Money Pump Research Articles

Probability discounting and money pumps

AbstractIn response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion on Independence generalizes to other views that also violate Independence.

Is economics credible? A critical appraisal of three examples from microeconomics

ABSTRACT Whether economics warrants public trust depends on the extent to which assertions by economists can be deemed credible. Three examples from microeconomics are examined to assess how the discipline performs in this regard. First, a purely theoretical argument with broad conceptual implications: a quasi-evolutionary argument for rational choice based on the notion of money pumps. Second, a modelling-related claim with significant social implications: economists’ objection to minimum wages based on a simple supply-demand model. Third, methodological choices with implications for all empirical work in microeconomics: the recent proclamation of a ‘credibility revolution’ in applied microeconomics through the use of experimental and quasi-experimental methods. These are assessed against proposed criteria for credibility: epistemic validity, epistemic reliability, and epistemic reflexivity. On the basis of the performance of the discipline against these criteria on the examples considered, I conclude that public distrust of economics and economists can be well-founded.

Rationality Now!

Rationality Now!

A Simpler, More Compelling Money Pump with Foresight

One might think that money pumps directed at agents with cyclic preferences can be avoided by foresight. This view was challenged two decades ago by the discovery of a money pump with foresight, which works against agents who use backward induction. But backward induction implausibly assumes that the agent would act rationally and retain her trust in her future rationality even at choice nodes that could only be reached if she were to act irrationally. This worry does not apply to BI-terminating decision problems, where at each choice node backward induction prescribes a move that terminates further action. For BI-terminating decision problems, it is enough to assume that rationality and trust in rationality are retained at choice nodes reachable by rational moves. The old money pump with foresight was not BI-terminating. In this paper, we present a new money pump with foresight, one that is both BI-terminating and considerably simpler.

Axiomatic rationality and ecological rationality

Axiomatic rationality is defined in terms of conformity to abstract axioms. Savage (The foundations of statistics, Wiley, New York, 1954) limited axiomatic rationality to small worlds (S, C), that is, situations in which the exhaustive and mutually exclusive set of future states S and their consequences C are known. Others have interpreted axiomatic rationality as a categorical norm for how human beings should reason, arguing in addition that violations would lead to real costs such as money pumps. Yet a review of the literature shows little evidence that violations are actually associated with any measurable costs. Limiting axiomatic rationality to small worlds, I propose a naturalized version of rationality for situations of intractability and uncertainty (as opposed to risk), all of which are not in (S, C). In these situations, humans can achieve their goals by relying on heuristics that may violate axiomatic rationality. The study of ecological rationality requires formal models of heuristics and an analysis of the structures of environments these can exploit. It lays the foundation of a moderate naturalism in epistemology, providing statements about heuristics we should use in a given situation. Unlike axiomatic rationality, ecological rationality can explain less-is-more effects (when using less information can be expected to generate more accurate predictions), formalize when one should move from ‘is’ to ‘ought,’ and be evaluated by goals beyond coherence, such as predictive accuracy, frugality, and efficiency. Ecological rationality can be seen as a formalization of means–end instrumentalist rationality, based on Herbert Simon’s insight that rational behavior is a function of the mind and its environment.

Opaque Sweetening and Transitivity

I argue that any plausible decision theory for agents with incomplete preferences which obeys the Never Worse Principle will violate Transitivity. The Never Worse Principle says that, if one option never does worse than another, you shouldn’t disprefer it. Transitivity says that, if you prefer X to Y and you prefer Y to Z, then you should prefer X to Z. Violating Transitivity allows one to be money pumped. Although agents with incomplete preferences are already, in virtue of having incomplete preferences, vulnerable to being money pumped, I argue that the money pump argument for Transitivity is more serious than the one for Completeness.

Ensemble prospectism

Incomplete preferences displaying ‘mildly sweetened’ structure are common, yet theoretically problematic. This paper examines the properties of the rankings induced by the set of all coherent completions of the mildly sweetened partial preference structure. Building on these properties, I propose an ensemble-based refinement of Hare’s (Analysis 70:237–247, 2010) prospectism criterion for rational choice when preferences are incomplete. Importantly, this ensemble-based refinement is immune to Peterson’s (Theory and Decision 78:451–456, 2015) weak money pump argument. Hence, ensemble prospectism ensures outcome rationality. Furthermore, by recognizing the structural isomorphism between mildly sweetened preference structures and Cover’s splitting rule in Blackwell’s Pick the Largest Number problem (Ann Math Stat 22:393–399, 1951), ensemble prospectism can be shown to yield better-than-even odds of selecting the ex-post higher utility option—despite the absence of all-things-considered preferences ex ante.

Pragmatic Considerations on Comparative Probability

While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative (comparative) judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and only if the subject’s comparative judgments preclude representation by a standard probability measure (or set of such measures).

Predictably Intransitive Preferences

The transitivity axiom is common to nearly all descriptive and normative utility theories of choice under risk. Recent experiments claim to show observed intransitive preference cycles are no more than noise. We take issue with this consensus position and its normative defence of transitivity. We draw upon the ‘Steinhaus-Trybula paradox’ as a recipe to bespoke design pairs of lotteries over which preferences might cycle. We run an experiment to look for cycles and transitivity’s implication of expansion/contraction consistency between binary and ternary choice sets. Even after considering possible stochastic but transitive explanations, we find cycles can be the modal preference pattern over these simple lotteries and also find systematic violations of expansion/contraction consistency. We conclude with a defence of these preferences, including a novel argument against the money pump.

Arbitrage in natural gas markets?

