The Tyranny of the Ideal

by Gaus, Gerald;

  Figure B-1. An example of predictive diversity

  The average individual error here is (1.25+2+1.13)/3, or 1.46. More generally, average individual

  The collective prediction (cp) is the average of the individual predictions; the models collectively predict that the ox weighs 1.42K and the bull 2.25K. We thus can now compute (ii), their collective error: (1.42−1)2 + (2.25−2)2 = (.42)2 + (.25)2 = .18 +.06 = .24. The collective error (.24) is less than the average individual error (1.46).

  The reason for this is the predictive diversity of the group, which is defined as

  where xi is the individual’s prediction and xcp is the collective prediction. To calculate the predictive diversity for our example:

  α’s squared distance from cp: (.5−1.42)2 + (1−2.25)2 = 2.4

  β’s squared distance from cp: (2−1.42)2 + (3−2.25)2 = .9

  γ’s squared distance from cp: (1.75−1.42)2 + (2.75−2.25)2 = .36

  This yields a prediction diversity (average of the squared distances) of 2.4 + .9 + .36 / 3, or 1.22.

  We thus arrive at Page’s Diversity Prediction Theorem that

  Collective Error = Average Individual − Predictive Diversity.

  In our example the collective error of .24 equals the average individual error of 1.46 minus predictive diversity of 1.22. Although in our example the collective prediction is better than any individual prediction, that does not generally hold: an excellent individual predictor can beat the collective prediction. But the collective prediction will always beat the average of individual predictions. This is an important result: even if our predictive models are not very good, a diverse perspective or society can draw on diverse predictive models (understood as predictive diversity as defined above), and so significantly enhance its confidence in its estimates of the justice of alternative social worlds.

  An especially interesting mechanism of collective intelligence is information markets. Perhaps the best known is the Iowa Election Markets, which is essentially a market for future political events. As I write (August 23, 2014) there is a market for predicting the 2014 congressional elections; there are basically four possibilities in the overall congressional prediction market: (1) Democrats control both the House and Senate; (2) Democrats control the House and the Republicans the Senate; (3) Republicans control the House and the Democrats the Senate; (4) the Republicans control both. For each “share” one buys, one gets $1 if correct, and nothing if one is not. At this moment the price for option 4 is roughly 64¢; if one buys an option at 64¢, and the Republicans control both houses on November 4, 2014 (as they did), one receives $1. Option (3) is selling at 25¢, and option (1) at 3/10 of a cent. An important feature of such markets is that predictors’ bets give information about the accuracy of their prediction—by putting their money where their predictions are, those predictors who have high confidence in their predictions have inordinate influence. If high confidence is correlated with possessing better models, information markets thus not only draw on predictive diversity but give extra influence to the best models. Moreover, not only does the market have a current price, but traders can issue bids and asks; it turns out that the traders who do this, rather than just take the current price, are those with most information, and have the greatest impact on the market.3

  1 I am following the presentations of Page, The Difference, pp. 205–12, and Wagner, Zhao, Schneider, and Chen, “The Wisdom of Reluctant Crowds.”

  2 “A little more than a year ago, I happened to be at Plymouth, and was interested in a Cattle exhibition, where a visitor could purchase a stamped and numbered ticket for sixpence, which qualified him to become a candidate in a weight-judging competition. An ox was selected, and each of about eight hundred candidates wrote his name and address on his ticket, together with his estimate of what the beast would weigh when killed and “dressed” by the butcher. The most successful of them gained prizes. The result of these estimates was analogous, under reservation, to the votes given by a democracy, and it seemed likely to be instructive to learn how votes were distributed on this occasion, and the value of the result. So I procured a loan of the cards after the ceremony was past, and worked them out. … It appeared that in this instance the vox populi was correct to within 1 per cent, of the real value; it was 1207 pounds instead of 1198 pounds, and the individual estimates were distributed in such a way that it was an equal chance whether one of them selected at random fell within or without the limits of −3.7 per cent, or +2.4 per cent, of the middlemost value of the whole.” Francis Galton, Memories of My Life, pp. 280–81.

  3 Sunstein, Infotopia, chap. 4.

  Works Cited

  Ahn, W. K., and D. L. Medin. “A Two-Stage Model of Category Construction.” Cognitive Science, vol. 16 (1992): 81–121.

  Aligica, Paul Dragos. Institutional Diversity and Political Economy: The Ostroms and Beyond. Oxford: Oxford University Press, 2014.

  Aligica, Paul Dragos, and Peter J. Boettke. Challenging Institutional Development: The Bloomington School. London: Routledge, 2009.

  Arneson, Richard. “Rejecting The Order of Public Reason.”Philosophical Studies, vol. 170 (September 2014): 537–44.

