Vorobyev, Oleg Yu. (2016): The theory of dual co~event means. Published in: Proceedings of the XV FAMEMS2016 Conference and the Workshop on Hilbert's sixth problem, Krasnoyarsk, Russia (30 September 2016): pp. 4493.

PDF
MPRA_paper_81893.pdf Download (14MB)  Preview 
Abstract
This work is the third, but not the last, in the cycle begun by the works [23, 22] about the new theory of experience and chance as the theory of co~events. Here I introduce the concepts of two co~event means, which serve as dual co~event characteristics of some co~event. The very idea of dual co~event means has become the development of two concepts meanmeasure set [16] and meanprobable event [20, 24], which were first introduced as two independent characteristics of the set of events, so that then, within the framework of the theory of experience and of chance, the idea can finally get the opportunity to appear as two dual faces of the same co~event. I must admit that, precisely, this idea, hopelessly long and lonely stood at the sources of an indecently long string of guesses and insights, did not tire of looming, beckoning to the new co~event description of the dual nature of uncertainty, which I called the theory of experience and chance or the certainty theory. The constructive final push to the idea of dual co~event means has become two surprisingly suitable examples, with which I was fortunate to get acquainted in 2015, each of which is based on the statistics of the experiencedrandom experiment in the form of a co~event.
Item Type:  MPRA Paper 

Original Title:  The theory of dual co~event means 
Language:  English 
Keywords:  Eventology, theory of experience and chance, event, co~event, experience, chance, to happen, to experience, to occur, probability, believability, meanbelievable (meanexperienced) terraced braevent, meanprobable (meanpossible) ketevent, meanbelievableprobability (meanexperiencedpossible) co~event, experiencedrandom experiment, dual event means, dual co~event means, bramenas, ketmeans, Bayesian analysis, approval voting, forest approval voting. 
Subjects:  A  General Economics and Teaching > A1  General Economics C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C18  Methodological Issues: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65  Miscellaneous Mathematical Tools Z  Other Special Topics > Z1  Cultural Economics ; Economic Sociology ; Economic Anthropology Z  Other Special Topics > Z1  Cultural Economics ; Economic Sociology ; Economic Anthropology > Z13  Economic Sociology ; Economic Anthropology ; Social and Economic Stratification 
Item ID:  81893 
Depositing User:  Prof Oleg Yu Vorobyev 
Date Deposited:  16 Oct 2017 20:24 
Last Modified:  16 Oct 2017 20:24 
References:  [1] Probability and Mathematical Statistics. Encyclopedia. Science publisher Great Russian Encyclopedia, Moscow, 1999. [2] Data from the Coed y Brenin Training Workshop for forest managers. “The King’s Forest”, NorthWales, UK, 2006. [3] M. M. Bakhtin. Toward a Philosophy of the Act. University of Texas Press, Austin (1993), St.Petersburg, 1920. [4] S. J. Brams and P.C. Fishburn. Approval voting. American Political Science Review, 72(3):831–847, 1978. [5] S. J. Brams and P.C. Fishburn. Paradoxes of preferential voting. Mathematics Magazine, 56(4):207–214, 1983. [6] S. J. Brams and P.C. Fishburn. Approval voting in scientific and engineering societies. Group Decision and Negotiations, 1:44–55 (http://bcn.boulder.co.us/government/approvalvote/scieng.html), April 1992. [7] S. J. Brams and J.H. Nagel. Approval voting in practice. Public Choice, 71:1–17, 1991. [8] Stoyan D. Kendall W. S. Chiu, S. N. and J. Mecke. Stochastic Geometry and its Applications. Wiley & Sons, 3 edition, Chichester, 2013. [9] M. Holquist. Dialogism. Bakhtin and his World. 2nd edition. Routledge, Taylor & Francis Group, London and New York, 2002. [10] A. N. Kolmogorov. Grundbegriffe derWahrscheinlichkeitrechnung. Ergebnisse der Mathematik, Berlin, 1933. [11] I. Molchanov. Theory of Random Sets. SpringerVerlag, London etc., 2005. [12] H. E. Robbins. On the measure of a random set. Ann. Math. Statist., 15/16:70–74/342–347, 1944/45. [13] D. Stoyan and A. Pommerening. Settheoretic Analysis of Voter Behaviour in Approval Voting Applied to Forest Management, October 2015, private communication, 18 pages. [14] D. Stoyan and H. Stoyan. Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. XIV. John Wiley & Sons, Chichester etc., 1994, 389p. [15] O. Yu. Vorobyev. On the set characteristics of states of distributed probability processes. Izvestia of SB AS USSR, 3(3):3–7, 1977. [16] O. Yu. Vorobyev. Mean Measure Modeling. Nauka, Moscow, 1984. [17] O. Yu. Vorobyev. Set Summation. Nauka, Novosibirsk, Russia, 1993. [18] O. Yu. Vorobyev. Eventology. Siberian Federal University, Krasnoyarsk, Russia, 2007, 435p., https://www.academia.edu/179393/. [19] O. Yu. Vorobyev. Event means in eventology, its asymptotic properties, interpretations, and visualization. In. Proc. of the XVI Intern. EM conference on eventological mathematics and related fields, Krasnoyarsk: SFU (Oleg Vorobyev ed.):50–56, 2012. [20] O. Yu. Vorobyev. A mean probability event for a set of events. In. Proc. of the XI Intern. FAMES Conf. on Financial and Actuarial Mathematics and Eventology of Safety, Krasnoyarsk, SFU (Oleg Vorobyev ed.):139–147, 2012, http://fam.conf.sfukras.ru/adds/fames20120516eversion.pdf. [21] O. Yu. Vorobyev. In search of a primary source: remaking the paper (1975) where at the first time a definition of the lattice (Vorob’ev) expectation of a random set was given. In. Proc. of the XII Intern. FAMES Conf. on Financial and Actuarial Mathematics and Eventology of Safety, Krasnoyarsk, SFU (Oleg Vorobyev ed.):33–39, 2013, https://www.academia.edu/3727012. [22] O. Yu. Vorobyev. Postulating the theory of experience and chance as a theory of co~events (co~beings). In. Proc. of the XIV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics & the Workshop on Hilbert’s Sixth Problem, Krasnoyarsk, SFU (Oleg Vorobyev ed.):28–47, 2016; ISBN 9785990335868, https://www.academia.edu/34373279. [23] O. Yu. Vorobyev. An elementset labelling a Cartesian product by measurable binary relations which leads to postulates of the theory of experience and chance as a theory of co~events. In. Proc. of the XIV Intern. FAMEMS Conf. on Financial and Actuarial Mathematics and Eventology of Multivariate Statistics & the Workshop on Hilbert’s Sixth Problem, Krasnoyarsk, SFU (Oleg Vorobyev ed.):11–27, 2016; ISBN 9785990335868, https://www.academia.edu/34390291. [24] O. Yu. Vorobyev and N. A. Lukyanova. A mean probability event for a set of events. Journal of Siberian Federal University. Mathematics & Physics, 6(1):128–136, 2013, https://www.academia.edu/2328936. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/81893 