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  1. Social choice of convex risk measures through Arrovian aggregation of variational preferences
    Autor*in: Herzberg, Frederik
    Erschienen: 2015
    Verlag:  Bielefeld University, Center for Mathematical Economics, Bielefeld

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  2. Aggregating infinitely many probability measures
    Autor*in: Herzberg, Frederik
    Erschienen: 2014
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single 'aggregate belief system' and... mehr

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    Helmut-Schmidt-Universität, Universität der Bundeswehr Hamburg, Universitätsbibliothek
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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
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    The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single 'aggregate belief system' and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected-utility preferences. We describe how McConway's (Journal of the American Statistical Association, vol. 76, no. 374, pp. 410-414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely-additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.

     
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    hdl: 10419/97218
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 499
    Institute of Mathematical Economics Working Paper ; No. 499
    Umfang: Online-Ressource (19 S.), graph. Darst.
  3. Aggregation of Monotonic Bernoullian Archimedean preferences
    Arrovian impossibility results
    Autor*in: Herzberg, Frederik
    Erschienen: 2013
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA)... mehr

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    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently proposed a very general axiomatisation of preferences in the presence of ambiguity, viz. Monotonic Bernoullian Archimedean (MBA) preference orderings. This paper investigates the problem of Arrovian aggregation of such preferences - and proves dictatorial impossibility results for both finite and infinite populations. Applications for the special case of aggregating expected-utility preferences are given. A novel proof methodology for special aggregation problems, based on model theory (in the sense of mathematical logic), is employed.

     
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    hdl: 10419/97235
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 488
    Institute of Mathematical Economics Working Paper ; No. 488
    Umfang: Online-Ressource ([15] S.)
  4. Weak approximation of G-expectation
    Autor*in: Fadina, Tolulope; Herzberg, Frederik
    Erschienen: 2014
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    We refine the discretization of G-expectation by Y. Dolinsky, M.Nutz, and M. Soner (Stochastic Processes and their Applications, 122 (2012), 664-675), in order to obtain a discretization of sublinear expectation where the martingale laws are defined... mehr

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    We refine the discretization of G-expectation by Y. Dolinsky, M.Nutz, and M. Soner (Stochastic Processes and their Applications, 122 (2012), 664-675), in order to obtain a discretization of sublinear expectation where the martingale laws are defined on a finite lattice rather than the whole set of reals.

     
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    hdl: 10419/97220
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 503
    Institute of Mathematical Economics Working Paper ; No. 503
    Umfang: Online-Ressource (12 S.)
  5. Failure of ad valorem and specific tax equivalence under uncertainty
    Autor*in: Goerke, Laszlo; Herzberg, Frederik; Upmann, Thorsten
    Erschienen: 2012
    Verlag:  IAAEU, Trier

    Applying a framework of perfect competition under uncertainty, we contribute to the discussion of whether or not ad valorem taxes and specific taxes are equivalent. While this equivalence holds without price uncertainty, we show that ad valorem taxes... mehr

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    Applying a framework of perfect competition under uncertainty, we contribute to the discussion of whether or not ad valorem taxes and specific taxes are equivalent. While this equivalence holds without price uncertainty, we show that ad valorem taxes and specific taxes are "almost never" equivalent in the presence of uncertainty if we demand equivalence to hold pathwise. Since we obtain this result under perfect competition, our analysis also provides a further rationale for why the equivalence must fail under imperfect competition. -- ad valorem taxes and specific taxes ; revenue neutrality ; price uncertainty ; concept of pathwise neutrality

     
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    hdl: 10419/80875
    Schriftenreihe: IAAEU discussion paper series in economics / IAAEG ; 05/2012
    Schlagworte: Umsatzsteuer; Verbrauchsteuer; Steuereinnahmen; Wettbewerb; Risiko; Theorie
    Umfang: Online-Ressource (PDF-Datei: 20 S., 332,11 KB)
  6. Failure of ad valorem and specific tax equivalence under uncertainty
    Autor*in: Goerke, Laszlo; Herzberg, Frederik; Upmann, Thorsten
    Erschienen: 2012
    Verlag:  CESifo, München

    Applying a framework of perfect competition under uncertainty, we contribute to the discussion of whether or not ad valorem taxes and specific taxes are equivalent. While this equivalence holds without price uncertainty, we show that ad valorem taxes... mehr

