Prisoners of Geography 2.0: The Theory Behind Where Validators Want to Run

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tl;dr

We develop a formal theory of why Ethereum’s block-building paradigms create geographic centralization pressure. The key results: (1) both paradigms incentivize reducing latency to payoff relevant parties; (2) under local block building, the latency advantage scales with the number of signal sources, creating strong pull toward network centers; (3) under external building, the advantage is bottlenecked by a single supplier but hits the proposer twice through a round-trip penalty; (4) the two paradigms react in opposite directions to information-source placement — local building centralizes faster when sources are in well-connected hubs, while external building centralizes faster when suppliers are in remote regions; (5) consensus parameters like attestation thresholds and slot times act as geographic levers, amplifying or dampening these effects in paradigm-specific ways.

In the ealier version of our work, we used agent-based simulations to show that Ethereum’s block-building architecture quietly shapes where validators end up geographically. Validators cluster along the Atlantic corridor not because the protocol tells them to, but because the economic incentives reward low-latency locations. We showed this by simulating thousands of slots and watching validators migrate.

But simulation alone tells you what happens — not why it has to happen, or how much it matters. In this follow-up, we present the theoretical foundations behind these dynamics, drawn from the theory section of our updated paper. The goal is to explain the structural reasons that Ethereum’s block-building paradigms are not geographically neutral — and to identify which protocol knobs amplify or dampen these effects.

Latency Buys You Time, and Time Is Money

The starting point is simple. In every Ethereum slot, the proposer faces a timing tradeoff: wait longer for a more valuable block as more MEV accumulates [1], or release early to make sure enough attesters see it before a cutoff time. The later you release, the more you earn — but the higher the risk of missing enough attestations and becoming canonical.

Where you are on the map determines how long you can afford to wait. If you’re located in a region with low latency to signal (transaction) sources and attesters, you can release later and still hit the quorum. A validator in US or EU has more timing slack than one in South America — and that slack translates directly into higher expected rewards.

We prove this formally: under both local block building or external block building (e.g., via MEV-Boost or ePBS), reducing delays to payoff-relevant parties (attesters, signal sources, or block suppliers) weakly increases both the optimal release time and the expected payoff. This doesn’t rely on specific distributional assumptions — it holds as long as block value grows over time and lower latency means stochastically faster delivery. Geography creates a payoff gradient, and assume no restrictions for relocation, rational validators will follow it.

Local vs. External Building: How Latency Advantages Scale

While both local and external block building create location-dependent payoffs, they do so through fundamentally different mechanisms — and this matters a lot for understanding centralization dynamics.

Local Block Building: The Scaling Effect

Under local block building, the proposer aggregates signals — transaction bundles, order flow, searchers — from multiple geographically distributed sources, then builds and broadcasts the block to attesters. This means the proposer’s location matters through two channels simultaneously:

  1. Value channel: Closer to signal sources → fresher information → higher block value.
  2. Timing channel: Closer to attesters → more slack before the deadline → can wait longer.

Assume that the value increases linearly in time [2], the value advantage scales linearly with the number of signal sources. If a proposer is 10 ms closer to each of 40 sources, the aggregate value gain is 40 × 10 ms × the MEV growth rate. Every additional source compounds the edge of a well-positioned validator.

This scaling explains why local block building produces such aggressive centralization in our simulations. Starting from a uniform validator distribution, local building drives the Gini coefficient above 0.75 within a few thousand slots — meaning the geography goes from perfectly even to heavily concentrated.

External Block Building: The Double Penalty

Under external block building, the proposer outsources block construction to a specialized block supplier. The proposer’s job reduces to: pick a supplier, commit to their block, and let the supplier handle propagation.

Here, the proposer’s location matters through a single bottleneck: the latency to the chosen supplier. The key structural insight is that the payoff advantage is bounded by the selected supplier — you only use one, so having 10 builders in different regions doesn’t compound your edge the way 40 signal sources do under local building.

However, there’s a subtlety that makes external building particularly sensitive to supplier latency: Proposer-supplier latency enters the payoff twice.

  1. Value observation: the proposer sees the supplier’s offered value with a lag, so the block value is stale by the time of commitment.
  2. Timing budget: the proposer must commit early enough for the round-trip (proposer → supplier → attesters) to complete before the deadline.

Thus, a proposer who moves 10 ms closer to their supplier gains up to 20 ms worth of value growth.

Putting the Two Together

These scaling properties predict that local building produces stronger migration incentives than external building when information sources are numerous. Our simulations confirm this directly:

Metric External Building Local Building
Final Gini (geographic inequality) 0.26 [0.255, 0.257] 0.75 [0.720, 0.786]
Final HHI (concentration) 0.18 [0.182, 0.184] 0.62 [0.514, 0.723]
Liveness coefficient (regions to break liveness) 2 [2, 2] 1 [1, 1]

Table 1: Final centralization metrics under baseline configuration (95% CI in brackets, from 20 independent runs). Local building produces roughly 3× the geographic concentration of external building.

The practical reading: PBS, for all its centralization concerns at the builder level, actually reduces geographic centralization pressure on validators compared to a world where validators build blocks themselves — at least in the baseline case where information sources are evenly distributed.

