Voting Block Entropy

DAO Decentralization: Voting-Bloc Entropy, Bribery, and Dark DAOs

This paper deals with voters in on-chain DAOs which use token voting and aims at producing results on decentralization. It introduces Voting Block Entropy (VBE) as a measure of decentralization, deduces some theorems – most notably on bribery – and applies the Dark DAO concept together with VBE as a prototype to produce a realistic threat on DAO decentralization via bribing.

We’ll focus below mostly on the VBE theory and the role played by the Dark DAO prototype, rather than on the specifics of the latter.

Method overview

Problem setting:

  • Intuition: It’s not enough to look into individual accounts to deduce anything useful about decentralization. Rather look into voter alignment.
  • Normative basis: DAO centralization should be avoided, aim at designs that help with decentralization or show impossibility results.
  • Identification of main problem categories: Apathy, delegation, herding, bribery.


  • Data: Not available. Hard to achieve, although some research have done it, like Feichtinger et al. 2023. Some guidelines are given with respect to measuring utility indirectly.
  • Attackability (see [tbd: attackability as a proxy for empirical data]): A Dark DAO prototype is built, that enables bribery coordination. Based on VBE results, this means effectively that decentralization is effectively reduced whenever the attack is performed.


  • Key definitions: Clustering metric, entropy, VBE, inactivity whale. High VBE relates to more decentralization, hence fulfilling the normative objective.
  • Key results: Results on aforementioned problems. Most importantly, on bribery:
    • Bribery is a threat to decentralization.
    • Bribery must involve a large number of tokens (large-scale coordination) iff the system is highly decentralized.
    • Notes: Decentralization reduces the costs of bribing (whales being more pivotal, they are more expensive). Also, thanks to smart contracts and DAOs, bribing is more realistic a threat than in usual secret-ballot elections.

Usefulness and challenges

VBE suggests an abstraction above individual accounts which proves very effective on a theoretical level.

Notably, it enables building positive results about decentralization and effects of bribery on it.

But it is noted that this depends heavily on the notion of voter utility which is not directly observable (latent variable). The authors suggest some VBE variants that can still be computed based on usual voting data.

Dark DAOs and attackability

The purpose of the Dark DAO prototype built in the paper is to demonstrate the feasibility of a fully functional Dark DAO, which is designed to facilitate vote-buying in DAOs on Ethereum.

The methodology ([tbd: attackability as a proxy for empirical data]) focuses on demonstrating the plausibility of attacks on DAO decentralization. This approach serves as a practical test of the theory’s applicability to real-world scenarios. By successfully illustrating how DAOs can be vulnerable to attacks, the theory proves its effectiveness in understanding and predicting real-world outcomes, even though it operates primarily in an abstract, theoretical realm.

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