Optimizing for deliberation
Measuring (and enforcing) a democratic process
I’m a researcher at the UC Berkeley Center for Long-Term Cybersecurity where I direct the Daylight Lab. This newsletter is my work as I do it: more than half-baked, less than peer-reviewed.
Abstract: I demonstrate the Herfindahl-Hirschman Index (HHI)’s utility as a measure of power concentration in proof-of-stake (PoS) networks. Existing work on measuring decentralization in PoS networks fails to capture the goal of a validator network: to enable the capacity for a deliberative democratic process. While no metric, including HHI, will by itself assure robust deliberation, HHI can help validators select a high-water mark—a point of no return, past which deliberation will surely be impossible. This high-water mark can guide foundations in distributing delegations without concentrating power. As a network parameter, this mark could disallow delegations to overly-powerful validators, or cut their rewards from inflation.
In proof-of-stake (PoS) networks,1 users—the people who hold that network’s tokens—can delegate some of their tokens to validators. Users earn interest from the network’s inflation, and validators take a small commission of that interest to fund their ongoing operation.
Validators then vote on governance proposals, which dictate how the network functions. Their voting weight (how much their vote counts) is determined by the size of their delegation. Like voting shares in a corporation, the size of one’s delegation dictates the power of their vote.
Concentration of power
An ongoing concern in PoS networks is that some validators will develop such large delegations that they will come to control the network.2 That the wealthy validators’ voting shares will be so large that management of the network will centralize in the hands of those validators, handing them unilateral control over the network’s governance.
Users are not the only ones delegating tokens to validators. Most PoS networks begin with a foundation: a founding team that controls some large amount, perhaps even a majority, of all existing tokens. They can delegate these tokens to validators at their discretion, often using those delegations to enforce or reward their ideological commitments.
Preventing power from concentrating
Recently, in the Stargaze network, an interesting discussion arose: how do we distribute the Stargaze foundation’s delegations equitably—that is, a way that neither distorts the governance of the network nor enforces the will of the foundation over the desires of the network’s other users?
My proposal was this:
The validators and the foundation agree on a metric of power concentration.
The validators and the foundation agree on a maximum acceptable value for that metric—a “high water mark,” past which the network should not become any more centralized.
The foundation delegates as it wishes, within the bounds of this metric of power concentration (removing validators from the set who are consistently inactive, have no delegation, and so on).
With this approach, the foundation can delegate as it wishes—unless its delegations threaten to concentrate power beyond acceptable limits.
The question then becomes: what’s an appropriate measure of power concentration?
Measuring the concentration of power
The PoS world has pondered this question extensively. Vitalik Buterin argues that the Gini coefficient is overused and misapplied in practice. Balaji Srinivasan and Leland Lee argue for a Nakamoto coefficient, which speaks more directly to the threat of a 51% attack on the network.
…we’re optimizing for is a deliberative democratic process, free from distortions inflicted by unequal political power.
A key limiter to this debate so far is that “decentralization” as a term is underspecified. The word can refer both to a network’s infrastructure and to how that infrastructure is governed. Semantic slippage ensues. What do we want to decentralize, and toward what end?
Optimizing for deliberation
I’d contend that we’re optimizing for is a deliberative democratic process, free from distortions inflicted by unequal political power. Yet enforcing a simple scheme, such as one-vote-per-validator, won’t do. We want users to be able to select the validators with whom they agree, giving them more of their vote. Delegating is how users can voice their preferences in the network’s governance.
How do we resolve this tension between minimizing distortion and giving users (and the foundation) a meaningful say in the network’s operation?
This question gives us a crisper vision of the problem at hand. It makes clear why the Gini coefficient won’t work for us: we don’t want there to be an even amount of delegation per validator—that’s not what we’re optimizing for. What we’re optimizing for is meaningful deliberation. The ability to reward popular ideas without creating an oligarchy.
Creating a high-water mark
While deliberation can and should be measured in the machinations of governance itself,3 we’d still like a simple, quantitative, and network-level view of a particular validator set’s capacity for deliberative governance. Is deliberative governance possible in this network, or has the concentration of power become so extreme that no deliberation is possible? While no metric will assure high-quality deliberation, we need some sort of alarm. A bright red line over which the network must not cross.
