critical Discussion of Zeuthen's, Hicks’, and Nash's Theories’. Econometrica, XXIV, 144–57.Google Scholar
Harsanyi, John C. (1959), ‘A Bargaining Model for the Cooperative n-Person Game’. In Luce, R. D. and Tucker, A. W., eds., Contributions to the Theory of Games, IV (Annals of Mathematics Studies, No. 40). Princeton, N.J.: Princeton University Press, pp. 325–56.Google Scholar
Harsanyi, John C. (1962a), ‘Bargaining in Ignorance of the Opponent's Utility Function’. Journal of Conflict Resolution, VI, 29–38.CrossRefGoogle Scholar
Harsanyi, John C. (1962b), ‘Models for the Analysis of Balance of Power in Society’. In Nagel, E., Suppes, P. and Tarski, A., eds., Logic, Methodology, and the Philosophy of Science. Stanford, Calif.: Stanford University Press, pp. 442–62.Google Scholar
Harsanyi, John C. (1966), ‘A Bargaining Model for Social Status in Informal Groups and Formal Organisations’. Behavioral Science, XI, 357–69.CrossRefGoogle Scholar
Harsanyi, John C. (1967a), ‘Games with Incomplete Information Played by “Bayesian” Players. Part I: The Basic Model’. Management Science, XIV, 159–82.CrossRefGoogle Scholar
Harsanyi, John C. (1967b), ‘Games with Incomplete Information Played by “Bayesian” Players. Part II: Bayesian Equilibrium Points’. Management Science, XIV, 320–34.Google Scholar
Harsanyi, John C. (1968), ‘Games with Incomplete Information Played by “Bayesian” Players. Part III: The Basic Probability Distribution of the Game’. Management Science, XIV, 486–502.CrossRefGoogle Scholar
Harsanyi, John C. (1969), ‘Rational-Choice Models of Political Behavior vs. Functionalist and Conformist Theories’. World Politics, XXII, 513–38.CrossRefGoogle Scholar
Haywood, O. G. (1954), ‘Military Decisions and Game Theory’. Journal of the Operations Society of America, XI, 365–85.CrossRefGoogle Scholar
Hildreth, Clifford (1953), ‘Alternative Conditions for Social Orderings’. Econometrica, XXI, 81–94.CrossRefGoogle Scholar
Hinich, Melvin, and Ordeshook, Peter C. (1969), ‘Abstentions and Equilibrium in the Electoral Process’. Public Choice, VII, 81–106.CrossRefGoogle Scholar
Hinich, Melvin, and Ordeshook, Peter C. (1970), ‘Plurality Maximisation vs. Vote Maximisation: A Spatial Analysis with Variable Participation’. American Political Science Review, LXIV, 772–91.CrossRefGoogle Scholar
Hinich, Melvin, Ledyard, John O., and Ordeshook, Peter C. (1970), ‘A Theory of Electoral Equilibrium: A Spatial Analysis Based on the Theory of Games’. Unpublished manuscript, School of Urban and Public Affairs, Carnegie-Mellon University.Google Scholar
Howard, Nigel (1966a), ‘The Theory of Meta-Games’. General Systems, XI, 167–86.Google Scholar
Howard, Nigel (1966b), ‘The Mathematics of Meta-Games’. General Systems, XI, 187–200.Google Scholar
Howard, Nigel (1970), ‘Some Developments in the Theory and Application of MetaGames’. General Systems, xv, 205–31.Google Scholar
Inada, Ken-Ichi (1955), ‘Alternative Incompatible Conditions for a Social Welfare Function’. Econometrica, XXIII, 396–9.CrossRefGoogle Scholar
Inada, Ken-Ichi (1964), ‘A Note on the Simple Majority Decision Rule’. Econometrica, XXXII, 525–31.CrossRefGoogle Scholar
Inada, Ken-Ichi (1969), ‘The Simple Majority Decision Rule’. Econometrica, XXXVII, 490–506.CrossRefGoogle Scholar