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    Applying a framework of perfect competition under uncertainty, we contribute to the discussion of whether or not ad valorem taxes and specific taxes are equivalent. While this equivalence holds without price uncertainty, we show that ad valorem taxes and specific taxes are "almost never" equivalent in the presence of uncertainty if we demand equivalence to hold pathwise. Since we obtain this result under perfect competition, our analysis also provides a further rationale for why the equivalence must fail under imperfect competition. -- ad valorem taxes and specific taxes ; revenue neutrality ; price uncertainty ; concept of pathwise neutrality

     
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    Weitere Identifier:
    hdl: 10419/65396
    RVK Klassifikation: QB 910
    Schriftenreihe: Array ; 3946
    Schlagworte: Umsatzsteuer; Verbrauchsteuer; Steuereinnahmen; Wettbewerb; Risiko; Theorie
    Umfang: Online-Ressource (PDF-Datei: 20 S., 225 KB)
  7. An algebraic approach to general aggregation theory
    propositional-attitude aggregators as MV-homomorphisms
    Autor*in: Herzberg, Frederik
    Erschienen: 2011
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework... mehr

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    This paper continues Dietrich and List's [2010] work on propositional-attitude aggregation theory, which is a generalised unification of the judgment-aggregation and probabilistic opinion-pooling literatures. We first propose an algebraic framework for an analysis of (many-valued) propositional-attitude aggregation problems. Then we shall show that systematic propositional-attitude aggregators can be viewed as homomorphisms in the category of C.C. Chang's [1958] MV-algebras. Since the 2-element Boolean algebra as well as the real unit interval can be endowed with an MV-algebra structure, we obtain as natural corollaries two famous theorems: Arrow's theorem for judgment aggregation as well as McConway's [1981] characterisation of linear opinion pools. -- propositional attitude aggregation ; judgment aggregation ; linear opinion pooling ; Arrow's impossibility theorem ; many-valued logic ; MV-algebra ; homomorphism ; Arrow's impossibility theorem ; functional equation

     
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    hdl: 10419/81123
    Schriftenreihe: Working papers / Institute of Mathematical Economics ; 445
    Schlagworte: Meinung; Aggregation; Unmöglichkeitstheorem; Theorie
    Umfang: Online-Ressource (PDF-Datei: 12 S., 278,18 KB)
  8. A representative individual from arrovian aggregation of parametric individual utilities
    Autor*in: Herzberg, Frederik
    Erschienen: 2009
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    This article investigates the representative-agent hypothesis for an infinite population which has to make a social choice from a given finite-dimensional space of alternatives. It is assumed that some class of admissible strictly concave utility... mehr

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    This article investigates the representative-agent hypothesis for an infinite population which has to make a social choice from a given finite-dimensional space of alternatives. It is assumed that some class of admissible strictly concave utility functions is exogenously given and that each individual's preference ordering can be represented cardinally through some admissible utility function. In addition, we assume that (i) the class of admissible utility functions allows for a smooth parametrization, and (ii) the social welfare function satisfies Arrovian rationality axioms. We prove that there exists an admissible utility function r, called representative utility function, such that any alternative which maximizes r also maximizes the social welfare function. The proof utilizes a special nonstandard model of the reals, viz. the ultraproduct of the reals with respect to the ultrafilter of decisive coalitions; this construction explicitly determines the parameter vector of the representative utility function. -- Representative individual ; Arrovian social choice ; Ultrafilter ; Ultraproduct ; Nonstandard analysis

     
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    hdl: 10419/43804
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 411
    Schlagworte: Nutzenfunktion; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie
    Umfang: Online-Ressource (PDF-Datei: 17 S., 169 KB)
  9. It all depends on independence
    Autor*in: Eckert, Daniel; Herzberg, Frederik
    Erschienen: 2009
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    Eliaz (2004) has established a "meta-theorem" for preference aggregation which implies both Arrow's Theorem (1963) and the Gibbard-Satterthwaite Theorem (1973, 1975). This theorem shows that the driving force behind impossibility theorems in... mehr

