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.

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.

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 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.