Centralization and Stability in Formal Constitutions
Ben-Gurion University Economics Seminar
April 2026
Yotam Gafni
Weizmann Institute of Science
Topic of this talk…
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In Formal Systems!
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“Blockchain Governance: An Empirical Analysis of User Engagement on DAOs”, Falk et. al 2024
A lot of assets under smart contract control…
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Source: https://defillama.com/treasuries, retrieved April 21st 2026
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” The key ingredients of a successful nonviolent resistance movement […]:
The ability to create loyalty shifts among key regime-supporting groups such as business elites, state media, and—most important—security elites such as the police and the military.”
Goals and general roadmap
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Two Conceptual Pillars
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Barbera & Jackson (QJE 2004)
Koray (Econometrica 2000)
Study qualified majority rules (simple majority -> consensus)
Threshold T
n voters
More Effective
More Conservative
Unanimous and neutral social choice functions are
``self-selective’’ iff they satisfy IIA (Independence of
Irrelevant Alternatives)
-> Only dictatorship is self-selective (by Arrow’s Theorem!)
Neutral rules!
Anonymous rules!
To understand centralization, we need non-anonymous rules.
To understand passing decisions, we need non-neutral rules.
We need new theory!
Model
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Still missing: Tie-breaking, belief specification
Example I (Stylized):
The Bolsheviks, the Mensheviks, and the Whites
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9 voters
3 Bolsheviks
2 Mensheviks
4 Whites
Example I (Stylized):
The Bolsheviks, the Mensheviks, and the Whites
Example I (Stylized):
The Bolsheviks, the Mensheviks, and the Whites
Example II:
Unanimity Vote in the European Union
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``Whether Unanimity is the best protector of national sovereignty depends on
whether a state believes that maximizing the possibility of inaction [...] is better
for the national interest than a qualified-majority voting rule which increases the
possibility of action” [EU Law: Text, Cases and Materials, Craig & de Burca ‘24]
Back to the Model:
Tie-Breaking and Beliefs
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Rationalizable!
Robust!
Highlights of Results:
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| Arbitrary Tie-Breaking | SQB Tie-Breaking |
Conditionally self-maintaining | All (and only) non-dual-passing rules | All (and only) non-dual-passing or respect rejective-consensus rules |
Universally self-maintaining | The constant-0 function | Dictatorship 3-oligopoly Conservative, flower-form, entangled SCFs (e.g., consensus-duopoly, 3-oligopoly with veto) A rule must be: Non-dual-passing, downward-closed, respect rejective-consensus, bounded monotonicity violation, bounded downward sensitivity… A gap exists between the necessary and sufficient conditions. |
I.i.d. self-maintaining | The constant-0 function, dictatorship, and anti-dictatorship. Other rules exist only for the biased setting, but not with better social/Nash welfare. | +Consensus-duopoly , has better social/Nash welfare than dictatorship when 0<p<1/2 |
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With arbitrary tie-breaking, an SCF is conditionally self-maintaining if and only if it is non-dual-passing.
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With arbitrary tie-breaking, an SCF is conditionally self-maintaining if and only if it is non-dual-passing.
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With arbitrary tie-breaking, an SCF is conditionally self-maintaining if and only if it is non-dual-passing.
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With arbitrary tie-breaking, an SCF is conditionally self-maintaining if and only if it is non-dual-passing.
Highlights of Results:
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| Arbitrary Tie-Breaking | SQB Tie-Breaking |
Conditionally self-maintaining | All (and only) non-dual-passing rules | All (and only) non-dual-passing or respect rejective-consensus rules |
Universally self-maintaining | The constant-0 function | Dictatorship 3-oligopoly Conservative, flower-form, entangled SCFs (e.g., consensus-duopoly, 3-oligopoly with veto) A rule must be: Non-dual-passing, downward-closed, respect rejective-consensus, bounded monotonicity violation, bounded downward sensitivity… A gap exists between the necessary and sufficient conditions. |
I.i.d. self-maintaining | The constant-0 function, dictatorship, and anti-dictatorship. Other rules exist only for the biased setting, but not with better social/Nash welfare. | Consensus-duopoly , has better social/Nash welfare than dictatorship when 0<p<1/2 |
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With SQB tie-breaking, a Dictatorship is universally self-maintaining.