Inada, Ken-Ichi (1970), ‘Majority Rule and Rationality’. Journal of Economic Theory, II, 27–40.CrossRefGoogle Scholar
Intriligator, Michael D. (1964), ‘Some Simple Models of Arms Races’. General Systems, IX, 143–7.Google Scholar
Intriligator, Michael D. (1967), ‘Strategy in a Missile War: Targets and Rates of Fire’. Security Studies Project, University of California, Los Angeles.Google Scholar
Intriligator, Michael D. (1968), ‘Arms Races and War Initiation; the Effect of Strategic Choices’. Unpublished manuscript, Department of Economics, University of California, Los Angeles.Google Scholar
Isaacs, Rufus (1965), Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimisation. New York: John Wiley.Google Scholar
Kemp, M. C. (1953–1954), ‘Arrow's General Possibility Theorem’. Review of Economic Studies, XXI, 240–3.CrossRefGoogle Scholar
Kramer, Gerald H. (1966), ‘A Decision Theoretic Analysis of a Problem in Political Campaigning’. In Bernd, J. L., ed., Mathematical Applications in Political Science, II. Dallas: Southern Methodist University Press, pp. 137–60.Google Scholar
Kramer, Gerald H. (1969), ‘On a Class of Equilibrium Conditions for Majority Rule’. Cowles Foundation Discussion Paper No. 284, Yale University.Google Scholar
Kramer, Gerald H. (1971), ‘An Empirical Analysis of Some Aggregative Hypotheses about U.S. Voting Behavior, 1896–1966’. American Political Science Review, LXV, 131–34.CrossRefGoogle Scholar
Kuhn, Harold W. (1967), ‘On Games of Fair Division’. Chapter 2 in Shubik, M., ed., Essays in Mathematical Economics in Honour of Oskar Morgenstern. Princeton, N.J.Princeton University Press.Google Scholar
Lanchester, F. W. (1916), Aircraft in Warfare: The Dawn of the Fourth Arm. London: Constable.Google Scholar
Leiserson, Michael (1966), ‘Coalitions in Polities’. Ph.D. Dissertation. New Haven: Yale University.Google Scholar
Leiserson, Michael (1968), ‘Factions and Coalitions in One-Party Japan: An Interpretation Based on the Theory of Games’. American Political Science Review, LXII, 770–87.CrossRefGoogle Scholar
Leiserson, Michael (1970a), ‘Power and Ideology in Coalition Behavior: An Experimental Study’. In Groenings, S., Kelley, E. W., and Leiserson, M., eds., The Study of Coalition Behavior. New York: Holt, Rinehart and Winston.Google Scholar
Leiserson, Michael (1970b), ‘Game Theory and the Study of Coalition Behavior’. In Groenings, S., Kelley, E. W., and Leiserson, M., eds., The Study of Coalition Behavior. New York: Holt, Rinehart and Winston.Google Scholar
Leiserson, Michael (1970c), ‘Coalition Government in Japan’. In Groenings, S., Kelley, E. W., and Leiserson, M., eds., The Study of Coalition Behavior. New York: Holt, Rinehart and Winston.Google Scholar
Luce, R. Duncan, and Raiffa, Howard (1957), Games and Decisions. New York: John Wiley.Google Scholar
Luce, R. Duncan, and Rogow, Arnold A. (1956), “A Game Theoretic Analysis of Congressional Power Distributions for a Stable Two-Party System’. Behavioral Science, I. 83–95.Google Scholar
MacCrimmon, K. R. (1968), Decision Making Among Multi-Attribute Alternatives. Santa Monica, Calif.: The RAND Corporation, RM 4823.Google Scholar