  Ashby, F. G., and W. T. Maddox. “Human Category Learning.” Annual Review of Psychology, vol. 56 (2005): 149–78.

  Ashby, S. Queller, and P. M. Berretty. “On The Dominance of Unidimensional Rules in Unsupervised Categorization.” Perception and Psychophysics, vol. 61 (1999): 1178–99.

  Auyang, Sunny Y. Foundations of Complex-Systems Theories in Economics, Evolutionary Biology and Statistical Physics. Cambridge: Cambridge University Press, 1998.

  Bacon, Francis. New Atlantis, edited by Alfred B. Gough. Oxford: Clarendon Press, 1915 [1627].

  Baier, Kurt. “Moral Obligation.” American Philosophical Quarterly, vol. 3 (July 1966): 210–26.

  Barry, Brian. “John Rawls and the Search for Stability.” Ethics, vol. 105 (July 1995): 874–915.

  Barry, Christian, and Laura Valentini. “Egalitarian Challenges to Global Egalitarianism: A Critique.” Review of International Studies, vol. 35 (2009): 485–512.

  Bellamy, Edward. Looking Backward. New York: Dover, 1996 [1880].

  Benn, Stanley. A Theory of Freedom. Cambridge: Cambridge University Press, 1988.

  Berlin, Isaiah. The Roots of Romanticism. Princeton, NJ: Princeton University Press, 1997.

  Berneri, Marie Louise. Journey through Utopia. London: Routledge and Kegan Paul, 1950.

  Bicchieri, Cristina. The Grammar of Society: The Nature and Dynamics of Norms. Cambridge: Cambridge University Press, 2006.

  ———. Norms in the Wild: How to Diagnose, Measure and Change Social Norms. New York: Oxford University Press, 2016.

  Bicchieri, Cristina, and Alex Chavez. “Behaving as Expected: Public Information and Fairness Norms.” Journal of Behavioral Decision Making, vol. 23 (2010): 161–78.

  ———. “Norm Manipulation, Norm Evasion: Experimental Evidence.” Economics and Philosophy, vol. 29 (special issue 2, July 2013): 175–98.

  Bicchieri, Cristina, and Hugo Mercier. “Norms and Beliefs: How Change Occurs.” In The Complexity of Social Norms, edited by Maria Xenitidou and Bruce Edmonds. New York: Springer, 2014: 37–54.

  Bicchieri, Cristina, and Hugo Mercier. “Self-Serving Biases and Public Justifications in Trust Games.” Synthese, vol. 190 (2013): 909–22.

  Binmore, Ken. Natural Justice. Oxford: Oxford University Press, 2005.

  Bowles, Samuel, and Herbert Gintis. A Cooperative Species: Human Reciprocity and Its Evolution. Princeton, NJ: Princeton University Press, 2011.

  Boyd, Robert, and Peter J. Richerson. The Origin and Evolution of Cultures. Oxford: Oxford University Press, 2005.

  Brennan, Geoffrey. “Feasibility in Optimizing Ethics,” Social Philosophy and Policy, vol. 30 (January 2013): 314–29.

  Brennan, Geoffrey, Lina Eriksson, Robert E. Goodin, and Nicholas Southwood. Explaining Norms. Oxford: Oxford University Press, 2013.

  Brennan, Geof
frey, and Philip Pettit. “The Feasibility Issue.” In The Oxford Handbook of Contemporary Philosophy. Oxford: Oxford University Press, 2005: 258–79.

  Bringhurst, Piper L., and Gerald Gaus. “Positive Freedom and the General Will.” In The Oxford Handbook of Freedom, edited by David Schmidtz. Oxford: Oxford University Press, forthcoming.

  Broome, John. Ethics Out of Economics. Cambridge: Cambridge University Press, 1999.

  Buchanan, James M., and Gordon Tullock. The Calculus of Consent: Logical Foundations of Constitutional Democracy. Ann Arbor: University of Michigan Press, 1962.

  Buck-Morss, Susan. Dreamworld and Catastrophe: The Passing of Mass Utopia in East and West. Cambridge, MA: MIT Press, 2000.

  Canini, K. R., T. L. Griffiths, W. Vanpaemel, and M. L. Kalish. “Revealing Human Inductive Biases for Category Learning by Simulating Cultural Transmission.” Psychonomic Bulletin and Review, vol. 21 (2014): 785–93.

  Carey, Brian. “Towards a ‘Non-ideal’ Non-ideal Theory.” Journal of Applied Philosophy, vol. 32 (May 2015): 148–62.