Regional LNG markets are characterized by substantial price differences since 2009. These regional differentials in prices suggest arbitrage possibilities which are incompatible with functioning markets; this creates a puzzle. This paper seeks to explain this puzzle by investigating potential explanations ranging from transport costs, bottlenecks in network (liquefaction, shipping and regasification), and restrictions arising from contracts. Of these factors, only the past and current constraints on U.S. liquefaction capacity has some explanatory power. However, this cannot be the entire story because given this past and current constraint, U.S. gas producers can engage in intertemporal speculation, i.e., keep their gas in the ground until the necessary liquefaction capacity exists and U.S. gas prices increase towards the prices in other regions (transport costs leave from price differences). Since it is difficult to believe that such obvious and simple money pumps are not exploited, further explanations are needed and linked to potential U.S. government interventions; high and irreversible investment costs and rational expectations (i.e., others too will exploit this opportunity, which will move regional prices closer) further add to keep investments low. Summarizing, these factors combined can explain the price differences of the past and their persistence, albeit at a lower level, in the future.

PLEASE DON'T REGULATE MY INTERNALITIES.

PLEASE DON'T REGULATE MY INTERNALITIES.

The Impotence of the Value Pump

Many philosophers have argued that agents must be irrational to lose out in a ‘value pump’ or ‘money pump’. A number of different conclusions have been drawn from this claim. The ‘Value Pump’ (VP) has been one of the main arguments offered for the axioms of expected utility theory; it has been used to show that options cannot be incomparable or on a par; and it has been used to show that our past choices have normative significance for our subsequent choices. In this article, I argue that the fact that someone loses out in a value pump provides no reason to believe that they are irrational. The VP is impotent.

REJOINDER TO HUDIK ON TRANSITIVITY

Block and Barnett (2012) was an attempt to defend Austrian economics against a neoclassical criticism of it based on the money pump, an attempted reductio ad absurdum of the praxeological school’s rejection of transitivity and stable preferences. Hudik (2012) is a critical response to Block and Barnett (2012). We regard Hudik (2012) as a defense of mainstream economics in this regard and thus a renewed attack on Austrianism. The present paper is an attempt to refute Hudik (2012).

Beatable imitation in symmetric games with perturbed payoffs

In a recent paper, Duersch et al. (2012) showed that in a rather broad class of repeated symmetric two-player games, a player who uses the simple “imitate-if-better” heuristic cannot be subject to a money pump. In this paper, we extend the analysis to games with randomly perturbed payoffs and we show that this result is not robust to, even arbitrarily small, payoff perturbations. In particular, we provide a necessary and sufficient condition that characterizes the class of perturbed games in which the imitator can be subject to a money pump.

Beatable Imitation in Symmetric Games with Perturbed Payoffs

In a recent paper, Duersch et.al (2012) showed that in a rather broad class of repeated symmetric two-player games, a player who uses the simple "imitate-if-better" heuristic cannot be subject to a money pump. In this paper, we extend the analysis to games with randomly perturbed payoffs and we show that this result is not robust to, even arbitrarily small, payoff perturbations. In particular, we provide a necessary and sufficient condition that characterizes the class of perturbed games in which the imitator can be subject to a money pump.

Safeguards of a Disunified Mind

The papers focuses on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on her beliefs or preferences. An argument of this kind typically targets constraint violations. It purports to show that a violator of a given constraint can be confronted with a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent herself. Examples of pragmatic arguments of this kind are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the acyclicity requirement on preferences. The paper suggests that the proposed exploitation set-ups share a common feature. If the violator of a given constraint is logically and mathematically competent, and if she prefers to be better off rather than worse off, she can be exploited only if she is disunified in her decision-making, i.e. only if she makes decisions on various issues she faces separately rather than jointly. Unification in decision making is relatively unproblematic in synchronic contexts, but it may be costly and inconvenient diachronically. On this view, therefore, pragmatic arguments should be seen as delivering conditional recommendations: If you want to afford disunification, then you’d better satisfy these constraints. They identify safeguards of a disunified mind. Isaac Levi’s position on these matters is diametrically different. According to Levi, only synchronic pragmatic arguments are valid (indeed, categorically so). The diachronic ones, he argues, lack any validity at all. This line of reasoning is questioned in the paper.

Prospectism and the weak money pump argument

Hare (Analysis 70:237–247, 2010) proposes a view he calls prospectism for making choices in situations in which preferences have a common, but problematic structure. I show that prospectism permits the decision-maker to make a series of choices she knows in advance will lead to a sure loss. I also argue that a theory that permits the decision-maker to make choices she knows in advance will lead to a sure loss should be rejected.

In Defence of My Favourite Theory

AbstractOne of the principles on how to act under moral uncertainty, My Favourite Theory, says roughly that a morally conscientious agent chooses an option that is permitted by the most credible moral theory. In defence of this principle, we argue that it prescribes consistent choices over time, without relying on intertheoretic comparisons of value, while its main rivals are either plagued by moral analogues of money pumps or in need of a method for making non‐arbitrary intertheoretic comparisons. We rebut the arguments that have been levelled against My Favourite Theory and offer some arguments against intertheoretic comparisons of value.

A Deluxe Money Pump

So-called money pump arguments aim to show that intransitive preferences are irrational because they will lead someone to accept a series of deals that leaves his/her financially worse off and better off in no respect. A common response to these arguments is the foresight response, which counters that the agent in question may see the exploitation coming, and refuse to trade at all. To obviate this response, I offer a "deluxe money pump argument" that applies dominance reasoning to a modified money pump case.

Satan, Saint Peter and Saint Petersburg

We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, repeated dominance reasoning (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid.