Vote Buying, On-Chain Governance, and Quadratic Plutocracy

This post is a continuation/expansion of a previous post, “On-Chain Vote Buying and the DAO Dark Ages“, published on HackingDistributed.  In this initial post, we provided an efficient private vote buying infrastructure that could be used to arbitrarily alter stable game theoretic equilibria in any on-chain voting protocol by allowing votes, identities, and restrictions on behaviors to be bought and sold on an efficient, private, trust-minimizing market.

We also explored an attack on blockchain systems we called a “Dark DAO”, in which a network of incentivized participants pooled to form a vote buying or consensus attacking cartel that was opaque to outsiders.  These attacks have implications on on-chain voting incentives, general blockchain security, and e-voting in the permissionless model (where users can generate their own keys using untrusted hardware).

We will now explore these ideas in the context of other complicating factors, such as direct on-chain governance for consensus rules, and schemes which explicitly allow for vote buying such as quadratic voting.

Self-Evolving Systems

Beyond their use as signaling, a natural extension of a voting model in blockchains is to use voting to decide critical community governance questions.  Such questions have led to coin splits, community strife, and personal and physical attacks on many occasions in past systems, and providing a natural upgrade mechanism for rules governing the system seems an intuitive solution to the strife.  Two concrete proposals include in Tezos and EOS.

Obviously, such schemes are vulnerable to the above attacks and pathologies.  Given the relatively high level of drama that has already been empirically observed in the EOS voting protocol, and as such votes in many cases directly incentivize vote buying for rational actors, it is likely that vote buying will prove a major problem should any such systems reach maturity.

Using coinvotes in this manner does not directly affect the possibilities available to a vote buyer, who could potentially buy any behavior they would like to on any system.  That being said, using a coinvote in this manner legitimizes any outcome of the community process, and provides a convenient default for users to converge on. Otherwise phrased, most users will likely accept most outcomes of most coinvotes, so rigging such votes can allow a malicious actor to impose their will on an ecosystem where the majority of honest actors disagree (but follow along anyway, because the vote appears clean).  This, along with the direct benefit provided by many consensus rule changes to actors within the system (consider for example the setting of block rewards, or the setting of block size / participation hardware requirements, or the setting of minimum stake, etc.) means that tampering with such votes is often directly financially incentivized.

Election instances in the US where a popular vote loser was declared victor.

Populations will accept vote outcomes regardless of how bitterly they disagree with the outcome or how nonsensical it seems… if they accept the process.

Incentives for hijacking signaling votes may in some cases be less direct, as these votes have less influence in forcing users to perform an upgrade or accept an unpopular change.  Such “loose coupling” is advocated for by both Vitalik Buterin and Vlad Zamfir, with the former opining

Here, note that there is a key difference between tightly coupled and loosely coupled votes. In a loosely coupled vote, direct or indirect vote bribing is also possible, but if the community agrees that some given proposal or set of votes constitutes a game-theoretic attack, they can simply socially agree to ignore it.

In my personal opinion, reality is a bit more subtle than this, as deciding whether there is an attack in the presence of a credible threat is a non-trivial social consensus problem vulnerable to false flag attacks to stall progress.  Furthermore, unilaterally agreeing to suspend in the presence of an attack simply does not go far enough, as it opens a trivial DoS vector on any vote (don’t like the majority opinion?  launch an attack and claim unfairness!).

In general, our previous post on this subject concluded that all on-chain coin-based voting systems essentially emulate plutocracy.  If they do not directly emulate plutocracy, perhaps through some external system of identity, they can be made to emulate plutocracy through the buying and selling of constraints on user actions, such as in the Dark DAO example we provided.  Lastly, attacks can be hidden in nature, and can (again as in the Dark DAO construction) remain undetectable and unmeasurable.  While a classic response may be that plutocrats are interested HODLers of the coin and will always vote in a coin’s best interests, the existence of vote buying clearly separates HODLing from voting behavior economically, and allows a range of new incentive changing mechanisms that in equilibrium likely degenerate into sheer plutocracy.

Such concerns are particularly severe when multiple ecosystem projects leverage on-chain voting, as rational users of any system will always be incentivized to pledge some funds to directly attacking the security of the competition.  The presence of multiple on-chain governance systems with intertwined incentives makes outcomes even less clear, and it would be an extremely surprising result if such a lack of clarity did not directly imply the existence of a large number of complex black swan events.

