We study metric distortion in distributed voting, where nvoters are partitioned into k groups, each selecting a local representative, and a final winner is chosen from these representatives (or from the entire set of candidates). This setting models systems like U.S. presidential elections, where state-level decisions determine the national outcome. We focus on four cost objectives from Anshelevich et al. [1]: avg-avg, avg-max, max-avg, and max-max. We present improved distortion bounds for both deterministic and randomized mechanisms, offering a near-complete characterization of distortion in this model. For deterministic mechanisms, we reduce the upper bound for avg-max from 11 to 7, establish a tight lower bound of 5 for max-avg (improving on 2+ 5), and tighten the upper bound for max-max from 5 to 3. For randomized mechanisms, we consider two settings: (i) only the second stage is randomized, and (ii) both stages may be randomized. In case (i), we prove tight bounds: 5 2/k for avg-avg, 3for avg-max and max-max, and 5for max-avg. In case (ii), we show tight bounds of 3 for max-avg and max-max, and nearly tight bounds for avg-avg and avg-max within [3 2/n, 3 2/(kn)]and [3 2/n, 3], respectively, where n denotes the largest group size.

Liquid democracy with ranked delegations is a novel voting scheme that unites the practicability of representative democracy with the idealistic appeal of direct democracy: Every voter decides between casting their vote on a question at hand or delegating their voting weight to some other, trusted agent. Delegations are transitive, and since voters may end up in a delegation cycle, they are encouraged to indicate not only a single delegate, but a set of potential delegates and a ranking among them. Based on the delegation preferences of all voters, a delegation rule selects one representative per voter. Previous work has revealed a trade-off between two properties of delegation rules called anonymity and copy-robustness. To overcome this issue we study two fractional delegation rules: MIXEDBORDA BRANCHING, which generalizes a rule satisfying copy-robustness, and the RANDOMWALKRULE, which satisfies anonymity. Using the Markov chain tree theorem, we show that the two rules are in fact equivalent, and simultaneously satisfy generalized versions of the two properties. Combining the same theorem with Fulkerson's algorithm, we develop a polynomial-time algorithm for computing the outcome of the studied delegation rule. This algorithm is of independent interest, having applications in semi-supervised learning and graph theory.

A.1 Background on graph neural networks Many GNN architectures iteratively update node features following a neighborhood aggregation scheme.

Voting systems have a wide range of applications including recommender systems, web search, product design and elections. Limited by the lack of general-purpose analytical tools, it is difficult to hand-engineer desirable voting rules for each use case. For this reason, it is appealing to automatically discover voting rules geared towards each scenario. In this paper, we show that set-input neural network architectures such as Set Transformers, fully-connected graph networks and DeepSets are both theoretically and empirically well-suited for learning voting rules. In particular, we show that these network models can not only mimic a number of existing voting rules to compelling accuracy -- both position-based (such as Plurality and Borda) and comparison-based (such as Kemeny, Copeland and Maximin) -- but also discover near-optimal voting rules that maximize different social welfare functions. Furthermore, the learned voting rules generalize well to different voter utility distributions and election sizes unseen during training.

We consider two-alternative elections where voters' preferences depend on a state variable that is not directly observable. Each voter receives a private signal that is correlated to the state variable. Voters may be "contingent" with different preferences in different states; or predetermined with the same preference in every state. In this setting, even if every voter is a contingent voter, agents voting according to their private information need not result in the adoption of the universally preferred alternative, because the signals can be systematically biased. We present an easy-to-deploy mechanism that elicits and aggregates the private signals from the voters, and outputs the alternative that is favored by the majority. In particular, voters truthfully reporting their signals forms a strong Bayes Nash equilibrium (where no coalition of voters can deviate and receive a better outcome).

We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective. The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PACBayes objectives - both with uninformed (data-independent) and informed (datadependent) priors.

Researchers spent five years developing an AI-based model to protect freshwater fish worldwide from extinction, with a particular focus on identifying threats to fish before they become endangered. "People sometimes go in to protect species when it's already too late," said Ivan Arismendi, an associate professor in Oregon State University's Department of Fisheries, Wildlife, and Conservation Sciences. "With our model, decision makers can deploy resources in advance before a species becomes imperiled." The findings were recently published in the journal Nature Communications. Nearly one-third of freshwater fish species face possible extinction, threatening food supplies, ecosystems and outdoor recreation.

We start by proving statement (ii). We now prove statement (iii). The last constraint is trivially satisfied. This can be easily shown by induction. 's constraint remains equal when Let's pick such a branching Moreover, observe that every edge in B is tight.