arXiv subjects
Publications and source records attributed to Ben Abramowitz.
We introduce capital games, which generalize the definition of standard games to incorporate dynamics. In capital games, payoffs are in units of capital which are not assumed to be units of utility. The dynamics allow us to infer player utilities from their individual payoffs and linearizable capital dynamics under the assumption that players aim to maximize the time-average growth rate of their capital.
People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic Choice as a framework for making and evaluating decisions based on formal normative statements about decisions. These statements, or axioms, capture a wide array of desiderata, e.g., ethical constraints, beyond the typical treatment in Social Choice. Using our model of axioms and decisions we define key properties and introduce a taxonomy of axioms which may be of general interest. We then use these properties and our taxonomy to define the Decision-Evaluation Paradox, formalize the concepts of transparency and deception in explaining and justifying decisions, and reveal the limits of existing methods using axioms to make decisions.
The Sleeping Beauty problem is a problem of imperfect recall that has received considerable attention. One approach to resolving the Sleeping Beauty problem has been to allow Sleeping Beauty to make decisions based on her beliefs, and then characterize what it takes for her decisions to be "rational". In particular, she can be allowed to make monetary bets based on her beliefs, with the assumption that she wants to gain wealth rather than lose it. However, this approach is often coupled with the erroneous assumption that Sleeping Beauty should maximize the expected value of her bets. Here, we show that (1) Sleeping Beauty's ex ante optimal betting strategy and de se optimal betting strategy are identical, and (2) under an asymptotically optimal betting strategy Sleeping Beauty is invulnerable to diachronic Dutch Books as a Thirder but remains vulnerable as a Halfer.
Aggregating agent preferences into a collective decision is an important step in many problems (e.g., hiring, elections, peer review) and across areas of computer science (e.g., reinforcement learning, recommender systems). As Social Choice Theory has shown, the problem of designing aggregation rules with specific sets of properties (axioms) can be difficult, or provably impossible in some cases. Instead of designing algorithms by hand, one can learn aggregation rules, particularly voting rules, from data. However, prior work in this area has required extremely large models or been limited by the choice of preference representation, i.e., embedding. We recast the problem of designing voting rules with desirable properties into one of learning probabilistic functions that output distributions over a set of candidates. Specifically, we use neural networks to learn probabilistic social choice functions. Using standard embeddings from the social choice literature we show that preference profile encoding has significant impact on the efficiency and ability of neural networks to learn rules, allowing us to learn rules faster and with smaller networks than previous work. Moreover, we show that our learned rules can be fine-tuned using axiomatic properties to create novel voting rules and make them resistant to specific types of "attack". Namely, we fine-tune rules to resist a probabilistic version of the No Show Paradox.
Few-shot action recognition aims at quickly adapting a pre-trained model to the novel data with a distribution shift using only a limited number of samples. Key challenges include how to identify and leverage the transferable knowledge learned by the pre-trained model. We therefore propose CDTD, or Causal Domain-Invariant Temporal Dynamics for knowledge transfer. To identify the temporally invariant and variant representations, we employ the causal representation learning methods for unsupervised pertaining, and then tune the classifier with supervisions in next stage. Specifically, we assume the domain information can be well estimated and the pre-trained image decoder and transition models can be well transferred. During adaptation, we fix the transferable temporal dynamics and update the image encoder and domain estimator. The efficacy of our approach is revealed by the superior accuracy of CDTD over leading alternatives across standard few-shot action recognition datasets.