Quadratic Plutocracy

Despite the poorly understood nature of on-chain voting, many cryptocurrencies wish to perform experiments that go further than standard voting mechanisms.  Such experiments, considered radical proposals in meatspace, are even less tested in the on-chain context. One example is a proposed scheme called quadratic voting, which explicitly aims to avoid plutocracy and solicit fair outcomes from users by allowing users to buy votes at an exponentially increasing cost for each vote.  In this way, intuitively, a large number of less-resourced but passionate voters cannot be overwhelmed by a few dispassionate wealthy voters. Also, a passionate minority cannot be overwhelmed by a passive but primarily indifferent minority, a known pathology in some traditional voting models.

Interestingly enough, rather than fighting vote buying as degenerating into plutocracy as our initial article does, quadratic voting enforces and enshrines vote buying as a feature of the system.  The exponentially increasing costs to buy these votes is the key mechanism that produces fair outcomes.

Unfortunately, quadratic voting comes with several drawbacks in an on-chain setting.  The first is the obvious requirement for identity; even small amounts of Sybil-vulnerabilities completely break the scheme by allowing wealthy users to amplify their funds through splitting.  Settings with identities that depend on user-generated keys are vulnerable to identity buying attacks through the same mechanisms used for vote buying in the Dark DAO.

Even after surmounting these drawbacks and assuming a perfect system of identity, the scheme inherently amplifies the effect of bribery attacks.  As one survey on vote buying in political elections points out:

“Many have argued that positive inducements should have a greater impact on the voting behavior of the poor because the marginal utility of income of low-income voters is higher (Dixit & Londregan 1996, Calvo & Murillo 2004, Stokes 2005, Stokes et al. 2013). The evidence that vote buying is principally aimed at the poor is virtually uncontested.  In cases ranging from Lebanon (Corstange 2011) to Nigeria (Bratton 2008) and Argentina (Stokes 2005), studies find that politicians target poor voters with positive inducements, such as gifts and offers of food or money.”

It is not clear that the blockchain context will differ.  Especially in quadratic voting, bribing poor voters even at a loss to what such votes would cost the rich themselves could be profitable, essentially creating an economic Sybil attack despite the identity system enforcing real-world identities on-chain.  This makes quadratic voting likely unsuitable for large blockchain elections with varied stakeholders, at least without substantial modification.

The authors of the quadratic voting proposal claim in recent analysis that the scheme is more resilient to bribery than traditional voting, with the key mechanism as follows:

However, in the bounded support case she would have to pass herself off as a number of identities comparable with the square root of the population size (many thousands of individuals in a state like California), which would be trivially easy for authorities to detect and prevent. Even when α = 3 she would have to pass herself off as being clones of the sixth root of population, or roughly a dozen individuals, which still seems quite detectable, before she would cause problems for efficiency.

They conclude that “collusion and fraud, except on a very large scale, are deterred either by unilateral deviation incentives or by the reactions of non-participants to the possibility of their occurring.”  While this is true in a paper ballot or off-chain setting, it is clear through the lens of our previous articles that such assumptions are not tenable on-chain.  Buying votes of on the order of a dozen individuals is likely extremely easily tractable, and also extremely hard to detect in such a setting.  It is in fact the very privacy provided by the Dark DAO scheme, combined with its ease of deployment, that provably violates the authors’ assumptions of reacting to collusion or fraud being a potentially feasible countermeasure.

This is all not to say that experimenting with new voting models in blockchain is not useful or interesting, but to assert that any voting deployments must be mindful of the unique and hostile environment on-chain voting demands.  It is unlikely that schemes that work well for in-person voting, boardroom meetings, or even coordinator-based protocols will simply port to blockchains without substantial additional work on defining and proving adversarial resilience to both technical and economic attacks in a blockchain-specific context.  It is clear that applying mechanisms that work in traditional information sciences or economics is not sufficient to analyze and represent the equilibria that will actually emerge when a given game is deployed (and matures to importance) in a permissionless blockchain environment.

It is likely that if schemes without blockchain-specific analyses are deployed for important political decisions, even past experimental success will not grant them freedom from manipulation.


So, it is clear that the dangers of on-chain voting are exacerbated by more complicated systems built on top of these technologies.

Self evolving systems directly incentivize vote buying and give the outcome of purchased and rigged votes large amounts of power over system operation.

Schemes like quadratic voting, that have been proposed in a blockchain context, explicitly allow vote buying and attempt to mitigate its impact through an identity-based scheme.  Such schemes may have unforeseen properties in a blockchain environment, where identity is a murky concept, and the existence of trusted hardware implies that a user can sell only behaviors of their identity without transferring the identity itself.

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