arXiv subjects

Joseph Y. Halpern

Publications and source records attributed to Joseph Y. Halpern.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying Harm

In earlier work we defined a qualitative notion of harm: either harm is caused, or it is not. For practical applications, we often need to quantify harm; for example, we may want to choose the least harmful of a set of possible interventions. In this work, which is an expanded version of an earlier conference paper, we develop a quantitative notion of harm. We first present a quantitative definition of harm in a deterministic context involving a single individual, then we consider the issues involved in dealing with uncertainty regarding the context and going from a notion of harm for a single individual to a notion of "societal harm", which involves aggregating the harm to individuals. We show that the "obvious" way of doing this (just taking the expected harm for an individual and then summing the expected harm over all individuals) can lead to counterintuitive or inappropriate answers, and discuss alternatives, drawing on work from the decision-theory literature. Finally, we connect our work to a recent debate over harm within the context of precision medicine.

cs.AI↗

arXiv2026

Unintended Consequences: Updating Causal Models

We examine how causal beliefs affect an agent's choices and how feedback on those choices leads to updated causal beliefs. Building on the structural-equations framework for modeling causality, we first examine the general problem of updating causal beliefs in the face of novel (and possibly inexplicable) data. We model an agent who is uncertain of the true causal model, and therefore entertains a probabilistic belief over the set of possible models. We then consider how causal beliefs influence choices by building a model of agency and utility on top of the usual structural-equations framework. Using these two components, we propose a notion of steady state, where the feedback received from an agent's optimal action, given her current beliefs about the true causal model, can be rationalized by those beliefs.

econ.TH↗

arXiv2025

Causality Without Causal Models

Perhaps the most prominent current definition of (actual) causality is due to Halpern and Pearl. It is defined using causal models (also known as structural equations models). We abstract the definition, extracting its key features, so that it can be applied to any other model where counterfactuals are defined. By abstracting the definition, we gain a number of benefits. Not only can we apply the definition in a wider range of models, including ones that allow, for example, backtracking, but we can apply the definition to determine if A is a cause of B even if A and B are formulas involving disjunctions, negations, beliefs, and nested counterfactuals (none of which can be handled by the Halpern-Pearl definition). Moreover, we can extend the ideas to getting an abstract definition of explanation that can be applied beyond causal models. Finally, we gain a deeper understanding of features of the definition even in causal models.

cs.AI↗

arXiv2025

Evolution of diverse (and advanced) cognitive abilities through adaptive fine-tuning of learning and chunking mechanisms

The evolution of cognition is frequently discussed as the evolution of cognitive abilities or the evolution of some neuronal structures in the brain. However, since such traits or abilities are often highly complex, understanding their evolution requires explaining how they could have gradually evolved through selection acting on heritable variations in simpler cognitive mechanisms. With this in mind, making use of a previously proposed theory, here we show how the evolution of cognitive abilities can be captured by the fine-tuning of basic learning mechanisms and, in particular, chunking mechanisms. We use the term chunking broadly for all types of non-elemental learning, claiming that the process by which elements are combined into chunks and associated with other chunks, or elements, is critical for what the brain can do, and that it must be fine-tuned to ecological conditions. We discuss the relevance of this approach to studies in animal cognition, using examples from animal foraging and decision-making, problem solving, and cognitive flexibility. Finally, we explain how even the apparent human-animal gap in sequence learning ability can be explained in terms of different fine-tunings of a similar chunking process.

q-bio.NC↗

arXiv2024

Tracking Truth with Liquid Democracy

The dynamics of random transitive delegations on a graph are of particular interest when viewed through the lens of an emerging voting paradigm, liquid democracy. This paradigm allows voters to choose between directly voting and transitively delegating their votes to other voters, so that those selected cast a vote weighted by the number of delegations they received. In the epistemic setting, where voters decide on a binary issue for which there is a ground truth, previous work showed that a few voters may amass such a large amount of influence that liquid democracy is less likely to identify the ground truth than direct voting. We quantify the amount of permissible concentration of power and examine more realistic delegation models, showing they behave well by ensuring that (with high probability) there is a permissible limit on the maximum number of delegations received. Our theoretical results demonstrate that the delegation process is similar to well-known processes on random graphs that are sufficiently bounded for our purposes. Along the way, we prove new bounds on the size of the largest component in an infinite Pólya urn process, which may be of independent interest. In addition, we empirically validate the theoretical results, running six experiments (for a total of $N=168$ participants, $62$ delegation graphs and over $11k$ votes collected). We find that empirical delegation behaviors meet the conditions for our positive theoretical guarantees. Overall, our work alleviates concerns raised about liquid democracy and bolsters the case for the applicability of this emerging paradigm.