Information-Source Placement: Opposite Effects Across Paradigms

A key finding is that the two paradigms respond in opposite directions to the same change in information-source geography.

Local block building centralizes faster when sources are in low-latency hubs. If you place signal sources in well-connected regions, validators near those hubs gain a double advantage — better signal freshness and better propagation to attesters. The result is a stronger pull toward already-central regions.

External block building centralizes faster when suppliers are in high-latency regions. When a supplier is located in a poorly connected region, validators who are not co-located with it suffer a large latency penalty — the double penalty we discussed above. The payoff gain from migrating toward the remote supplier is therefore larger, creating stronger co-location pressure. If the supplier were already in a well-connected hub, the latency differences between regions would be smaller, and there would be less reason to move.

Source Placement External HHI Local HHI
Baseline (uniform) 0.18 [0.182, 0.184] 0.62 [0.514, 0.723]
Low-latency hubs 0.79 [0.787, 0.787] 1.00 [1.000, 1.000]
High-latency regions 0.97 [0.969, 0.969] 1.00 [0.999, 1.000]

Table 2: Final HHI under different information-source placements (95% CI in brackets, from 20 independent runs). Under external building, high-latency placement drives stronger concentration (0.97 vs 0.79). Under local building, both placements converge to near-total concentration, but low-latency placement gets there faster. Note the extremely tight CIs for the asymmetric placements — all 20 runs converge to essentially the same outcome.

This result connects directly to the empirical reality described in DataAlways’s analysis: relay and builder locations act as geographic anchors that pull the rest of the ecosystem toward them. Our theory offers one lens for understanding why this happens: the strength of the pull depends not just on the relay’s location, but on how well-connected that location is to the rest of the network. In our framework, poorly connected locations may create stronger co-location incentives.

Consensus Parameters Are Geographic Levers

Beyond block-building paradigms, consensus parameters modulate how much latency matters for relocation incentives.

Attestation Threshold

Raising the attestation threshold - the fraction of attesters who must vote for a block to become canonical - tightens the effective timing window. But the effect on migration incentives depends on the paradigm:

  • External block building: Higher threshold → stronger centralization. A higher threshold means the supplier needs to reach more attesters in time, making each millisecond of proposer-supplier latency proportionally more costly. The incentive to co-locate with the supplier intensifies.

  • Local block building: Higher threshold → weaker centralization. Here, the proposer must balance proximity to attesters (for attestation) against proximity to signal sources (for value). A higher threshold shifts this balance toward attesters, which prevents validators from clustering solely around information hubs by introducing inertia. The tension between these two factors actually reduces the benefit of migrating to any one region.

This asymmetry is relevant to some consensus discussions in the community. The geographic implications of such a change cut both ways. Our results suggest that raising the finality threshold would amplify centralization under external building by making each millisecond of proposer-supplier latency more costly.

Slot Duration

With EIP-7782 proposing to halve the slot time from 12s to 6s, a natural question is: does this worsen geographic centralization?

Our stylized model shows that this is not the case. Reducing the slot duration subtracts the same constant from every region’s payoff, thus pairwise differences are unchanged. But the mean payoff drops, so the same fixed latency edge now represents a larger fraction of total rewards.

We can see this through simulation. The HHI barely moves between 12s and 6s slots — the actual geographic distribution of validators is essentially the same. But the CV — the coefficient of variation of the best proposer payoffs across regions within a slot, which measures how unequal the reward landscape is across locations — increases by roughly 5–10% under both paradigms.

Slot Duration External HHI Local HHI External CV Local CV
Δ = 12s 0.18 [0.182, 0.184] 0.62 [0.514, 0.723] 0.0018 [0.0018, 0.0018] 0.0037 [0.0037, 0.0038]
Δ = 6s 0.18 [0.181, 0.182] 0.55 [0.454, 0.643] 0.0019 [0.0019, 0.0020] 0.0040 [0.0040, 0.0041]

Table 3: Centralization and reward disparity under different slot durations (95% CI in brackets, from 20 independent runs). The HHI (geographic concentration) barely changes, but CV (cross-regional reward inequality) rises — meaning validators in different regions earn more unevenly even though they haven’t moved.

What This Means

Our theoretical analysis surfaces several insights:

  1. PBS reduces validator clustering pressure in the common case — but transfers the centralization risk to supplier/builder geography. If builders concentrate, validators follow. The empirical trends documented in DataAlways’s work are consistent with the incentive structure our theory predicts.

  2. Information-source diversity matters. Encouraging geographically diverse builders, or diverse signal sources, can structurally reduce the payoff gradient that drives concentration.

  3. Consensus parameters are geographic levers. Attestation thresholds and slot durations change which latency components dominate, and can inadvertently amplify co-location pressure.

  4. ePBS might change the game by removing relay chokepoints. Our framework can be used to analyze how ePBS reshapes the payoff landscape — and whether the new equilibrium is more geographically decentralized than the status quo.

The broader message: geography is an emergent outcome of protocol design, not just an infrastructure concern. The rules of the protocol — how blocks are built, who propagates them, what fraction of attesters must respond, and how long a slot lasts — implicitly define a payoff landscape over the surface of the Earth. Validators respond to that landscape rationally. If we want a different map, we need to reshape the terrain.

References

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