Mann, Irwin, and Shapley, L. S. (1960, 1962), ‘Values of Large Games IV: Evaluating the Electoral College by Monte Carlo Techniques’. Santa Monica, Calif.: The RAND Corporation RM 2651 (1960) and RM 3158 (1962). Excerpts reprinted as ‘The a Priori Voting Strength of the Electoral College’. Chapter 10 in M. Shubik, ed., Game Theory and Related Approaches to Social Behavior. New York: John Wiley (1964).Google Scholar
May, Kenneth O. (1952), ‘A Set of Independent, Necessary and Sufficient Conditions for Simple Majority Decision’. Econometrica, XX, 680–4.CrossRefGoogle Scholar
May, Kenneth O. (1953), ‘A Note on the Complete Independence of the Conditions for Simple Majority Decision’. Econometrica, XXI, 172–3.CrossRefGoogle Scholar
May, Kenneth O. (1954), ‘Intransitivity, Utility, and the Aggregation of Preference Patterns’. Econometrica, XXII, 1–13.CrossRefGoogle Scholar
Maschler, Michael (1963), ‘n-Person Games with only 1, n-I, and n-Person Permissible Coalitions’. Journal of Mathematical Analysis and Applications, VI, 230–56.CrossRefGoogle Scholar
Maschler, Michael (1965), Playing an n-Person Game: an Experiment. Princeton, N.J.: Econometric Research Program RM 28, Princeton University.Google Scholar
Maschler, Michael, and Peleg, B. (1966), ‘A Characterization, Existence Proof and Dimension Bounds for the Kernel of a Game: Applications to the Study of Simple Games’. Pacific Journal of Mathematics, XVIII, 289–328.CrossRefGoogle Scholar
Mathematica studies for the U.S. Arms Control and Disarmament Agency: (a) Applications of Statistical Methodology to Arms Control. Contract No. ACDA/ST-3 (1963). (b) Development of Utility Theory for Arms Control and Disarmanent. Contract No. ACD A/ST-80 (1966). (c) Models of Gradual Reduction of Arms. Contract No. ACDA/ST-116 (1967). Princeton, N.J.Google Scholar
McGuire, Martin C. (1965), Secrecy and the Arms Race. Cambridge, Mass.: Harvard University Press.Google Scholar
Murakami, Yasusuke (1966), ‘Formal Structure of Majority Decision’. Econometrica, XXXIV, 709–18.CrossRefGoogle Scholar
Murakami, Yasusuke (1968), Logic and Social Choice. London: Routledge and Kegan Paul; New York: Dover.Google Scholar
Musgrave, Richard A. (1959), The Theory of Public Finance. New York: McGraw-Hill.Google Scholar
Nash, John F. (1950), ‘The Bargaining Problem’. Econometrica, XVIII, 155–62.CrossRefGoogle Scholar
Nash, John F. (1951), ‘Non-Cooperative Games’. Annals of Mathematics, LIV, 286–95.Google Scholar
Nash, John F. (1953), ‘Two-Person Cooperative Games’. Econometrica, XXI, 128–40.CrossRefGoogle Scholar
Nicholson, Michael (1965), ‘Conditions for the “Voting Paradox0” in Committee Decision’. Metroeconomica, XLII, 29–44.CrossRefGoogle Scholar
Nicholson, Michael (1967a), ‘The Resolution of Conflict.’ Journal of the Royal Statistical Society, Series A, cxxx, 529–40.CrossRefGoogle Scholar
Nicholson, Michael (1967b), ‘Tariff Wars and a Model of Conflict’. Journal of Peace Research, 1, 26–38.CrossRefGoogle Scholar
Niemi, Richard G. (1969), ‘Majority Decision-Making with Partial Unidimensionality’. American Political Science Review, LXIII, 488–97.Google Scholar
Olson, Mancur (1965), The Logic of Collective Action. Cambridge, Mass.: Harvard University Press.CrossRefGoogle Scholar
Olson, Mancur, and Zeckhauser, Richard (1966), ‘An Economic Theory of Alliances’. Review of Economics and Statistics, XXXXVIII, 266–79.CrossRefGoogle Scholar
Pattanaik, Prasanta K. (1970a), ‘Sufficient Conditions for the Existence of a Choice Set Under Majority Rule’. Econometrica, XXXVIII 165–70.CrossRefGoogle Scholar
