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An axiomatic approach to predictability of outcomes in an interactive setting

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Abstract

This article is an axiomatic approach to the problem of ranking game forms in terms of the predictability they offer to individuals. Two criteria are proposed and characterized, the CardMin and the CardMax. Both compare game forms on the basis of the number of distinct outcomes that can result from the choice of a CardMin (resp. CardMax) strategy. The CardMin (resp. CardMax) strategy is defined as a strategy leading to the smallest (resp. highest) number of different outcomes. In both cases, the lower these numbers the better the game form.

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References

  • Barberà S., Bossert W., Pattanaik P. K. (2004) Ranking sets of objects. In: Barberà S., Hammond P., Seidl C. (eds) Handbook of utility theory, Vol. 2: Extensions. Kluwer, Dordrecht

    Google Scholar 

  • Bervoets S. (2007) Freedom of choice in a social context: Comparing game forms. Social Choice and Welfare 29: 295–315

    Article  Google Scholar 

  • Bervoets S., Gravel N. (2007) Appraising diversity with an ordinal notion of similarity: An axiomatic approach. Mathematical Social Sciences 53: 259–273

    Article  Google Scholar 

  • Bossert W. (1997) Uncertainty aversion in non-probabilistic decision models. Mathematical Social Sciences 34: 191–203

    Article  Google Scholar 

  • Bossert W., Pattanaik P. K., Xu Y. (2000) Choice under complete uncertainty: Axiomatic characterization of some decision rules. Economic Theory 16: 295–312

    Article  Google Scholar 

  • Deb R. (1994) Waiver, effetivity and rights as game forms. Economica 61: 167–178

    Article  Google Scholar 

  • Deb R. (2004) Rights as alternative game forms. Social Choice and Welfare 22: 83–111

    Article  Google Scholar 

  • Deb R., Pattanaik P. K., Razzolini L. (1997) Game forms, rights and the efficiency of social outcomes. Journal of Economic Theory 72: 74–95

    Article  Google Scholar 

  • Dowding, K., & van Hees, M. (2008). Freedom of choice. In P. Anand, P. K. Pattanaik, & C. Puppe (Eds.), The Oxford handbook of rational and social choice. Oxford: Oxford U.P. (forthcoming).

  • Gaertner W., Pattanaik P. K., Suzumura K. (1992) Individual rights revisited. Economica 59: 161–177

    Article  Google Scholar 

  • Gardenförs P. (1981) Rights, games and social choice. Nous 15: 341–356

    Google Scholar 

  • Gravel N. (2008) What is freedom? In: Peil J., Van Staveren I. (eds) Handbook of economics and ethics. Edward Edgar Publishing, London

    Google Scholar 

  • Kreps D. M. (1979) A representation theorem for ’preference for flexibility’. Econometrica 47: 565–577

    Article  Google Scholar 

  • Kreps D. M. (1988) Notes on the theory of choice. Boulder, Westview

    Google Scholar 

  • Machina M. (1987) Choices under uncertainty: Problems solved and unsolved. Journal of Economic Perspectives 1: 121–154

    Google Scholar 

  • Moulin H. (1983) The strategy of social choice. North Holland, New York

    Google Scholar 

  • Nehring K., Puppe C. (2002) A theory of diversity. Econometrica 70: 1155–1190

    Article  Google Scholar 

  • Nitzan S., Pattanaik P. K. (1984) Median-based extensions of an ordering over a set to the power set: An axiomatic characterization. Journal of Economic Theory 34: 252–261

    Article  Google Scholar 

  • Pattanaik P. K., Peleg B. (1984) An axiomatic characterization of the lexicographic maximin extension of an ordering over a set to the power set. Social Choice and Welfare 1: 113–122

    Article  Google Scholar 

  • Pattanaik P. K., Xu Y. (1990) On ranking opportunity sets in terms of freedom of choice. Recherches Economiques de Louvain 56: 383–390

    Google Scholar 

  • Peleg B. (1984) Game theoretical analysis of voting in committees. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Peleg B. (1998) Effectivity functions, games and rights. In: Laslier J. F., Fleurbaey M., Gravel N., Trannoy A. (eds) Freedom in economics: New perspective in normative analysis. Routledge, London

    Google Scholar 

  • Sen A. K. (1970) The impossibility of a paretian liberal. Journal of Political Economy 78: 152–157

    Article  Google Scholar 

  • Sen A. K. (1983) Liberty and social choice. Journal of Philosophy 80: 5–28

    Article  Google Scholar 

  • Weitzman M. L. (1992) On diversity. Quarterly Journal of Economics 107: 363–406

    Article  Google Scholar 

  • Weitzman M. L. (1993) What to preserve? An application of diversity theory to crane conservation. Quarterly Journal of Economics 108: 157–183

    Article  Google Scholar 

  • Weitzman M. L. (1998) The Noahs ark problem. Econometrica 66: 1279–1298

    Article  Google Scholar 

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Bervoets, S. An axiomatic approach to predictability of outcomes in an interactive setting. Theory Decis 68, 311–323 (2010). https://doi.org/10.1007/s11238-009-9185-8

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