Standard Axioms Research Articles

The Nudging Divide in the Digital Big Data Era

Since the end of the 1970ies a wide range of psychological, economic and sociological laboratory and field experiments proved human beings deviating from rational choices and standard neo-classical profit maximization axioms to fail to explain how human actually behave. Behavioral economists proposed to nudge and wink citizens to make better choices for them with many different applications. While the motivation behind nudging appears as a noble endeavor to foster peoples’ lives around the world in very many different applications, the nudging approach raises questions of social hierarchy and class division. The motivating force of the nudgital society may open a gate of exploitation of the populace and – based on privacy infringements – stripping them involuntarily from their own decision power in the shadow of legally-permitted libertarian paternalism and under the cloak of the noble goal of welfare-improving global governance. Nudging enables nudgers to plunder the simple uneducated citizen, who is neither aware of the nudging strategies nor able to oversee the tactics used by the nudgers. The nudgers are thereby legally protected by democratically assigned positions they hold or by outsourcing strategies used, in which social media plays a crucial rule. Social media forces are captured as unfolding a class dividing nudgital society, in which the provider of social communication tools can reap surplus value from the information shared of social media users. The social media provider thereby becomes a capitalist-industrialist, who benefits from the information shared by social media users, or so-called consumer-workers, who share private information in their wish to interact with friends and communicate to public. The social media capitalist-industrialist reaps surplus value from the social media consumer-workers’ information sharing, which stems from nudging social media users. For one, social media space can be sold to marketers who can constantly penetrate the consumer-worker in a subliminal way with advertisements. But also nudging occurs as the big data compiled about the social media consumer-worker can be resold to marketers and technocrats to draw inferences about consumer choices, contemporary market trends or individual personality cues used for governance control, such as, for instance, border protection and tax compliance purposes. The law of motion of the nudging societies holds an unequal concentration of power of those who have access to compiled data and who abuse their position under the cloak of hidden persuasion and in the shadow of paternalism. In the nudgital society, information, education and differing social classes determine who the nudgers and who the nudged are. Humans end in different silos or bubbles that differ in who has power and control and who is deceived and being ruled. The owners of the means of governance are able to reap a surplus value in a hidden persuasion, protected by the legal vacuum to curb libertarian paternalism, in the moral shadow of the unnoticeable guidance and under the cloak of the presumption that some know what is more rational than others. All these features lead to an unprecedented contemporary class struggle between the nudgers (those who nudge) and the nudged (those who are nudged), who are divided by the implicit means of governance in the digital scenery. In this light, governing our common welfare through deceptive means and outsourced governance on social media appears critical. In combination with the underlying assumption of the nudgers knowing better what is right, just and fair within society, the digital age and social media tools hold potential unprecedented ethical challenges.

Proportional rules for state contingent claims

We consider rationing problems where the claims are state contingent. Before the state is realized individuals submit claims for every possible state of the world. A rule distributes resources before the realization of the state of the world. We introduce two natural extensions of the proportional rule in this framework, namely, the ex-ante proportional rule and the ex-post proportional rule, and then we characterize them using standard axioms from the literature.

Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories

Assuming the standard axioms for quaternionic quantum theory and a spatially localized scattering interaction, the $S$-matrix in quaternionic quantum theory is complex valued, not quaternionic. Using the standard connections between the $S$-matrix, the forward scattering amplitude for electromagnetic wave scattering, and the index of refraction, we show that the index of refraction is necessarily complex, not quaternionic. This implies that the recent optical experiment of Procopio et al. based on the Peres proposal does not test for hyper-complex or quaternionic quantum effects arising within the standard Hilbert space framework. Such a test requires looking at near zone fields, not radiation zone fields.

No interesting sequential groups

We prove that it is consistent with ZFC that no sequential topological groups of intermediate sequential orders exist. This shows that the answer to a 1981 question of P. Nyikos is independent of the standard axioms of set theory. The model constructed also provides consistent answers to several questions of D. Shakhmatov, S. Todorčević and Uzcátegui. In particular, we show that it is consistent with ZFC that every countably compact sequential group is Fréchet–Urysohn.