cs.DM↗

arXiv2024

A Knowledge-Based Analysis of Intersection Protocols

The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run protocols among themselves to determine right of way. In this paper, we define the intersection problem to model this scenario abstractly, without any assumptions on the specific structure of the intersection or a bound on the number of vehicles. Protocols solving the intersection problem must guarantee safety (no collisions) and liveness (every vehicle eventually goes through). In addition, we would like these protocols to satisfy various optimality criteria, some of which turn out to be achievable only in a subset of the contexts. In particular, we show a partial equivalence between eliminating unnecessary waiting, a criterion of interest in the distributed mutual-exclusion literature, and a notion of optimality that we define called lexicographical optimality. We then introduce a framework to design protocols for the intersection problem by converting an intersection policy, which is based on a global view of the intersection, to a protocol that can be run by the vehicles through the use of knowledge-based programs. Our protocols are shown to guarantee safety and liveness while also being optimal under sufficient conditions on the context. Finally, we investigate protocols in the presence of faulty vehicles that experience communication failures and older vehicles with limited communication capabilities. We show that intersection protocols can be made safe, live and optimal even in the presence of faulty behavior.

cs.DC↗

arXiv2024

Intervention and Conditioning in Causal Bayesian Networks

Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.

cs.AI↗

arXiv2024

Explaining Image Classifiers

We focus on explaining image classifiers, taking the work of Mothilal et al. [2021] (MMTS) as our point of departure. We observe that, although MMTS claim to be using the definition of explanation proposed by Halpern [2016], they do not quite do so. Roughly speaking, Halpern's definition has a necessity clause and a sufficiency clause. MMTS replace the necessity clause by a requirement that, as we show, implies it. Halpern's definition also allows agents to restrict the set of options considered. While these difference may seem minor, as we show, they can have a nontrivial impact on explanations. We also show that, essentially without change, Halpern's definition can handle two issues that have proved difficult for other approaches: explanations of absence (when, for example, an image classifier for tumors outputs "no tumor") and explanations of rare events (such as tumors).

cs.AI↗

arXiv2024

Subjective Causality

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called structural equations models), where the world is described by a collection of variables, related by equations. We show that if a preference relation over interventions satisfies certain axioms (related to standard axioms regarding counterfactuals), then we can define (i) a causal model, (ii) a probability capturing the decision-maker's uncertainty regarding the external factors in the world and (iii) a utility on outcomes such that each intervention is associated with an expected utility and such that intervention $A$ is preferred to $B$ iff the expected utility of $A$ is greater than that of $B$. In addition, we characterize when the causal model is unique. Thus, our results allow a modeler to test the hypothesis that a decision maker's preferences are consistent with some causal model and to identify causal judgements from observed behavior.

econ.TH↗

arXiv2024

Communication games, sequential equilibrium, and mediators

We consider $k$-resilient sequential equilibria, strategy profiles where no player in a coalition of at most $k$ players believes that it can increase its utility by deviating, regardless of its local state. We prove that all $k$-resilient sequential equilibria that can be implemented with a trusted mediator can also be implemented without the mediator in a synchronous system of $n$ players if $n >3k$. In asynchronous systems, where there is no global notion of time and messages may take arbitrarily long to get to their recipient, we prove that a $k$-resilient sequential equilibrium with a mediator can be implemented without the mediator if $n > 4k$. These results match the lower bounds given by Abraham, Dolev, and Halpern (2008) and Geffner and Halpern (2023) for implementing a Nash equilibrium without a mediator (which are easily seen to apply to implementing a sequential equilibrium) and improve the results of Gerardi, who showed that, in the case that $k=1$, a sequential equilibrium can be implemented in synchronous systems if $n \ge 5$.

cs.GT↗

arXiv2023

Mathematical Explanations

A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical facts cannot be part of an explanation (under the standard notion of explanation). This problem is solved using impossible possible worlds.

cs.AI↗

arXiv2023

Bounding the Communication Complexity of Fault-Tolerant Common Coin Tossing

Protocols for tossing a common coin play a key role in the vast majority of implementations of consensus. Even though the common coins in the literature are usually \emph{fair} (they have equal chance of landing heads or tails), we focus on the problem of implementing a \emph{biased} common coin such that the probability of landing heads is $p \in [0,1]$. Even though biased common coins can be implemented using fair common coins, we show that this can require significant inter-party communication. In fact, we show that there is no bound on the number of messages needed to generate a common coin of bias $p$ in a way that tolerates even one malicious agent, even if we restrict $p$ to an arbitrary infinite subset of $[0,1]$ (e.g., rational numbers of the form $1/2^n$) and assume that the system is synchronous. By way of contrast, if we do not require the protocol to tolerate a faulty agent, we can do this. Thus, the cause of the message complexity is the requirement of fault tolerance.

