Lennart B. Ackermans

Philosophical discussion of the two-envelope paradox has suffered from a lack of formal precision. I discuss various versions of the paradoxical argument using formal probability theory, which helps to make diagnoses that are simpler, more insightful, and provably correct. Paradoxical arguments are revealed to be fallacious for one of three reasons: (1) the argument makes a formal mistake such as an equivocation fallacy; (2) the argument disregards relevant uncertainty about or variability in a unit of measurement; (3) the argument uses an invalid decision rule. I improve upon various existing diagnoses and discuss what kind of philosophical and decision-theoretic import the paradox has.

In ‘Factual Difference-Making’, Holger Andreas and Mario Günther (2025) propose a theory of model-relative actual causation which performs remarkably well on a number of known problematic cases. They take this to show that we should abandon our counterfactual way of thinking about causation in favour of their factual alternative. I cast doubt on this argument by offering two similar theories. First, I show that the theory of Factual Difference-Making is equivalent to a partly counterfactual theory. Second, I give a fully counterfactual theory that makes the same judgments in the scenarios discussed by Andreas and Günther.

Titelbaum (2012) introduced a variant of the Sleeping Beauty problem in which a coin is tossed on both Monday and Tuesday, with the Tuesday toss not affecting Beauty's condition. Titelbaum argues that double halfers are committed to the embarrassing position that Beauty's credence that today's coin toss lands heads is greater than 1/2. Pust (2023) agrees with the result, but argues that it is not a distinctive embarrassment for halfers. I argue that thirders need not be embarrassed. Double halfers, on the other hand, must hold that Beauty's evidence is admissible for direct inference with respect to Monday's coin toss, but not with respect to today's coin toss. This is embarrassing because (1) a plausible argument exists for the opposite position, and (2) the position conflicts with the central motivation guiding double halfism.

The last two decades have seen a heated debate between "halfers" and "thirders": those who believe Sleeping Beauty’s credence in a coin landing heads is 1/2 and those who believe it is 1/3 – as well as quite some alternative positions. This paper attempts to settle the debate in favour of thirdism. I present a new argument for thirdism which cannot be resisted using any of the previously used halfer strategies. My argument uses an analogy in which Sleeping Beauty has a lucid dream on each day. To arrive at thirdism, she uses an unproblematic type of Bayesian conditionalisation, the principle of indifference, and the principal principle. I argue that all of these reasoning steps should be uncontroversial. Finally, I argue that all published defences of halfism are untenable.

The 2021 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to David Card “for his empirical contributions to labour economics”, and to Joshua Angrist and Guido Imbens “for their methodological contributions to the analysis of causal relationships”. Lennart B. Ackermans reflects on Card, Angrist, and Imben's work. Ackermans argues, first, that advances in causal methodology from Angrist and Imbens have helped solve the credibility crisis in econometrics and revealed shortcomings in past and present graduate textbooks in econometrics. Second, for the field to develop further, economists must resolve the current disputes surrounding causal frameworks. The article compares the merits of the three frameworks for causal modelling proposed by, respectively, Donald Rubin, Judea Pearl, and James Heckman.

In recent decades, economists have developed methods for measuring the country-wide level of inequality of opportunity. The most popular method, called the ex-ante method, uses data on the distribution of outcomes stratified by groups of individuals with the same circumstances, in order to estimate the part of outcome inequality that is due to these circumstances. I argue that these methods are potentially biased, both upwards and downwards, and that the unknown size of this bias could be large. To argue that the methods are biased, I show that they ought to measure causal or counterfactual quantities, while the methods are only capable of identifying correlational information. To argue that the bias is potentially large, I illustrate how the causal complexity of the real world leads to numerous non-causal correlations between circumstances and outcomes and respond to objections claiming that such correlations are nonetheless indicators of unfair disadvantage, that is, inequality of opportunity.

According to an infinite frequency principle, it is rational, under certain conditions, to set your credence in an outcome to the limiting frequency of that outcome if the experiment were repeated indefinitely. I argue that most infinite frequency principles are undesirable in at least one of the following ways: (1) accepting the principle would lead you to accept bets with sure losses, (2) the principle gives no guidance in the case of deterministic experiments like coin tosses and (3) the principle relies on a metaphysical property, ‘chanciness’, whose necessary and sufficient conditions are unknown. I show that a frequency principle that is based on the principal principle suffers from problems related to the definition of ‘chance’ or ‘chanciness’, which could lead to all three of the above problems. I introduce a version of the infinite frequency principle that does not rely on a notion of chance or chanciness and does not suffer from any of these problems.

The traditional Lockean justification of property rights has been argued to be no longer valid in a world in which much wealth does not derive from acquisitions of natural resources, and in which much property, such as money, is intangible. This means that libertarians need to reconsider whether and why property rights are justified for objects that fall outside of the scope of the Lockean justification. This paper gives a justification of property rights in relation to modern money, which uses the self-ownership principle as its central premise. Since modern money is a form of credit, I start with a justification of credit property rights. I then consider both money under gold convertibility and present-day fiat systems, showing that the justification of credit property rights remains valid under these conditions.