The axiom of equivalence to individual power and the Banzhaf index

I introduce a new axiom for power indices on the domain of finite simple games that requires the total power of any given pair i,j of players in any given game v to be equivalent to some individual power, i.e., equal to the power of some single player k in some game w. I show that the Banzhaf power index is uniquely characterized by this new “equivalence to individual power” axiom in conjunction with the standard semivalue axioms: transfer (which is the version of additivity adapted for simple games), symmetry or equal treatment, positivity (which is strengthened to avoid zeroing-out of the index on some games), and dummy.

Nudgitize Me! A Behavioral Finance Approach to Minimize Losses and Maximize Profits from Heuristics and Biases

Behavioral Finance is one of the most novel developments in Behavioral Economics. Since the end of the 1970ies a wide range of psychological, economic and sociological laboratory and field experiments proved human beings deviating from rational choices and standard neo-classical profit maximization axioms that fail to explain how human actually behave. Human beings were rather found to use heuristics in the day-to-day decision making. These mental short cuts enable to cope with information overload in a complex world. Behavioral economists proposed to nudge and wink citizens to make better choices for them with many different applications in very many different domains. This paper reviews and proposes how to use mental heuristics, biases and nudges in the finance domain to profit from markets.

Nudgital: Critique of Behavioral Political Economy

Behavioral Economics revolutionized mainstream neo-classical economics. A wide range of psychological, economic and sociological laboratory and field experiments proved human beings deviating from rational choices as standard neo-classical profit maximization axioms failed to explain how human actually behave. Human beings rather use heuristics in their day-to-day decision making. These mental short cuts enable to cope with a complex world yet also often leave individuals biased and falling astray to decision making failures. What followed was the powerful extension of these behavioral insights for public administration and public policy making. Behavioral economists proposed to nudge and wink citizens to make better choices for them and the community. Many different applications of rational coordination followed ranging from improved organ donations, health, wealth and time management, to name a few. Yet completely undescribed remains that the implicit hidden persuasion opens a gate to deception and is an unprecedented social class division means. Social media forces are captures as unfolding a class dividing nudgital society, in which the provider of social communication tools can reap surplus value from the information shared of social media users. The social media provider is outlined as capitalist-industrialist, who benefits from the information shared by social media users, or so-called consumer-workers, who share private information in their wish to interact with friends and communicate to public. The social media capitalist-industrialist reaps surplus value from the social media consumer-workers’ information sharing, which stems from nudging social media users. For one, social media space can be sold to marketers who can constantly penetrate the consumer-worker in a subliminal way with advertisements. But also nudging occurs as the big data compiled about the social media consumer-worker can be resold to marketers and technocrats to draw inferences about consumer choices, contemporary market trends or individual personality cues used for governance control, such as, for instance, border protection and tax compliance purposes. To draw attention to this implicit struggle within society is important for various reasons: Addressing the nudgital society allows to better understand the laws of motion of governance in the digital age, leading to the potentially unequal accumulation and concentration of power. Technological improvement in the age of information has increased the possibilities to control the innocent social media users and reap the benefits of their existence in hidden persuasion. In the age of populism, nudging can be criticized to be used by the ruling class to exploit the governed populace. In modern democracies, the right to rule was recently proven to be plundered in democratic votes through misguiding information of alternative facts and fake news circulated on social media. The socio-ethical crises that are rooted in the contradictory class division of the nudgital society are presented in this paper for the first time and from there on demand for further description and research on capitalism and democracy in the digital age. The paper advocates for a democratisation of information, education about nudges and well-informed distribution of transparent governance control.

Allais, Ellsberg, and preferences for hedging

Two of the most well-known regularities of preferences under risk and uncertainty are ambiguity aversion and the Allais paradox. We study the behavior of an agent who can display both tendencies at the same time. We introduce a novel notion of preference for hedging that applies to both objective lotteries and uncertain acts, and captures both aversion to ambiguity and attraction towards certainty in objective lotteries. We show that this axiom, together with other standard axioms, is equivalent to two representations that generalize the MaxMin Expected Utility model of Gilboa and Schmeidler (1989). In both representations the agent evaluates ambiguity using multiple priors, but does not use Expected Utility to evaluate objective lotteries. In the rst representation, lotteries are evaluated by distorting probabilities as in the Rank Dependent Utility model, but using the worst from a set of such distortions. In the second, equivalent, representation the agent treats objective lotteries as ‘ambiguous objects,’ and uses a set of priors to evaluate them. We show that a preference for hedging is not sucient to guarantee an Ellsberg-like behavior if the agent violates Expected

Normative Utility Models for Pareto Scalar Equilibria in n-Person, Semi-Cooperative Games in Strategic Form

Semi-cooperative games in strategic form are considered in which either a negotiation among the n players determines their actions or else an arbitrator specifies them. Methods are presented for selecting such action profiles by using multiple-objective optimization techniques. In particular, a scalar equilibrium (SE) is an action profile for the n players that maximize a utility function over the acceptable joint actions. Thus the selection of “solutions” to the game involves the selection of an acceptable utility function. In a greedy SE, the goal is to assign individual actions giving each player the largest payoff jointly possible. In a compromise SE, the goal is to make individual player payoffs equitable, while a satisficing SE achieves a target payoff level while weighting each player for possible additional payoff. These SEs are formally defined and shown to be Pareto optimal over the acceptable joint actions of the players. The advantage of these SEs is that they involve only pure strategies that are easily computed. Examples are given, including some well-known coordination games, and the worst-case time complexity for obtaining these SEs is shown to be linear in the number of individual payoffs in the payoff matrix. Finally, the SEs of this paper are checked against some standard game-theoretic bargaining axioms.

Boundedly Rational Expected Utility Theory

We build a satisficing model of probabilistic choice under risk which embeds Expected Utility Theory (EUT) into a boundedly rational deliberation process. The decision maker accumulates evidence for and against alternative options by repeatedly sampling from her underlying set of EU preferences until the evidence favouring one option satisfies her desired level of confidence. Notwithstanding its EUT core, the model produces patterns of behaviour that violate standard axioms, while at the same time capturing the systematic relationship between choice probabilities, response times and confidence judgments, which is beyond the scope of theories that do not take deliberation into account.

Supporters and Underminers: Reply to Chandler

I argue that two of the standard axioms of the AGM theory of belief revision stand in the way of it serving as the basis for an adequate account of defeasible reasoning, because they respectively disallow the adoption of beliefs not logically entailed by those previously learned and the abandonment of those not contradicted by them.

Stability concepts in matching under distributional constraints

Many real matching markets are subject to distributional constraints. To guide market designers faced with constraints, we propose new stability concepts. A matching is strongly stable if satisfying blocking pairs inevitably violates a constraint. We show that a strongly stable matching may not exist, and that existence is guaranteed if and only if all distributional constraints are trivial. To overcome this difficulty, we propose a more permissive concept, weak stability. We demonstrate a weakly stable matching always exists, implies efficiency, and is characterized by standard normative axioms. These results are obtained in a more general environment than those in existing studies, accommodating a wide variety of applications.

Towards a Constructive Foundation of Quantum Mechanics

I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of Quantum Mechanics. The quantum mechanical description is identified as a tool that allows describing objects with discrete degrees of freedom in space-time covariant with respect to coordinate transformations. An inherent property of this description is a quantum mechanical interaction mechanism. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of Quantum Mechanics.

A characterization of the Gini segregation index

This paper gives an axiomatic characterization of the Gini index of segregation. We use some standard axioms along with an independence axiom that is related to the dual independence axiom of Yaari’s dual theory of choice under risk.