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    Eliaz (2004) has established a "meta-theorem" for preference aggregation which implies both Arrow's Theorem (1963) and the Gibbard-Satterthwaite Theorem (1973, 1975). This theorem shows that the driving force behind impossibility theorems in preference aggregation is the mutual exclusiveness of Pareto optimality, individual responsiveness (preference reversal) and non-dictatorship. Recent work on judgment aggregation has obtained important generalizations of both Arrow's Theorem (List and Pettit 2003, Dietrich and List 2007a) and the Gibbard-Satterthwaite Theorem (Dietrich and List 2007b). One might ask, therefore, whether the impossibility results in judgment aggregation can be unified into a single theorem, a meta-theorem which entails the judgment-aggregation analogues of both Arrow's Theorem and the Gibbard-Satterthwaite Theorem. For this purpose, we study strong monotonicity properties (among them non-manipulability) and their mutual logical dependences. It turns out that all of these monotonicity concepts are equivalent for independent judgment aggregators, and the strongest monotonicity concept, individual responsiveness, implies independence. We prove the following meta-theorem: Every systematic non-trivial judgment aggregator is oligarchic in general and even dictatorial if the collective judgment set is complete. However, systematicity is equivalent to independence for blocked agendas. Hence, as a corollary, we obtain that every independent (in particular, every individually responsive) non-trivial judgment aggregator is oligarchic. This result is a mild generalization of a similar theorem of Dietrich and List (2008), obtained by very different methods. Whilst Eliaz (2004) and Dietrich and List (2008) use sophisticated combinatorial and logical arguments to prove their results, we utilize the filter method (cf. e.g. Dietrich and Mongin, unpublished) and obtain a much simpler and more intuitive derivation of our meta-theorem. -- Judgment aggregation ; Independence axiom ; Monotonicity axiom ; Oligarchy ; Impossibility results ; Non-manipulability ; Partial rationality

     
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    hdl: 10419/43766
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 412
    Schlagworte: Nutzenfunktion; Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie
    Umfang: Online-Ressource (PDF-Datei: 18 S., 366 KB)
  10. Judgement aggregators and boolean algebra homomorphism
    Autor*in: Herzberg, Frederik
    Erschienen: 2009
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii)... mehr

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    The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent complete judgment aggregators and (ii) 2-valued Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Since the shell of such a homomorphism equals the set of winning coalitions and since (ultra)filters are shells of (2-valued) Boolean algebra homomorphisms, we suggest an explanation for the effectiveness of the (ultra)filter method in social choice theory. From the (ultra)filter property of the set of winning coalitions, one obtains two general impossibility theorems for judgment aggregation on finite electorates, even without the Pareto principle. -- Judgment aggregation ; Systematicity ; Impossibility theorems ; Filter ; Ultrafilter ; Boolean algebra homomorphism

     
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    hdl: 10419/43814
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 414
    Schlagworte: Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie
    Umfang: Online-Ressource (PDF-Datei: 11 S., 216 KB)
  11. Judgment aggregation functions and ultraproducts
    Autor*in: Herzberg, Frederik
    Erschienen: 2008
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic... mehr

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    The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic judgment aggregation functions is established. The proof constructs an ultraproduct of profiles, viewed as propositional structures, with respect to the ultrafilter of decisive coalitions. This representation theorem can be used to prove other properties of such judgment aggregation functions, in particular sovereignty and monotonicity, as well as an impossibility theorem for judgment aggregation in finite populations. As a corollary, Lauwers and Van Liedekerke's (1995) representation theorem for preference aggregation functions is derived. -- Judgment aggregation function ; Ultraproduct ; Ultrafilter

     
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    hdl: 10419/43817
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 405
    Schlagworte: Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Theorie
    Umfang: Online-Ressource (PDF-Datei: 14 S., 180 KB)
  12. Linear hyperfinite Lévy integrals
    Autor*in: Herzberg, Frederik
    Erschienen: 2008
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 functions of) jump-diffusions... mehr

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    This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 functions of) jump-diffusions with finite-variation jump part. It is proven that internal stochastic integrals with respect to hyperfinite Lévy processes possess right standard parts, and that these standard parts coincide with the classical pathwise stochastic integrals, provided the integrator's jump part is of finite variation. If the integrator's Lévy measure is bounded from below, one can obtain a similar result for stochastic integrals with respect to C^2 functions of Lévy processes. As a by-product, this yields a short, direct nonstandard proof of the generalized Itô formula for stochastic differentials of smooth functions of Lévy processes. -- Lévy processes ; Stochastic integration ; Nonstandard analysis ; Itô formula

     
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    hdl: 10419/43770
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 404
    Schlagworte: Analysis; Stochastischer Prozess; Theorie
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  13. On the foundations of Lévy finance
    equilibrium for a single-agent financial market with jumps
    Autor*in: Herzberg, Frederik
    Erschienen: 2008
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before,... mehr