Pattanaik, Prasanta K. (1970b), ‘On Social Choice with Quasitransitive Individual Preferences’. Journal of Economic Theory, II, 267–75.CrossRefGoogle Scholar
Pattanaik, Prasanta K. (1971), Aspects of the Theory of Voting and Social Choice. Cambridge: The University Press.Google Scholar
Peleg, Bezalel (1967), ‘Existence Theorem for the Bargaining Set M1(1). Chapter 4 in Shubik, M., ed., Studies in Mathematical Ecpnmics: Essays Honour of Oskar Morgenstern. Princeton, N.J.: Princeton University Press.Google Scholar
Pen, Jan (1952) ‘A General Theory of Bargaining’. American Economic Review, XLII 24–42.Google Scholar
Plott, Charles R. (1967), ‘A Notion of Equilibrium and its Possibility under Majority Rule’. American Economic Review, LVII, 788–806.Google Scholar
Plott, Charles R (1971), ‘Some Recent Results in the Theory of Voting’. In Intriligator, M., ed., Frontiers of Quantitative Economics. Amsterdam: North Holland Publishing Company.Google Scholar
Rae, Douglas W. (1969), ‘Decision-Rules and Individual Values in Collective Choice’. American Political Science Review, LXIII, 40–56.CrossRefGoogle Scholar
Rae, Douglas W (1971), ‘Decisiveness in Election Outcomes’. In Liebermann, B., ed., Social Choice (Proceedings of a Conference at the University of Pittsburgh, 09 1968). New York: Gordon and Breach.Google Scholar
Rae, Douglas W., and Taylor, Michael (1970), The Analysis of Political Cleavages. New Haven: Yale University Press.Google Scholar
Rae, Douglas W., and Taylor, Michael (1971), ‘Decision Rules and Policy Outcomes’. British Journal of Political Science, I, 1–20.Google Scholar
Raiffa, Howard (1953), ‘Arbitration Schemes for Generalized Two-Person Games’. In Kuhn, H. W. and Tucker, A. W., eds., Contributions to the Theory of Games, II (Annals of Mathematics Studies, No. 28). Princeton, N.J.: Princeton University Press, pp. 361–87.Google Scholar
Rapoport, Anatol (1953a), ‘Spread of Information through a Population with Sociostructural Bias: I. Assumption of Transitivity’. Bulletin of Mathematical Biophysics, xv, 523–33.CrossRefGoogle Scholar
Rapoport, Anatol (1953b), ‘Spread of Information through a Population with Sociostructural Bias: II. Various Models with Partial Transitivity’. Bulletin of Mathematical Biophysics, xv, 535–46.CrossRefGoogle Scholar
Rapoport, Anatol (1954), ‘Spread of Information through a Population with Sociostructural Bias: III. Suggested Experimental Procedures’. Bulletin of Mathematical Biophysics, XVI, 75–81.CrossRefGoogle Scholar
Rapoport, Anatol (1957), ‘Richardson's Mathematical Theory of War’. Journal of Conflict Resolution, 1, 249–99.CrossRefGoogle Scholar
Rapoport, Anatol (1960), Fights, Games, and Debates. Ann Arbor: The University of Michigan Press.Google Scholar
Rapoport, Anatol (1964), Strategy and Conscience. New York: Harper and Row.Google Scholar
Rapoport, Anatol (1968), Introduction to his edition of Carl von Clausewitz, On War. Harmondsworth, Middlesex: Penguin Books.Google Scholar
Rapoport, Anatol (1970), N-Person Game Theory: Concepts and Applications. Ann Arbor: University of Michigan Press.Google Scholar
Rapoport, Anatol, and Chammah, Albert M. (1965), Prisoner's Dilemma: A Study in Conflict and Cooperation. Ann Arbor: The University of Michigan Press.CrossRefGoogle Scholar