  Castelli, Ilaria, Davide Massaro, Cristina Bicchieri, Alex Chavez, and Antonella Marchetti. “Fairness Norms and Theory of Mind in an Ultimatum Game: Judgments, Offers, and Decisions in School-Aged Children.” Plos One, vol. 9, no. 8 (August 2014). www.plosone.org.

  Chapman, John W. “Justice, Freedom and Property.” In Nomos XXII: Property, edited by J. Roland Pennock and John W. Chapman. New York: New York University Press, 1980: 289–324.

  Chwe, Michael Suk-Young. Rational Ritual: Culture, Coordination and Common Knowledge. Princeton, NJ: Princeton University Press, 2001.

  Cialdini, Robert B., Carl A. Kallgren, and Raymond B. Reno. “A Focus Theory of Normative Conduct: A Theoretical Refinement and Reevaluation of the Role of Norms in Human Behavior.” Advances in Experimental Social Psychology, vol. 24 (1990): 201–34.

  Cohen, G. A. Rescuing Justice and Equality. Cambridge, MA: Harvard University Press, 2008.

  ———. Why Not Socialism? Princeton, NJ: Princeton University Press, 2009.

  Cummins, Denise Dellarosa. “Evidence for the Innateness of Deontic Reasoning.” Mind and Language, vol. 11 (June 1996): 160–90.

  ———. “Evidence of Deontic Reasoning in 3- and 4-Year-Olds.” Memory and Cognition, vol. 24 (1996): 823–29.

  D’Agostino, Fred. “From the Organization to the Division of Cognitive Labor.” Politics, Philosophy and Economics, vol. 8 (2009): 101–29.

  ———. Incommensurability and Commensuration: The Common Denominator. Burlington, VT: Ashgate, 2003.

  ———. Naturalizing Epistemology: Thomas Kuhn and the Essential Tension. London: Palgrave, 2010.

  ———. “The Orders of Public Reason.” Analytic Philosophy, vol. 54 (March 2013): 129–55.

  de Waal, Frans. The Bonobo and the Atheist: In Search for Humanism among the Primates. New York: W. W, Norton, 2013.

  Dewey, John. Individualism, Old and New. London: George Allen and Unwin, 1931.

  Dworkin, Ronald. “Liberalism.” In Public and Private Morality, edited by Stuart Hampshire. Cambridge: Cambridge University Press, 1978: 113–43.

  Economic Freedom in the World 2013 Annual Report. Fraser Institute. www.fraserinstitute.org.

  Ellison, Sara Fisher, and Wallace P. Mullin. “Diversity, Social Goods Provision, and Performance in the Firm.” Journal of Economics and Management Strategy, vol. 23 (Summer 2014): 465–81.

  Elster, Jon, Logic and Society: Contradictions and Possible Worlds. New York: John Wiley and Sons. 1978.

  Engels, Friedrich. “Socialism: Utopian and Scientific.” In The Marx-Engels Reader, 2nd ed., edited by Robert C. Tucker. New York: W. W. Norton, 1978: 681–717.

  Enoch, David. “The Disorder of Public Reason.” Ethics, vol. 124 (October 2013): 141–76.

  Estlund, David. Democratic Authority: A Philosophical Framework. Princeton, NJ: Princeton University Press, 2008.

  ———. “Human Nature and the Limits (If Any) of Political Philosophy.” Philosophy and Public Affairs, vol. 39 (2011): 207–35.

  ———. “Prime Justice.” In Political Utopias: Contemporary Debates, edited by Michael Weber and Kevin Vallier. Oxford: Oxford University Press, forthcoming.

  ———. “Utopophobia.” Philosophy and Public Affairs, vol. 42 (2014): 114–34.

  Farrelly, Colin. “Justice in Ideal Theory: A Refutation.” Political Studies, vol. 55 (2007): 844–64.

  Fehr, Ernst, and Urs Fischbacher. “Third Party Punishment and Social Norms.” Evolution and Human Behavior, vol. 25 (2004): 63–87.

  Feinberg, Joel. Harm to Others. New York: Oxford University Press, 1984.

  Forst, Ranier. “Political Liberty: Integrating Five Conceptions of Autonomy.” In Autonomy and Challenges to Liberalism: New Essays, edited by John Christman and Joel Anderson. Cambridge: Cambridge University Press, 2006: 226–42.

  Foucault, Michel. Discipline and Punish: The Birth of the Prison, 2nd ed., translated by A. Sheridan. New York: Vintage Books, 1995.

  Freedom House Freedom in the World 2014 Report. http://www.freedomhouse.org/report-types/freedom-world#.U-QOVIBdW2A.

  Freeman, Samuel. Justice and the Social Contract. New York: Oxford University Press, 2007.

  Friedman, David. The Machinery of Freedom. New York: Harper and Row, 1973.

