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INTRACTABILITY#32 of 56 by βWPaper #3
Proof-of-Stake Protocols
Welfare costs are materially lower than Proof-of-Work, but the domain-level Monte Carlo result remains above beta-W = 1. Primary risks are validator concentration, staking governance, MEV, and custody.
WELFARE BETA
candidate beta-W 2.13
source-reported average; admission pending independent channel and denominator review
THEOREM TYPE
Intractability
institutionally reformable
SOURCE STATUS
Summary + deck generated
verified by paper record
Reading welfare beta
Welfare beta, written as βW and pronounced beta W, means annual system-welfare loss divided by annual industry revenue, written as Π and pronounced capital pi. Revenue is the denominator, never profit; ΔW and Π must use the same domain, same time period, and same activity boundary. See the welfare-beta methodology manual.
OPEN HTML DECK ↗Deck mode is an on-site reading view, not a PowerPoint download.
Theorem status: evidence-traced claim under the cited paper's assumptionsMC interval status: re-estimation required; legacy template bands are withheldWelfare beta is a source-reported candidate average; channel and denominator admission is pendingAnnual industry revenue is the denominator, not profit; both quantities must share the activity boundaryFalsification: show the same game preserving system welfare without changing the payoff structure
2.13
welfare beta
$170.6B
annual loss ($B/yr)
$80B
annual revenue ($B/yr)
KEY FINDINGS
THE CROSS-CHAIN WELFARE FLOOR
Protocol Welfare Floor (Impossibility Theorem). Permissionless architecture guarantees βW ≥ 1.0 regardless of consensus mechanism.
PLAIN ENGLISH
Proof-of-Stake eliminates Bitcoin's energy problem but replaces it with validator concentration and front-running. Maximal Extractable Value extracts rent from users through transaction ordering manipulation. The Protocol Welfare Floor still holds: no permissionless blockchain achieves βW < 1.0.
six-lane CONFLICTORING ADVICE
EVIDENCE & LIMITATIONS
- Theorem status: evidence-traced claim under the cited paper's assumptions
- MC interval status: re-estimation required; legacy template bands are withheld
- Welfare beta is a source-reported candidate average; channel and denominator admission is pending
- Annual industry revenue is the denominator, not profit; both quantities must share the activity boundary
- Falsification: show the same game preserving system welfare without changing the payoff structure
REFERENCES / CITATION STATUS
Reference counts for this manuscript have not been published yet. Treat its citations as unverified until a source list is available.
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EXECUTIVE SUMMARY
The companion paper (Postnieks, 2026b) applied the System Asset Pricing Model (SAPM) to Bitcoin and found that each dollar of industry revenue destroys approximately $5.00 of system welfare, driven primarily by energy consumption. The paper extends the SAPM to Proof-of-Stake (PoS) blockchains, which replace energy-intensive mining with economic collateral. Using empirical data from 2020–2026, the
SOURCE QUESTIONS
WHY THIS MATTERS
For the economist
Classified Intractability. The source-reported candidate beta-W of 2.13 is the average system-welfare loss per dollar of industry revenue. Its channel inputs, denominator, and uncertainty packet still require independent admission.
For the regulator
The constraint is institutional, so a well-designed rule can reach a better outcome. Check whether a proven policy model already exists for this domain.
For the executive
This is where a privately efficient decision can degrade the system the business depends on. The governance question is which decision records would make that system cost visible before it is normalized.
For the teacher
An on-site HTML deck and the expanded curriculum cover the argument, the evidence, and the measurement. Use the deck as a self-contained class session, then route deeper through the 45-50h core course or 100+h full curriculum.
For the affected community
In plain terms: who gains from the current arrangement, who pays for it, and what rule change would alter that split. The summary states each without jargon.
RELATED BY WELFARE BETA
Welfare beta is shown on the same scale for each card: annual system-welfare loss divided by annual industry revenue, with both measured on the same domain, same time period, and same activity boundary.
© 2026 Erik Postnieks · Independent Researcher · Salt Lake City