Rapoport, Anatol, and Rebhun, Lionel I. (1952), ‘On the Mathematical Theory of Rumour Spread’. Bulletin of Mathematical Biophysics, XIV, 375–83.CrossRefGoogle Scholar
Rashevsky, Nicholas (1951), Mathematical Biology of Social Behavior. Chicago: University of Chicago Press.Google Scholar
Rescher, Nicholas (1969), Introduction to Value Theory. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Richardson, Lewis F. (1960a), Arms and Insecurity. Pittsburgh: The Boxwood Press; and Chicago: Quadrangle Books.Google Scholar
Richardson, Lewis F. (1960b), Statistics of Deadly Quarrels. Pittsburgh: The Boxwood Press; and Chicago: Quadrangle Books.Google Scholar
Riker, William H. (1958), ‘The Paradox of Voting and Congressional Rules for Voting on Amendments’. American Political Science Review, LII, 349–66.CrossRefGoogle Scholar
Riker, William H. (1959), ‘A Test of the Adequacy of the Power Index’. Behavioral Science, IV, 120–31.Google Scholar
Riker, William H. (1962), The Theory of Political Coalitions. New Haven: Yale University Press.Google Scholar
Riker, William H. (1967), ‘Bargaining in a Three-Person Game’. American Political Science Review, LXI, 642–56.CrossRefGoogle Scholar
Riker, William H., and Niemi, Richard G. (1962), ‘The Stability of Coalitions on Roll Calls in the House of Representatives’. American Political Science Review, LVI, 58–65.Google Scholar
Riker, William H., and Ordeshook, Peter C. (1968), ‘A Theory of the Calculus of Voting’. American Political Science Review, LXII, 25–42.CrossRefGoogle Scholar
Rothenberg, Jerome (1961), The Measurement of Social Welfare. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
Rothenberg, Jerome (1969), ‘The Process of Group Choice in a Legislative Context’. In Guilbaud, G. T., ed., La Décision: Aggregation et Dynamique des Ordres de Préférence. Paris: Editions du Centre National de la Recherche Scientifique, pp. 205–24.Google Scholar
Saaty, Thomas L. (1968), Mathematical Models of Arms Control and Disarmament: Application of Mathematical Structures in Politics. New York: John Wiley.Google Scholar
Samuelson, Paul (1967), ‘Arrow's Mathematical Polities’. In Hook, S., ed., Human Values and Economic Policy. New York: New York University Press, pp. 41–51.Google Scholar
Schelling, Thomas C. (1963a), ‘War Without Pain, and Other Models’. World Politics, xv, 465–87.CrossRefGoogle Scholar
Selten, Reinhard (1964), ‘Valuation of n-Person Games’. In Dresher, M. et al. , eds., Advances in Game Theory (Annals of Mathematics Studies, No. 52). Princeton, N.JPrinceton University Press.Google Scholar
Sen, Amartya K. (1966), ‘A Possibility Theorem on Majority Decisions’. Econometrica, XXXIV, 491–9.CrossRefGoogle Scholar
Sen, Amartya K. (1969), ‘Quasi-Transitivity, Rational Choice and Collective Decisions’. Review of Economic Studies, XXXVI, 381–93.CrossRefGoogle Scholar
Sen, Amartya K. (1970a), ‘The Impossibility of a Paretian Liberal’. Journal of Political Economy, LXXVII, 152–7.CrossRefGoogle Scholar
Sen, Amartya K. (1970b), ‘Interpersonal Aggregation and Partial Comparability’. Econometrica, XXXVIII, 393–409.CrossRefGoogle Scholar
Sen, Amartya K. (1970c), ‘On Pareto Optimality’. (Abstract). Econometrica, XXXVIII, 6.Google Scholar