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    For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's utility function is assumed to be additive, defined via strictly increasing, strictly concave smooth felicity functions which are bounded below (thus, many CRRA and CARA utility functions are included). For technical reasons we require that only pathwise continuous trading strategies are permitted in the demand set. The resulting equilibrium prices depend on the agent's risk-aversion through the felicity functions. It turns out that these prices will be the (stochastic) exponential of a Lévy process essentially only if this process is geometric Brownian motion. -- Financial equilibrium ; Asset pricing ; Representative agent models ; Lévy processes ; Nonstandard analysis

     
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    hdl: 10419/43761
    Schriftenreihe: Working papers //Institute of Mathematical Economics ; 406
    Schlagworte: CAPM; Stochastischer Prozess; Kapitalmarkttheorie; Theorie
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  14. General aggregation problems and social structure
    a model-theoretic generalisation of the Kirman-Sondermann correspondence
    Autor*in: Herzberg, Frederik; Eckert, Daniel
    Erschienen: 2009
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    This article proves a very general version of the Kirman-Sondermann [Journal of Economic Theory, 5(2):267-277, 1972] correspondence by extending the methodology of Lauwers and Van Liedekerke [Journal of Mathematical Economics, 24(3):217-237, 1995].... mehr

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    This article proves a very general version of the Kirman-Sondermann [Journal of Economic Theory, 5(2):267-277, 1972] correspondence by extending the methodology of Lauwers and Van Liedekerke [Journal of Mathematical Economics, 24(3):217-237, 1995]. The paper first proposes a unified framework for the analysis of the relation between various aggregation problems and the social structure they induce, based on first-order predicate logic and model theory. Thereafter, aggregators satisfying Arrow-type rationality axioms are shown to be restricted reduced product constructions with respect to the filter of decisive coalitions; an oligarchic impossibility result follows. Under stronger assumptions, aggregators are restricted ultraproduct constructions, whence a generalized Kirman-Sondermann correspondence as well as a dictatorial impossiblity result follow. -- Arrow-type preference aggregation ; Judgment aggregation ; Systematicity ; Model theory ; First-order predicate logic ; Filter ; Ultrafilter

     
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    hdl: 10419/43824
    Schriftenreihe: Working papers / Institute of Mathematical Economics ; 424
    Schlagworte: Nutzenfunktion; Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie
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  15. Existence of financial equilibria in continuous time with potentially complete markets
    Autor*in: Riedel, Frank; Herzberg, Frederik
    Erschienen: 2010
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist. -- Potentially complete market ; Continuous-time financial ; market ; Radner equilibrium... mehr

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    We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist. -- Potentially complete market ; Continuous-time financial ; market ; Radner equilibrium ; Itô diffusion ; Analytic transition density

     
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    hdl: 10419/43800
    Schriftenreihe: Working papers / Institute of Mathematical Economics ; 443
    Schlagworte: Kapitalmarkttheorie; Gleichgewichtsmodell; Stochastischer Prozess; Unvollkommener Markt; Theorie
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  16. Social choice of convex risk measures through Arrovian aggregation of variational preferences
    Autor*in: Herzberg, Frederik
    Erschienen: 2010
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    This paper studies collective decision making with regard to convex risk measures: It addresses the question whether there exist nondictatorial aggregation functions of convex risk measures satisfying Arrow-type rationality axioms (weak universality,... mehr

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    This paper studies collective decision making with regard to convex risk measures: It addresses the question whether there exist nondictatorial aggregation functions of convex risk measures satisfying Arrow-type rationality axioms (weak universality, systematicity, Pareto principle). Herein, convex risk measures are identified with variational preferences on account of the Maccheroni-Marinacci-Rustichini (2006) axiomatisation of variational preference relations and the Föllmer-Schied (2002, 2004) representation theorem for concave monetary utility functionals. We prove a variational analogue of Arrow's impossibility theorem for finite electorates. For infinite electorates, the possibility of rational aggregation depends on a uniform continuity condition for the variational preference profiles; we prove variational analogues of both Campbell's impossibility theorem and Fishburn's possibility theorem. The proof methodology is based on a model-theoretic approach to aggregation theory inspired by Lauwers-Van Liedekerke (1995). An appendix applies the Dietrich-List (2010) analysis of majority voting to the problem of variational preference aggregation. -- Arrow-type preference aggregation ; judgment aggregation ; abstract aggregation theory ; variational preferences ; multiple priors preferences ; convex risk measure ; model theory ; first-order predicate logic ; ultrafilter ; ultraproduct