Here enters the Herfindahl-Hirschman Index, or HHI. Originally developed to measure market competition in antitrust, the HHI is outrageously simple to compute: take the market shares of each firm competing in a market, square them, then add them together.
Is deliberative governance possible in this network, or has the concentration of power become so extreme that no deliberation is possible?
I’ve used HHI to understand concentration in various core internet services in some of my work with the Internet Society. This metric “works” in that domain—say, identifying monopoly in the market for content distribution networks (CDNs)—because there exist some finite number of CDN-using websites in the world over which providers compete.
Proof of state networks present an analogous problem. A finite number of delegated tokens exist, over which the validators compete. Competitiveness of this market for delegations—or, phrased differently, concentration in this market—is a reasonable proxy of the concentration of political power. If there is no competitiveness—if a few validators dominate this market—we can be assured that deliberation is impossible: wealthy validators can exert their will without it.
What do we observe?
What HHI values do we observe in PoS networks? I computed the HHI of the “market” of validators in Stargaze and various other chains. (All source code is available on GitHub).
While none of these networks are particularly concentrated by traditional antitrust standards,4 there’s decent variation in values between networks. So what’s a reasonable upper bound on acceptable concentration? This data allows us to set a normative bound of about 600, beyond which we should not allow the network to concentrate any further.5 Beyond that level, a given network would be more concentrated than all but the most concentrated PoS network.
A normative upper bound on concentration is better than no bound at all. But a descriptive upper bound—one that borrows from political science methods—would be best. Political science methods can help us understand quality of deliberation in, for example, Commonwealth threads or Discord channels. Theories of deliberative democracy can help us understand what makes such systems strong. Only then could we understand how (and if) HHI relates to these measures.
We should also remember that any metric we introduce into governance is subject to gaming. We should red-team this metric, understanding how it might be manipulated to hide concentration in a way that eludes detection.
Finally, stake-weight voting need not be the end-all voting mechanism. Voting systems like alternative vote (AV) or single transferrable vote (STV) could serve the goals of PoS networks better than stake-weight voting. Future work should divine specific threat models in which stake-weight voting fails, but some other voting mechanism succeeds.
Nevertheless, the prospect of having some agreed-upon metric—some high-water mark of maximum allowable concentration—is a promising one. Once a network settles on a particular figure for a maximum acceptable HHI, that figure could become a network parameter—one that prevents delegations to validators who already have “too much,” slashing their rewards or commission, or some combination thereof.
Network governance is incredibly complex, but—in analogy to inflation and employment rates in national economies—imperfect models and metrics, iteratively improved through experience and analysis, beat flying blind.
No metric is perfect. But, without metrics, we’re doomed to replicate the systems we aspire to replace. No metric will assure success, but a good metric will sound the alarms before we condemn ourselves to failure.
Proof-of-stake replaces the extreme computational demands (and ecological pressure) of proof-of-work chains like Bitcoin and Ethereum with a more energy-efficient scheme. Validators—a group of volunteers—are chosen at random by the network to sign blocks. As long as two-thirds of the validators honestly report the transactions they observe, the network will operate securely. Here’s a more detailed explainer:
Validators run by large, commercial exchanges like Binance or Coinbase, for example, may stake their users’ tokens automatically or by default, giving them a leg up. Alternatively, validators may charge no commission, attracting delegations from price-sensitive users. Perhaps they’ll do both.
See Mitchell et al., 2021, who use textual analysis to understand the quality of deliberation in the governance of a health research project.
By the U.S. Department of Justice’s standards, a moderately concentrated (i.e., uncompetitive) market might have an HHI of 1,500-2,500. Over 2,500, they consider a market highly concentrated.
Are some of these networks manipulating this metric, e.g., by having the foundation run multiple validators surreptitiously? Perhaps. Network analysis could suss out this behavior by tracing delegations and transfers. But the goal of this HHI measure is not to identify shenanigans in other networks. It’s to empower a well-intentioned network to balance the need for incentivization against the need for fairness.