Sen, Amartya K. (1970d), Collective Choice and Social Welfare. Edinburgh: Oliver an Boyd; New York: Holden-Day.Google Scholar
Sen, Amartya K., and Pattanaik, Prasanta K. (1969), ‘Necessary and Sufficient Conditions for Rational Choice under Majority Decision’. Journal of Economic Theory, 1, 178–202.CrossRefGoogle Scholar
Sen, Subrata, (1969), ‘Models of Political Campaign Strategies’. Paper read at the 65th Annual Meeting of the American Political Science Association, New York.Google Scholar
Shapley, L. S., (1953), ‘A Value for n-Person Games’. In Kuhn, H. W. and Tucker, A. W., eds., Contributions to the Theory of Games, II (Annals of Mathematics Studies, No. 28). Princeton, N.J.: Princeton University Press, pp. 307–17.Google Scholar
Shapley, L. S. (1962), ‘Simple Games: An Outline of the Descriptive Theory’. Behavioral Science, VII, 59–66.Google Scholar
Shapley, L. S. (1964), ‘Solutions of Compound Simple Games’. In Dresher, M. et al. , eds., Advances in Game Theory (Annals of Mathematics Studies, No. 52). Princeton N.J.: Princeton University Press, pp. 443–76.Google Scholar
Shapley, L. S. (1967), Compound Simple Games;.Ill: On Committees. Santa Monica Calif.: The RAND Corporation, RM-5438-PR.Google Scholar
Shapley, L. S., and Shubik, Martin (1954), ‘A Method for Evaluating the Distribution of Power in a Committee System’. American Political Science Review, XLVIII, 787–92.CrossRefGoogle Scholar
Shapley, L. S., and Shubik, Martin (1967), ‘Concepts and Theories of Pure Competition’. Chapter 6 in Shubik, M., ed., Essays in Mathematical Economics in Honor of Oskar Morgenstern. Princeton, N.J.: Princeton University Press.Google Scholar
Shubik, Martin (1959), Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games. New York: John Wiley.Google Scholar
Shubik, Martin, ed., (1964), Game Theory and Related Approaches to Social Behavior. New York: John Wiley.Google Scholar
Shubik, Martin (1968), ‘A Two-Party System, General Equilibrium, and the Voters’ Paradox’. Santa Monica, Calif.: The RAND Corporation, RM-5770.CrossRefGoogle Scholar
Shubik, Martin (1970a), ‘Voting, or a Price System in a Competitive Market’. American Political Science Review, LXIV, 179–81.CrossRefGoogle Scholar
Shubik, Martin (1970b), ‘Game Theory, Behavior, and the Paradox of the Prisoner's Dilemma: Three Solutions’. Journal of Conflict Resolution, XIV, 181–93.CrossRefGoogle Scholar
Siegel, Sidney, and Fouraker, Lawrence E. (1960), Bargaining and Group Decision Making: Experiments in Bilateral Monopoly. New York: McGraw-Hill.Google Scholar
Simon, Herbert A. (1955), ‘A Behavioral Model of Rational Choice’. Quarterly Journal of Economics, LVIX, 99–118. Reprinted in H. A. Simon, Models of Man. New York: John Wiley, pp. 241–60.CrossRefGoogle Scholar
Simpson, Paul B. (1969), ‘On Denning Areas of Voter Choice.’ Quarterly Journal of Economics, LXXXIII, 478–95.CrossRefGoogle Scholar
Smoker, , Paul, (1964), ‘Fear in the Arms Race: A Mathematical Study’. Journal of Peace Research, I, 55–64.CrossRefGoogle Scholar
Stokes, Donald E. (1963), ‘Spatial Models of Party Competition’. American Political Science Review, LVII, 368–77.CrossRefGoogle Scholar
Taylor, Michael (1968), ‘Towards a Mathematical Theory of Influence and Attitude Change’. Human Relations, XXI, 121–39.CrossRefGoogle Scholar