cs.DC↗

arXiv2023

Inference for Probabilistic Dependency Graphs

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this inconsistency. We present the first tractable inference algorithm for PDGs with discrete variables, making the asymptotic complexity of PDG inference similar that of the graphical models they generalize. The key components are: (1) the observation that, in many cases, the distribution a PDG specifies can be formulated as a convex optimization problem (with exponential cone constraints), (2) a construction that allows us to express these problems compactly for PDGs of boundeed treewidth, (3) contributions to the theory of PDGs that justify the construction, and (4) an appeal to interior point methods that can solve such problems in polynomial time. We verify the correctness and complexity of our approach, and provide an implementation of it. We then evaluate our implementation, and demonstrate that it outperforms baseline approaches. Our code is available at http://github.com/orichardson/pdg-infer-uai.

cs.DS↗

arXiv2023

Colordag: An Incentive-Compatible Blockchain

We present Colordag, a blockchain protocol where following the prescribed strategy is, with high probability, a best response as long as all miners have less than 1/2 of the mining power. We prove the correctness of Colordag even if there is an extremely powerful adversary who knows future actions of the scheduler: specifically, when agents will generate blocks and when messages will arrive. The state-of-the-art protocol, Fruitchain, is an epsilon-Nash equilibrium as long as all miners have less than 1/2 of the mining power. However, there is a simple deviation that guarantees that deviators are never worse off than they would be by following Fruitchain, and can sometimes do better. Thus, agents are motivated to deviate. Colordag implements a solution concept that we call epsilon-sure Nash equilibrium and does not suffer from this problem. Because it is an epsilon-sure Nash equilibrium, Colordag is an epsilon Nash equilibrium and with probability (1 - epsilon) is a best response.

cs.GT↗

arXiv2023

Strategic Play By Resource-Bounded Agents in Security Games

Many studies have shown that humans are "predictably irrational": they do not act in a fully rational way, but their deviations from rational behavior are quite systematic. Our goal is to see the extent to which we can explain and justify these deviations as the outcome of rational but resource-bounded agents doing as well as they can, given their limitations. We focus on the well-studied ranger-poacher game, where rangers are trying to protect a number of sites from poaching. We capture the computational limitations by modeling the poacher and the ranger as probabilistic finite automata (PFAs). We show that, with sufficiently large memory, PFAs learn to play the Nash equilibrium (NE) strategies of the game and achieve the NE utility. However, if we restrict the memory, we get more "human-like" behaviors, such as probability matching (i.e., visiting sites in proportion to the probability of a rhino being there), and avoiding sites where there was a bad outcome (e.g., the poacher was caught by the ranger), that we also observed in experiments conducted on Amazon Mechanical Turk. Interestingly, we find that adding human-like behaviors such as probability matching and overweighting significant events (like getting caught) actually improves performance, showing that this seemingly irrational behavior can be quite rational.

cs.GT↗

arXiv2023

Sequential Language-based Decisions

In earlier work, we introduced the framework of language-based decisions, the core idea of which was to modify Savage's classical decision-theoretic framework by taking actions to be descriptions in some language, rather than functions from states to outcomes, as they are defined classically. Actions had the form "if psi then do(phi)", where psi and phi were formulas in some underlying language, specifying what effects would be brought about under what circumstances. The earlier work allowed only one-step actions. But, in practice, plans are typically composed of a sequence of steps. Here, we extend the earlier framework to sequential actions, making it much more broadly applicable. Our technical contribution is a representation theorem in the classical spirit: agents whose preferences over actions satisfy certain constraints can be modeled as if they are expected utility maximizers. As in the earlier work, due to the language-based specification of the actions, the representation theorem requires a construction not only of the probability and utility functions representing the agent's beliefs and preferences, but also the state and outcomes spaces over which these are defined, as well as a "selection function" which intuitively captures how agents disambiguate coarse descriptions. The (unbounded) depth of action sequencing adds substantial interest (and complexity!) to the proof.

cs.LO↗

arXiv2023

Joint Behavior and Common Belief

For over 25 years, common belief has been widely viewed as necessary for joint behavior. But this is not quite correct. We show by example that what can naturally be thought of as joint behavior can occur without common belief. We then present two variants of common belief that can lead to joint behavior, even without standard common belief ever being achieved, and show that one of them, action-stamped common belief, is in a sense necessary and sufficient for joint behavior. These observations are significant because, as is well known, common belief is quite difficult to achieve in practice, whereas these variants are more easily achievable.

cs.MA↗

arXiv2023

The Benefits of Coarse Preferences

We study the strategic advantages of coarsening one's utility by clustering nearby payoffs together (i.e., classifying them the same way). Our solution concept, coarse-utility equilibrium (CUE) requires that (1) each player maximizes her coarse utility, given the opponent's strategy, and (2) the classifications form best replies to one another. We characterize CUEs in various games. In particular, we show that there is a qualitative difference between CUEs in which only one of the players clusters payoffs, and those in which all players cluster their payoffs, and that the latter type induce players to treat co-players better than in Nash equilibria in the large class of games with monotone externalities.

econ.TH↗