Decentralized Autonomous Organizations (DAOs) use smart contracts to foster communities working toward common goals. Existing definitions of decentralization, however -- the 'D' in DAO -- fall short of capturing the key properties characteristic of diverse and equitable participation. This work proposes a new framework for measuring DAO decentralization called Voting-Bloc Entropy (VBE, pronounced ''vibe''). VBE is based on the idea that voters with closely aligned interests act as a centralizing force and should be modeled as such. VBE formalizes this notion by measuring the similarity of participants' utility functions across a set of voting rounds. Unlike prior, ad hoc definitions of decentralization, VBE derives from first principles: We introduce a simple (yet powerful) reinforcement learning-based conceptual model for voting, that in turn implies VBE. We first show VBE's utility as a theoretical tool. We prove a number of results about the (de)centralizing effects of vote delegation, proposal bundling, bribery, etc. that are overlooked in previous notions of DAO decentralization. Our results lead to practical suggestions for enhancing DAO decentralization. We also show how VBE can be used empirically by presenting measurement studies and VBE-based governance experiments. We make the tools we developed for these results available to the community in the form of open-source artifacts in order to facilitate future study of DAO decentralization.

It is important to study how strategic agents can affect the outcome of an election. There has been a long line of research in the computational study of elections on the complexity of manipulative actions such as manipulation and bribery. These problems model scenarios such as voters casting strategic votes and agents campaigning for voters to change their votes to make a desired candidate win. A common assumption is that the preferences of the voters follow the structure of a domain restriction such as single peakedness, and so manipulators only consider votes that also satisfy this restriction. We introduce the model where the preferences of the voters define their own restriction and strategic actions must ``conform'' by using only these votes. In this model, the election after manipulation will retain common domain restrictions. We explore the computational complexity of conformant manipulative actions and we discuss how conformant manipulative actions relate to other manipulative actions.

Determining the complexity of election attack problems is a major research direction in the computational study of voting problems. The paper "Towards completing the puzzle: complexity of control by replacing, adding, and deleting candidates or voters" by Erd\'elyi et al. (JAAMAS 2021) provides a comprehensive study of the complexity of control problems. The sole open problem is constructive control by replacing voters for 2-Approval. We show that this case is in P, strengthening the recent RP (randomized polynomial-time) upper bound due to Fitzsimmons and Hemaspaandra (IJCAI 2022). We show this by transforming 2-Approval CCRV to weighted matching. We also use this approach to show that priced bribery for 2-Veto elections is in P. With this result, and the accompanying (unsurprising) result that priced bribery for 3-Veto elections is NP-complete, this settles the complexity for $k$-Approval and $k$-Veto standard control and bribery cases.

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We study the problem of bribery in multiwinner elections, for the case where the voters cast approval ballots (i.e., sets of candidates they approve) and the bribery actions are limited to: adding an approval to a vote, deleting an approval from a vote, or moving an approval within a vote from one candidate to the other. We consider a number of approval-based multiwinner rules (AV, SAV, GAV, RAV, approval-based Chamberlin--Courant, and PAV). We find the landscape of complexity results quite rich, going from polynomial-time algorithms through NP-hardness with constant-factor approximations, to outright inapproximability. Moreover, in general, our problems tend to be easier when we limit out bribery actions on increasing the number of approvals of the candidate that we want to be in a winning committee (i.e., adding approvals only for this preferred candidate, or moving approvals only to him or her). We also study parameterized complexity of our problems, with a focus on parameterizations by the numbers of voters or candidates.

The spread of online reviews and opinions and its growing influence on people's behavior and decisions, boosted the interest to extract meaningful information from this data deluge. Hence, crowdsourced ratings of products and services gained a critical role in business and governments. Current state-of-the-art solutions rank the items with an average of the ratings expressed for an item, with a consequent lack of personalization for the users, and the exposure to attacks and spamming/spurious users. Using these ratings to group users with similar preferences might be useful to present users with items that reflect their preferences and overcome those vulnerabilities. In this paper, we propose a new reputation-based ranking system, utilizing multipartite rating subnetworks, which clusters users by their similarities using three measures, two of them based on Kolmogorov complexity. We also study its resistance to bribery and how to design optimal bribing strategies. Our system is novel in that it reflects the diversity of preferences by (possibly) assigning distinct rankings to the same item, for different groups of users. We prove the convergence and efficiency of the system. By testing it on synthetic and real data, we see that it copes better with spamming/spurious users, being more robust to attacks than state-of-the-art approaches. Also, by clustering users, the effect of bribery in the proposed multipartite ranking system is dimmed, comparing to the bipartite case.

The classic Bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win. Its important generalizations consider voters who are weighted and also have different prices. We provide an approximate solution for these problems for a broad family of scoring rules (which includes Borda, t-approval, and Dowdall), in the following sense: for constant weights and prices, if there exists a strategy which costs Ψ, we efficiently find a strategy which costs at most Ψ Õ( Ψ). An extension for non-constant weights and prices is also given. Our algorithm is based on a randomized reduction from these Bribery generalizations to weighted coalitional manipulation (WCM). To solve this WCM instance, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding a solution in the truncated search space yields a new algorithm for WCM, which is of independent interest.

Given an election, a preferred candidate p, and a budget, the SHIFT BRIBERY problem asks whether p can win the election after shifting p higher in some voters' preference orders. Of course, shifting comes at a price (depending on the voter and on the extent of the shift) and one must not exceed the given budget. We study the (parameterized) computational complexity of S HIFT BRIBERY for multiwinner voting rules where winning the election means to be part of some winning committee. We focus on the well-established SNTV, Bloc, k-Borda, and Chamberlin-Courant rules, as well as on approximate variants of the Chamberlin-Courant rule, since the original rule is NP-hard to compute. We show that SHIFT BRIBERY tends to be harder in the multiwinner setting than in the single-winner one by showing settings where SHIFT BRIBERY is easy in the single-winner cases, but is hard (and hard to approximate) in the multiwinner ones. Moreover, we show that the non-monotonicity of those rules which are based on approximation algorithms for the Chamberlin-Courant rule sometimes affects the complexity of SHIFT BRIBERY.

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The classic bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win.We find an approximate solution for this problem for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: if there is a strategy which requires bribing k voters, we efficiently find a strategy which requires bribing at most k + Õ(√ k ) voters. Our algorithm is based on a randomized reduction from bribery to coalitional manipulation (UCM). To solve the UCM problem, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding the optimal solution in the truncated search space yields a new algorithm for UCM, which is of independent interest.