Taylor, Michael (1969), ‘Proof of a Theorem on Majority Rule’. Behavioral Science, XIV, 228–31.CrossRefGoogle Scholar
Taylor, Michael (1970), ‘The Problem of Salience in the Theory of Collective Decision-Making’. Behavioral Science, XVI, 415–30.CrossRefGoogle Scholar
Taylor, Michael (1971), ‘The Theory of Government Coalition Formation’. Unpublished manuscript, Department of Political Science, Yale University.Google Scholar
Taylor, Michael (Forthcoming), ‘Mathematical Theories of Social Choice’. In Greenstein, F. and Polsby, N., eds., Handbook of Political Science. Reading, Mass.: Addison-Wesley.Google Scholar
Taylor, Michael, and Herman, V. M. (1971), ‘Party Systems and Government Stability’. American Political Science Review, LXV, 28–37.CrossRefGoogle Scholar
Theil, Henri (1963), ‘On the Symmetry Approach to the Committee Decision Problem’. Management Science, IX, 380–93.CrossRefGoogle Scholar
Theil, Henri (1964), Optimal Decision Rules for Government and Industry. Amsterdam: North Holland.Google Scholar
Tullock, Gordon (1967), ‘The General Irrelevance of the General Impossibility Theorem’. Quarterly Journal of Economics, LXXXI, 256–70.CrossRefGoogle Scholar
van den Bogaard, P. J., and Versluis, J. (1962), ‘The Design of Optimal Committee Decisions’. Statistica Neerlandica, XVI, 271–89.CrossRefGoogle Scholar
Vickrey, William (1960), ‘Utility, Strategy, and Social Decision Rules’. Quarterly Journal of Economics, LXXIV, 507–35.CrossRefGoogle Scholar
Neumann, Von, John, , and Morgenstern, , Oskar, (1947), Theory of Games and Economic Behaviour, (Second Edition). Princeton, N.J.: Princeton University Press.Google Scholar
Ward, Benjamin (1961), ‘Majority Rule and Allocation’. Journal of Conflict Resolution, v, 379–89.CrossRefGoogle Scholar
Ward, Benjamin (1965), ‘Majority Voting and Alternative Forms of Public Enterprise’. In Margolis, J., ed., The Public Economy of Urban Communities. Baltimore: Johns Hopkins Press.Google Scholar
Weinstein, A. A. (1968), ‘Individual Preference Intransitivity’. Southern Economic Journal, XXXIV, 335–43.CrossRefGoogle Scholar
WilliamsonOliver, E. Oliver, E., and Sargent, Thomas J. (1967), ‘Social Choice: A Probabilistic Approach’. Economic Journal, LXXVII, 797–813.CrossRefGoogle Scholar
Wilson, Robert (1968), ‘The Theory of Syndicates’. Econometrica, XXXVI, 119–32.CrossRefGoogle Scholar
Wilson, Robert (1969a), ‘An Axiomatic Model of Logrolling’. American Economic Review, LIX, 331–41.Google Scholar
Wilson, Robert (1969b), ‘The Role of Uncertainty and the Value of Logrolling in Collective Choice Processes’. In Guilbaud, G., ed., La Decision: Aggregation et Dynamique des Ordres de Préférence. Paris: Editions du Centre National de la Recherche Scientifique, pp. 309–15.Google Scholar
Wilson, Robert (1971a), ‘A Game-Theoretic Analysis of Social Choice’. In Liebermann, B., ed., Social Choice (Proceedings of a Conference at the University of Pittsburgh, 09 1968). New York: Gordon and Breach.Google Scholar
Wilson, Robert (1971b), ‘Stable Coalition Proposals in Majority Rule Voting’. Journal of Economic Theory, III.Google Scholar
Wolfson, Murray (1968), ‘A Mathematical Model of the Cold War’. Peace Research Society (International) Papers, IX, 107–23.Google Scholar
Zeuthen, Frederik (1930), Problems of Monopoly and Economic Warfare. London: Routledge.Google Scholar