     
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    hdl: 10419/43803
    Schriftenreihe: Working papers / Institute of Mathematical Economics ; 432
    Schlagworte: Nutzenfunktion; Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Risikomaß; Unmöglichkeitstheorem; Theorie
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  17. Impossibility results for infinite-electorate abstract aggregation rules
    Autor*in: Herzberg, Frederik; Eckert, Daniel
    Erschienen: 2009
    Verlag:  Inst. of Mathematical Economics, IMW, Bielefeld

    It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultrafilter on... mehr

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    It is well known that the literature on judgment aggregation inherits the impossibility results from the aggregation of preferences that it generalises. This is due to the fact that the typical judgment aggregation problem induces an ultrafilter on the the set of individuals, as was shown in a model theoretic framework by Herzberg and Eckert (2009), generalising the Kirman-Sondermann correspondence and extending the methodology of Lauwers and Van Liedekerke (1995). In the finite case, dictatorship then immediately follows from the principality of an ultrafilter on a finite set. This is not the case for an infinite set of individuals, where there exist free ultrafilters, as Fishburn already stressed in 1970. The main problem associated with free ultrafilters in the literature on aggregation problems is however, the arbitrariness of their selection combined with the limited anonymity they guarantee (which already led Kirman and Sondermann (1972) to speak about invisible dictators). Following another line of Lauwers and Van Liedekerke's (1995) seminal paper, this note explores another source of impossibility results for free ultrafilters: The domain of an ultraproduct over a free ultrafilter extends the individual factor domains, such that the preservation of the truth value of some sentences by the aggregate model --- if this is as usual to be restricted to the original domain --- may again require the exclusion of free ultrafilters, leading to dictatorship once again. -- Arrow-type preference aggregation ; judgment aggregation ; model theory ; first-order predicate logic ; filter ; ultrafilter ; reduced product ; ultraproduct ; existential quantifier

     
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    hdl: 10419/43798
    Schriftenreihe: Working papers / Institute of Mathematical Economics ; 427
    Schlagworte: Nutzenfunktion; Präferenztheorie; Aggregation; Soziale Wohlfahrtsfunktion; Unmöglichkeitstheorem; Theorie
    Umfang: Online-Ressource (PDF-Datei: 9 S., 324,24 KB)
  18. Arrovian aggregation of MBA preferences
    an impossibility result ; conference paper
    Autor*in: Herzberg, Frederik
    Erschienen: 2013
    Verlag:  ZBW, [Kiel

    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently axiomatised preferences in the presence of ambiguity as Monotonic Bernoullian Archimedean (MBA) preferences. We investigate the... mehr

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    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently axiomatised preferences in the presence of ambiguity as Monotonic Bernoullian Archimedean (MBA) preferences. We investigate the problem of Arrovian aggregation of MBA preferences - and prove dictatorial impossibility results for both finite and infinite populations.

     
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    hdl: 10419/79957
    Schriftenreihe: Array ; V2
    Umfang: Online-Ressource (11 S.)
  19. Microeconomic foundations of representative agent models by means of ultraproducts
    Autor*in: Bedrosian, Geghard; Herzberg, Frederik
    Erschienen: 2014
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    This paper builds on a recent proposal for microeconomic foundations for "representative agents". Herzberg [Journal of Mathematical Economics, vol. 46, no. 6, 1115-1124 (2010)] constructed a representative utility function for infinite-dimensional... mehr

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    This paper builds on a recent proposal for microeconomic foundations for "representative agents". Herzberg [Journal of Mathematical Economics, vol. 46, no. 6, 1115-1124 (2010)] constructed a representative utility function for infinite-dimensional social decision problems and since the decision problems of macroeconomic theory are typically infinite-dimensional, Herzberg's original result is insufficient for many applications. We therefore generalise his result by allowing the social alternatives to belong to a general reflexive Banach space and provide sufficient conditions for our new results to be satisfied in economic applications.