  Friedman, Milton. “The Methodology of Positive Economics.” In The Philosophy of Economics: An Anthology, 3rd ed., edited by Daniel Hausman. Cambridge: Cambridge University Press, 2008: 145–78.

  Galton, Francis. Memories of My Life. New York: Dutton, 1909.

  Gaus, Gerald. “Constructivist and Ecological Modeling of Group Rationality.” Episteme, vol. 9 (September 2012): 245–54.

  ———. “The Egalitarian Species.” Social Philosophy and Policy, vol. 31 (Spring 2015): 1–27.

  ———. Justificatory Liberalism: An Essay on Epistemology and Political Theory. Oxford: Oxford University Press, 1996.

  ———. “The Limits of Homo Economicus.” In Essays on Philosophy, Politics and Economics: Integration and Common Research Projects, edited by Christi Favor, Gerald Gaus, and Julian Lamont. Stanford, CA: Stanford University Press, 2010: 14–37.

  ———. “Locke’s Liberal Theory of Public Reason.” In Public Reason in the History of Political Philosophy, edited by Piers Norris Turner and Gerald Gaus. New York: Routledge, forthcoming.

  ———. “Mill’s Normative Economics.” In The Blackwell Companion to Mill, edited by Christopher Macleod and Dale Miller. New York: Wiley-Blackwell, forthcoming.

  ———. “Moral Constitutions.” Harvard Review of Philosophy, vol. 19 (2013): 4–22.

  ———. “On Dissing Public Reason: A Reply to Enoch.” Ethics, vol. 125 (July 2015): 1078–95.

  ———. On Philosophy, Politics, and Economics. Belmont, CA: Wadsworth-Thomson, 2008.

  ———. The Order of Public Reason. Cambridge: Cambridge University Press, 2011.

  ———. “Retributive Justice and Social Cooperation.” In Retributivism: Essays on Theory and Practice, edited by Mark D. White. Oxford: Oxford University Press, 2011: 73–90.

  ———. “Sectarianism without Perfection? Quong’s Political Liberalism.” Philosophy and Public Issues, vol. 2 (Fall 2012): 7–15.

  ———. “Social Complexity and Evolved Moral Principles.” In Liberalism, Conservatism, and Hayek’s Idea of Spontaneous Order, edited by Peter McNamara. London: Palgrave Macmillan, 2007: 149–76.

  ———. “Social Contract and Social Choice.” Rutgers Law Journal, vol. 43 (Spring/Summer 2012): 243–76.

  ———. Social Philosophy. Armonk, NY: M. E. Sharpe, 1999.

  ———. “A Tale of Two Sets: Public Reason in Equilibrium.” Public Affairs Quarterly, vol. 25 (October 2011): 305–25.

  ———. “The Turn to a Political Liberalism.” In The Blackwell Companion to Rawls, edited by David Reidy and Jon Mandle. New York: Wiley-Blackwell, 2014: 235–50.

  Gaus, Gerald, and Keith Hankins. “Searching for the Ideal.
” In Political Utopias: Contemporary Debates, edited by Michael Weber and Kevin Vallier. Oxford: Oxford University Press, forthcoming.

  Gaus, Gerald, and Shaun Nichols. “Moral Learning in the Open Society: The Theory and Practice of Natural Liberty.” Social Philosophy and Policy, forthcoming.

  Gaus, Gerald, and John Thrasher. “Rational Choice and the Original Position: The (Many) Models of Rawls and Harsanyi.” In The Original Position, edited by Timothy Hinton. Cambridge: Cambridge University Press, 2016: 39–58.

  Gauthier, David. Morals by Agreement. Oxford: Clarendon Press, 1986.

  ———. “Twenty-Five On.” Ethics, vol. 123 (July 2013): 601–24.

  Gavrilets, Sergey. “High-Dimensional Fitness Landscapes and Speciation.” In Evolution—the Extended Synthesis, edited by Massimo Pigliucci and Gerd B. Müller. Cambridge, MA: MIT Press, 2010: 45–80.

  Gilabert, Pablo. “Comparative Assessments of Justice, Political Feasibility, and Ideal Theory.” Ethical Theory and Practice, vol. 15 (2012): 39–56.

  Gilabert, Pablo, and Holly Lawford-Smith. “Political Feasibility: A Conceptual Exploration.” Political Studies, vol. 60 (2012): 809–25.

  Godwin, William. An Enquiry concerning Political Justice, and Its Influence on General Virtue and Happiness, 2 vols. London: G.G.J. and J. Robinson, 1793.

  ———. Of Population: An Enquiry concerning the Power of Increase in the Numbers of Mankind, Being an Answer to Mr. Malthus’s Essay on that Subject. London: Longman, Hurst, Rees, Orme, and Brown, 1820.