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Why Are Certain Properties of Binary Relations Relatively More Common in Natural Language?

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  • Rubinstein, Ariel

Abstract

The aim of this paper is to explain the fact that certain properties of binary relations are frequently observed in natural language while others do not appear at all. Three features of binary relation are studied: (1) The ability to use the relation to indicate nameless elements. (2) The accuracy with which the vocabulary spanned by the relation can be used to approximate the actual terms to which a user of the language wishes to refer. (3) The ease with which the relation can be described by means of examples. It is argued that linear orderings are optimal according to the first criteria while asymmetric relations are optimal according to second. From among complete and asymmetric relations (tournaments) those which are transitive are optimal according to the third criterion. Copyright 1996 by The Econometric Society.

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  • Rubinstein, Ariel, 1996. "Why Are Certain Properties of Binary Relations Relatively More Common in Natural Language?," Econometrica, Econometric Society, vol. 64(2), pages 343-355, March.
  • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:2:p:343-55
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    Cited by:

    1. Kalai, Gil, 2003. "Learnability and rationality of choice," Journal of Economic Theory, Elsevier, vol. 113(1), pages 104-117, November.
    2. Blume, Andreas & Franco, April Mitchell, 2007. "Decentralized learning from failure," Journal of Economic Theory, Elsevier, vol. 133(1), pages 504-523, March.
    3. repec:kap:expeco:v:20:y:2017:i:4:d:10.1007_s10683-017-9518-3 is not listed on IDEAS
    4. Archishman Chakraborty & Rick Harbaugh, 2003. "Ordinal Cheap Talk," Claremont Colleges Working Papers 2003-05, Claremont Colleges.
    5. Hernández, Penélope & Urbano, Amparo & Vila, José E., 2012. "Pragmatic languages with universal grammars," Games and Economic Behavior, Elsevier, vol. 76(2), pages 738-752.
    6. Blume, Andreas & Gneezy, Uri, 2010. "Cognitive forward induction and coordination without common knowledge: An experimental study," Games and Economic Behavior, Elsevier, vol. 68(2), pages 488-511, March.
    7. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions II: Ascending Auctions," Discussion Paper Series dp382, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    8. Mandler, Michael & Manzini, Paola & Mariotti, Marco, 2012. "A million answers to twenty questions: Choosing by checklist," Journal of Economic Theory, Elsevier, vol. 147(1), pages 71-92.
    9. Blume, Andreas, 2000. "Coordination and Learning with a Partial Language," Journal of Economic Theory, Elsevier, vol. 95(1), pages 1-36, November.
    10. Uriarte Ayo, José Ramón, 2015. "A Game-Theoreteic Analysis of Minority Language Use in Multilingual Societies," IKERLANAK Ikerlanak;2015-93, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    11. Blume, Andreas & Gneezy, Uri, 2000. "An Experimental Investigation of Optimal Learning in Coordination Games," Journal of Economic Theory, Elsevier, vol. 90(1), pages 161-172, January.
    12. Hong, Fuhai & Lim, Wooyoung & Zhao, Xiaojian, 2017. "The emergence of compositional grammars in artificial codes," Games and Economic Behavior, Elsevier, vol. 102(C), pages 255-268.
    13. Knoblauch, Vicki, 2013. "A simple voting scheme generates all binary relations on finite sets," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 230-233.
    14. Andreas Blume, 2004. "A Learning-Efficiency Explanation of Structure in Language," Theory and Decision, Springer, vol. 57(3), pages 265-285, November.
    15. Gil Kalai, 2001. "Learnability and Rationality of Choice," Discussion Paper Series dp261, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    16. Glazer, Jacob & Rubinstein, Ariel, 2001. "Debates and Decisions: On a Rationale of Argumentation Rules," Games and Economic Behavior, Elsevier, vol. 36(2), pages 158-173, August.
    17. Devetag, Giovanna & Warglien, Massimo, 2008. "Playing the wrong game: An experimental analysis of relational complexity and strategic misrepresentation," Games and Economic Behavior, Elsevier, vol. 62(2), pages 364-382, March.
    18. Birger Wernerfelt, 2004. "Organizational Languages," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 13(3), pages 461-472, September.
    19. Salant, Yuval, 2007. "On the learnability of majority rule," Journal of Economic Theory, Elsevier, vol. 135(1), pages 196-213, July.
    20. repec:pit:wpaper:346 is not listed on IDEAS
    21. Yuval Salant, 2003. "Learning the decisions of small committees," Discussion Paper Series dp332, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    22. Andreas Blume & April Franco, 2002. "Learning from failure," Staff Report 299, Federal Reserve Bank of Minneapolis.
    23. Stéphane Luchini, 2002. "De la singularité de la méthode d'évaluation contingente," Économie et Statistique, Programme National Persée, vol. 357(1), pages 141-152.
    24. Beard, Rodney, 2001. "A note on Rubinstein's ``Why are certain properties of binary relations relatively more common in natural language?"," MPRA Paper 5377, University Library of Munich, Germany, revised Oct 2007.

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