Potential Infinity, Abstraction Principles and Arithmetic (Leśniewski Style)

This paper starts with an explanation of how the logicist research program can be approached within the framework of Leśniewski’s systems. One nice feature of the system is that Hume’s Principle is derivable in it from an explicit definition of natural numbers. I generalize this result to show that all predicative abstraction principles corresponding to second-level relations, which are provably equivalence relations, are provable. However, the system fails, despite being much neater than the construction of Principia Mathematica (PM). One of the key reasons is that, just as in the case of the system of PM, without the assumption that infinitely many objects exist, (renderings of) most of the standard axioms of Peano Arithmetic are not derivable in the system. I prove that introducing modal quantifiers meant to capture the intuitions behind potential infinity results in the (renderings of) axioms of Peano Arithmetic (PA) being valid in all relational models (i.e. Kripke-style models, to be defined later on) of the extended language. The second, historical part of the paper contains a user-friendly description of Leśniewski’s own arithmetic and a brief investigation into its properties.

An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise

In this paper, we offer for two-person games an alternative characterization of Iterated Kalai-Smorodinsky-Nash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$-person games. We present an axiom called Gamma-Decomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by Gamma-Decomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry.

Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions

We reconsider the class of weighted Kalai-Smorodinsky solutions of Dubra (Econ Lett 73:131–136, 2001), and using methods of Imai (Econometrica 51:389–401, 1983), extend their characterization to the domain of multilateral bargaining problems. Aside from standard axioms in the literature, this result involves a new property that weakens the axiom Bilateral Consistency (Lensberg, J Econ Theory 45:330–341, 1988), by making the notion of consistency dependent on how ideal values in a reduced problem change relative to the original problem.

VPHL: A Verified Partial-Correctness Logic for Probabilistic Programs

We introduce a Hoare-style logic for probabilistic programs, called VPHL, that has been formally verified in the Coq proof assistant. VPHL features propositional, rather than additive, assertions and a simple set of rules for reasoning about these assertions using the standard axioms of probability theory. VPHL's assertions are partial correctness assertions, meaning that their conclusions are dependent upon (deterministic) program termination. The underlying simple probabilistic imperative language, PrImp, includes a probabilistic toss operator, probabilistic guards and potentially-non-terminating while loops.

Subjective probability, confidence, and Bayesian updating

I define subjective probabilities for an ambiguity averse agent who is given an exogenous information set\(\varDelta \) containing the true probability law on the state space S. The agent in my model evaluates every uncertain prospect via a mixture of the least favorable scenario in \(\varDelta \) and her unique subjective beliefp. This parametric utility structure is characterized by four standard axioms—order, continuity, monotonicity, and Independence—where the last two conditions are modified via the information set \(\varDelta \). Any pair of preferences \(\succeq _1\) and \(\succeq _2\) in my model can be compared in terms of confidence—the weights attached to the subjective beliefs \(p_1\) and \(p_2\), respectively. The corresponding behavioral condition extends Epstein’s comparative ambiguity aversion that leaves some rankings \(\succeq _1\) and \(\succeq _2\) unrelated. Moreover, I relax the well-known dynamic consistency principle and characterize the Bayesian updating rule for the belief p conditional on any non-null event in S.

An Argument Against Cobb-Douglas Production Functions (in Multi-Sector-Growth Modeling)

The Cobb-Douglas production function (henceforth, "CDPF") is a widespread and useful tool in growth theory. However, the empirical evidence regarding the adequacy of the (aggregate) CDPF has been discussed controversially. By using an axiomatic/geometrical approach, we show that sector-level CDPFs are not consistent with standard theory axioms and long-run stylized facts of sector and aggregate dynamics. This result can be regarded as an empirical rejection of the CDPF (at sector level) on the basis of qualitative, very long-run data. We discuss the implications of this result for the growing structural change literature.