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.

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: Mixed Borda branching, which generalizes a rule satisfying copy-robustness, and the random walk rule, 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.

In voting theory, when voters have ranked preferences over candidates, the celebrated Gibbard-Satterthwaite Theorem essentially rules out the existence of reasonable strategyproof methods for picking a winner. What if we weaken strategyproofness to only hold for Bayesian voters with beliefs over others' preferences? When voters believe other participants' rankings are drawn independently from a fixed distribution, the impossibility persists. However, it is quite reasonable for a voter to believe that other votes are correlated, either to each other or to their own ranking. We consider such beliefs induced by classic probabilistic models in social choice such as the Mallows, Placket-Luce, and Thurstone-Mosteller models. We single out the plurality rule (choosing the candidate ranked first most often) as a particularly promising choice as it is strategyproof for a large class of beliefs containing the specific ones we introduce. Further, we show that plurality is unique among positional scoring rules in having this property: no other scoring rule is strategyproof for beliefs induced by the Mallows model when there are a sufficient number of voters. Finally, we give examples of prominent non-scoring voting rules failing to be strategyproof on beliefs in this class, further bolstering the case for plurality.

A new Fox News poll shows 8 in 10 voters support careful artificial intelligence development to manage risks, while only 2 in 10 prefer rapid advancement.

In shift bribery, a briber seeks to promote his preferred candidate by paying voters to raise their ranking. Classical models of shift bribery assume voters act independently, overlooking the role of social influence. However, in reality, individuals are social beings and are often represented as part of a social network, where bribed voters may influence their neighbors, thereby amplifying the effect of persuasion. We study Shift bribery over Networks, where voters are modeled as nodes in a directed weighted graph, and arcs represent social influence between them. In this setting, bribery is not confined to directly targeted voters its effects can propagate through the network, influencing neighbors and amplifying persuasion. Given a budget and individual cost functions for shifting each voter's preference toward a designated candidate, the goal is to determine whether a shift strategy exists within budget that ensures the preferred candidate wins after both direct and network-propagated influence takes effect. We show that the problem is NP-Complete even with two candidates and unit costs, and W[2]-hard when parameterized by budget or maximum degree. On the positive side, we design polynomial-time algorithms for complete graphs under plurality and majority rules and path graphs for uniform edge weights, linear-time algorithms for transitive tournaments for two candidates, linear cost functions and uniform arc weights, and pseudo-polynomial algorithms for cluster graphs. We further prove the existence of fixed-parameter tractable algorithms with treewidth as parameter for two candidates, linear cost functions and uniform arc weights and pseudo-FPT with cluster vertex deletion number for two candidates and uniform arc weights. Together, these results give a detailed complexity landscape for shift bribery in social networks.

AI is eminently capable of political persuasion and could automate it at a mass scale. In January 2024, the phone rang in homes all around New Hampshire. On the other end was Joe Biden's voice, urging Democrats to "save your vote" by skipping the primary. It sounded authentic, but it wasn't. The call was a fake, generated by artificial intelligence. Today, the technology behind that hoax looks quaint.

AI can influence voters' minds. What does that mean for democracy? AI chatbots may have the power to influence voters' opinions Does the persuasive power of AI chatbots spell the beginning of the end for democracy? In one of the largest surveys to date exploring how these tools can influence voter attitudes, AI chatbots were more persuasive than traditional political campaign tools including advertisements and pamphlets, and as persuasive as seasoned political campaigners. But at least some researchers identify reasons for optimism in the way in which the AI tools shifted opinions.

This paper bridges two perspectives: it studies the multi-secretary problem through the fairness lens of social choice, and examines multi-winner elections from the viewpoint of online decision making. After identifying the limitations of the prominent proportionality notion of Extended Justified Representation (EJR) in the online domain, the work proposes a set of mechanisms that merge techniques from online algorithms with rules from social choice -- such as the Method of Equal Shares and the Nash Rule -- and supports them through both theoretical analysis and extensive experimental evaluation.

Voters hold divided opinions on artificial intelligence impact, with college-educated and higher-income Americans more optimistic than others, Fox News survey finds.