     
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    hdl: 10419/103929
    Auflage/Ausgabe: Preliminary and incompletet
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 514
    Umfang: Online-Ressource (12 S.)
  20. Hyperfinite construction of G-expectation
    Autor*in: Fadina, Tolulope; Herzberg, Frederik
    Erschienen: 2015
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    We prove a lifting theorem, in the sense of Robinsonian nonstandard analysis, for the G-expectation. Herein, we use an existing discretization theorem for the G-expectation by T. Fadina and F. Herzberg (Bielefeld University, Center for Mathematical... mehr

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    We prove a lifting theorem, in the sense of Robinsonian nonstandard analysis, for the G-expectation. Herein, we use an existing discretization theorem for the G-expectation by T. Fadina and F. Herzberg (Bielefeld University, Center for Mathematical Economics in its series Working Papers, 503, (2014)).

     
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    hdl: 10419/111073
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 540
    Umfang: Online-Ressource (10 S.)
  21. Arrovian aggregation of MBA preferences
    an impossibility result ; conference paper
    Autor*in: Herzberg, Frederik
    Erschienen: 2013
    Verlag:  ZBW, [Kiel

    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently axiomatised preferences in the presence of ambiguity as Monotonic Bernoullian Archimedean (MBA) preferences. We investigate the... mehr

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    Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci and Siniscalchi (Economic Theory, 48:341-375, 2011) have recently axiomatised preferences in the presence of ambiguity as Monotonic Bernoullian Archimedean (MBA) preferences. We investigate the problem of Arrovian aggregation of MBA preferences - and prove dictatorial impossibility results for both finite and infinite populations.

     
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    hdl: 10419/79957
    Schriftenreihe: Array ; V2
    Umfang: Online-Ressource (11 S.)
  22. Respect for experts or respect for unanimity?
    the liberal paradox in probabilistic opinion pooling
    Autor*in: Herzberg, Frederik
    Erschienen: 2014
    Verlag:  Center for Mathematical Economics, IMW, Bielefeld

    Amartya Sen (1970) has shown that three natural desiderata for social choice rules are inconsistent: universal domain, respect for unanimity, and respect for some minimal rights - which can be interpreted as either expert rights or liberal rights.... mehr

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    Amartya Sen (1970) has shown that three natural desiderata for social choice rules are inconsistent: universal domain, respect for unanimity, and respect for some minimal rights - which can be interpreted as either expert rights or liberal rights. Dietrich and List (2008) have generalised this result to the setting of binary judgement aggregation. This paper proves that the liberal paradox holds even in the framework of probabilistic opinion pooling and discusses options to circumvent this impossibility result: restricting the aggregator domain to profiles with no potential for conflicting rights, or considering agendas whose issues are not all mutually interdependent.

     
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    hdl: 10419/103917
    Auflage/Ausgabe: Preliminary and incompletet
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 513
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  23. The birth of social choice theory from the spirit of mathematical logic
    Arrow's theorem in the framework of model theory
    Autor*in: Eckert, Daniel; Herzberg, Frederik
    Erschienen: March 2016
    Verlag:  Department of Economics, Department of Public Economics, University of Graz, Graz

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    Schriftenreihe: Graz economics papers ; GEP 2016-04
    Schlagworte: Arrow’s theorem; model theory; winning coalitions; ultrafilter; ultraproducts; Boolean algebra; homomorphism
    Umfang: 1 Online-Ressource (circa 19 Seiten)
  24. The transfer principle holds for definable nonstandard models under countable choice
    Autor*in: Herzberg, Frederik
    Erschienen: July 2016
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    Łos's theorem for (bounded) D-ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [Journal of Symbolic Logic, 69(1):159-164, 2004], can be established within Zermelo-Fraenkel set theory plus Countable Choice (ZF+ACw). Thus, the... mehr

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    Łos's theorem for (bounded) D-ultrapowers, D being the ultrafilter introduced by Kanovei and Shelah [Journal of Symbolic Logic, 69(1):159-164, 2004], can be established within Zermelo-Fraenkel set theory plus Countable Choice (ZF+ACw). Thus, the Transfer Principle for both Kanovei and Shelah's definable nonstandard model of the reals and Herzberg's definable nonstandard enlargement of the superstructure over the reals [Mathematical Logic Quarterly, 54(2):167-175; 54(6):666- 667, 2008] can be shown in ZF+ACw. This establishes a conjecture by Mikhail Katz [personal communication].

     
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    hdl: 10419/149017
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 560
    Umfang: 1 Online-Ressource (circa 9 Seiten)