In representative democracies, the election of new representatives in regular election cycles is meant to prevent corruption and other misbehavior by elected officials and to keep them accountable in service of the ``will of the people." This democratic ideal can be undermined when candidates are dishonest when campaigning for election over these multiple cycles or rounds of voting. Much of the work on COMSOC to date has investigated strategic actions in only a single round. We introduce a novel formal model of \emph{pandering}, or strategic preference reporting by candidates seeking to be elected, and examine the resilience of two democratic voting systems to pandering within a single round and across multiple rounds. The two voting systems we compare are Representative Democracy (RD) and Flexible Representative Democracy (FRD). For each voting system, our analysis centers on the types of strategies candidates employ and how voters update their views of candidates based on how the candidates have pandered in the past. We provide theoretical results on the complexity of pandering in our setting for a single cycle, formulate our problem for multiple cycles as a Markov Decision Process, and use reinforcement learning to study the effects of pandering by both single candidates and groups of candidates across a number of rounds.
We consider the problem of determining a binary ground truth using advice from a group of independent reviewers (experts) who express their guess about a ground truth correctly with some independent probability (competence). In this setting, when all reviewers are competent (competence greater than one-half), the Condorcet Jury Theorem tells us that adding more reviewers increases the overall accuracy, and if all competences are known, then there exists an optimal weighting of the reviewers. However, in practical settings, reviewers may be noisy or incompetent, i.e., competence below half, and the number of experts may be small, so the asymptotic Condorcet Jury Theorem is not practically relevant. In such cases we explore appointing one or more chairs (judges) who determine the weight of each reviewer for aggregation, creating multiple levels. However, these chairs may be unable to correctly identify the competence of the reviewers they oversee, and therefore unable to compute the optimal weighting. We give conditions when a set of chairs is able to weight the reviewers optimally, and depending on the competence distribution of the agents, give results about when it is better to have more chairs or more reviewers. Through numerical simulations we show that in some cases it is better to have more chairs, but in many cases it is better to have more reviewers.
Agents care not only about the outcomes of collective decisions but also about how decisions are made. In many cases, both the outcome and the procedure affect whether agents see a decision as legitimate, justifiable, or acceptable. We propose a novel model for collective decisions that takes into account both the preferences of the agents and their higher order concerns about the process of preference aggregation. To this end we (1) propose natural, plausible preference structures and establish key properties thereof, (2) develop mechanisms for aggregating these preferences to maximize the acceptability of decisions, and (3) characterize the performance of our acceptance-maximizing mechanisms. We apply our general approach to the specific setting of dichotomous choice, and compare the worst-case rates of acceptance achievable among populations of agents of different types. We also show in the special case of rule selection, i.e., amendment procedures, the method proposed by Abramowitz, Shapiro, and Talmon (2021) achieves universal acceptance with certain agent types.
Aggregating signals from a collection of noisy sources is a fundamental problem in many domains including crowd-sourcing, multi-agent planning, sensor networks, signal processing, voting, ensemble learning, and federated learning. The core question is how to aggregate signals from multiple sources (e.g. experts) in order to reveal an underlying ground truth. While a full answer depends on the type of signal, correlation of signals, and desired output, a problem common to all of these applications is that of differentiating sources based on their quality and weighting them accordingly. It is often assumed that this differentiation and aggregation is done by a single, accurate central mechanism or agent (e.g. judge). We complicate this model in two ways. First, we investigate the setting with both a single judge, and one with multiple judges. Second, given this multi-agent interaction of judges, we investigate various constraints on the judges' reporting space. We build on known results for the optimal weighting of experts and prove that an ensemble of sub-optimal mechanisms can perform optimally under certain conditions. We then show empirically that the ensemble approximates the performance of the optimal mechanism under a broader range of conditions.
Any community in which membership is optional may eventually break apart, or fork. For example, forks may occur in political parties, business partnerships, social groups, cryptocurrencies, and federated governing bodies. Forking is typically the product of informal social processes or the organized action of an aggrieved minority, and it is not always amicable. Forks usually come at a cost, and can be seen as consequences of collective decisions that destabilize the community. Here, we provide a social choice setting in which agents can report preferences not only over a set of alternatives, but also over the possible forks that may occur in the face of disagreement. We study this social choice setting, concentrating on stability issues and concerns of strategic agent behavior.
Consider n agents forming an egalitarian, self-governed community. Their first task is to decide on a decision rule to make further decisions. We start from a rather general initial agreement on the decision-making process based upon a set of intuitive and self-evident axioms, as well as simplifying assumptions about the preferences of the agents. From these humble beginnings we derive a decision rule. Crucially, the decision rule also specifies how it can be changed, or amended, and thus acts as a de facto constitution. Our main contribution is in providing an example of an initial agreement that is simple and intuitive, and a constitution that logically follows from it. The naive agreement is on the basic process of decision making - that agents approve or disapprove proposals; that their vote determines either the acceptance or rejection of each proposal; and on the axioms, which are requirements regarding a constitution that engenders a self-updating decision making process.
We develop new voting mechanisms for the case when voters and candidates are located in an arbitrary unknown metric space, and the goal is to choose a candidate minimizing social cost: the total distance from the voters to this candidate. Previous work has often assumed that only ordinal preferences of the voters are known (instead of their true costs), and focused on minimizing distortion: the quality of the chosen candidate as compared with the best possible candidate. In this paper, we instead assume that a (very small) amount of information is known about the voter preference strengths, not just about their ordinal preferences. We provide mechanisms with much better distortion when this extra information is known as compared to mechanisms which use only ordinal information. We quantify tradeoffs between the amount of information known about preference strengths and the achievable distortion. We further provide advice about which type of information about preference strengths seems to be the most useful. Finally, we conclude by quantifying the ideal candidate distortion, which compares the quality of the chosen outcome with the best possible candidate that could ever exist, instead of only the best candidate that is actually in the running.
We introduce Flexible Representative Democracy (FRD), a novel hybrid of Representative Democracy (RD) and Direct Democracy (DD) in which voters can alter the issue-dependent weights of a set of elected representatives. In line with the literature on Interactive Democracy, our model allows the voters to actively determine the degree to which the system is direct versus representative. However, unlike Liquid Democracy, Flexible Representative Democracy uses strictly non-transitive delegations, making delegation cycles impossible, and maintains a fixed set of accountable, elected representatives. We present FRD and analyze it using a computational approach with issues that are binary and symmetric. We compare the outcomes of various voting systems using Direct Democracy with majority voting as an ideal baseline. First, we demonstrate the shortcomings of Representative Democracy in our model. We provide NP-Hardness results for electing an ideal set of representatives, discuss pathologies, and demonstrate empirically that common multi-winner election rules for selecting representatives do not perform well in expectation. To analyze the effects of adding flexibility, we begin by providing theoretical results on how issue-specific delegations determine outcomes. Finally, we provide empirical results comparing the outcomes of Representative Democracy, proxy voting with fixed sets of proxies across issues, and Flexible Representative Democracy with issue-specific delegations. Our results show that variants of Proxy Voting yield no discernible benefit over unweighted representatives and reveal the potential for Flexible Representative Democracy to improve outcomes as voter participation increases.
We consider ordinal approximation algorithms for a broad class of utility maximization problems for multi-agent systems. In these problems, agents have utilities for connecting to each other, and the goal is to compute a maximum-utility solution subject to a set of constraints. We represent these as a class of graph optimization problems, including matching, spanning tree problems, TSP, maximum weight planar subgraph, and many others. We study these problems in the ordinal setting: latent numerical utilities exist, but we only have access to ordinal preference information, i.e., every agent specifies an ordering over the other agents by preference. We prove that for the large class of graph problems we identify, ordinal information is enough to compute solutions which are close to optimal, thus demonstrating there is no need to know the underlying numerical utilities. For example, for problems in this class with bounded degree $b$ a simple ordinal greedy algorithm always produces a ($b+1$)-approximation; we also quantify how the quality of ordinal approximation depends on the sparsity of the resulting graphs. In particular, our results imply that ordinal information is enough to obtain a 2-approximation for Maximum Spanning Tree; a 4-approximation for Max Weight Planar Subgraph; a 2-approximation for Max-TSP; and a 2-approximation for various Matching problems.