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With SQB tie-breaking, a 3-oligopoly is universally self-maintaining.
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With SQB tie-breaking, any conservative, flower-form, entangled SCF is universally self-maintaining.
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With SQB tie-breaking, any conservative, flower-form, entangled SCF is universally self-maintaining.
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With SQB tie-breaking, any conservative, flower-form, entangled SCF is universally self-maintaining.
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With SQB tie-breaking, any conservative, flower-form, entangled SCF is universally self-maintaining.
Highlights of Results:
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| Arbitrary Tie-Breaking | SQB Tie-Breaking |
Conditionally self-maintaining | All (and only) non-dual-passing rules | All (and only) non-dual-passing or respect rejective-consensus rules |
Universally self-maintaining | The constant-0 function | Dictatorship 3-oligopoly Conservative, flower-form, entangled SCFs (e.g., consensus-duopoly, 3-oligopoly with veto) A rule must be: Non-dual-passing, downward-closed, respect rejective-consensus, bounded monotonicity violation, bounded downward sensitivity… A gap exists between the necessary and sufficient conditions. |
I.i.d. self-maintaining | The constant-0 function, dictatorship, and anti-dictatorship. Other rules exist only for the biased setting, but not with better social/Nash welfare. | Consensus-duopoly , has better social/Nash welfare than dictatorship when 0<p<1/2 |
No gap for Weighted Voting Games!
Weighted Voting Games:
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| Arbitrary Tie-Breaking | SQB Tie-Breaking |
Conditionally self-maintaining | All rules | All rules |
Universally self-maintaining | No rules | Exactly: Dictatorship 3-oligopoly Conservative, flower-form, entangled SCFs (e.g., consensus-duopoly, 3-oligopoly with veto) |
I.i.d. self-maintaining | Exactly dictatorships. | All the SQB universally self-maintaining rules ??? |
Zoom out: What’s missing in our model?
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A Restaurant Story…
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Re-examining Our Model
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Condorcet’s Jury Theorem
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p
Pr[Majority = True State]
A Revised Model
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Stability in the Revised Model
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Takeaways, Part 1
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Takeaways, Part 2
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A Call for Future Work
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Thanks for listening!�
Email: yotam.gafni@gmail.com
Website: https://www.yotamgafni.com
We Can Believe In?
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“A more serious issue is collusion between the proposer and some transaction senders.“
[Vitalik Buterin, “Blockchain Resource Pricing” 2018]
“Frequent exchanges of information that facilitate a better common understanding of the market and monitoring of deviations increase the risks of a collusive outcome.“
[European Commission Guidelines to Horizontal Cooperation Agreements 2023]
Change
New�Technology
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🡪
New�Assumptions
New�Mechanisms
🡪
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Security
Align Incentives
with System Goals
Fairness
Make the System Work
for Everyone
Optimality
Tune the System
to Maximize Objectives
Robustness to Collusion
Safety of Data-Sharing Protocols
Weak Identity & Recourse
Consumer Effects of Learning
Fair Exploration & Allocation
Centralization Dynamics
Minority Rights
Prizes in Data Science Contests
Outsourcing
Priority under Time-Sensitivity
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Security
Align Incentives
with System Goals
Fairness
Make the System Work
for Everyone
Optimality
Tune the System
for Max Performance
Robustness to Collusion
[GY EC’24 Revision@GEB,
FGR TLDR’24 🏭,
GY MARBLE’24, G’25]
Safety of Data-Sharing Protocols
[GT EC’22]
Weak Identity & Recourse
[GLT AAAI’20, GT TARK’23]
[GLT IJCAI’21, JAIR’22]
Prizes in Data Science Contests
[DGLLL AAAI’23, GEB’25]
Outsourcing
[FG’26]
Priority under Time-Sensitivity
[GY’22]
Consumer Effects of Learning
[GGT SAGT’24, Revision@TEAC]
Fair Exploration & Allocation
[BP-GM’25, GHLT-C TEAC’23]
Centralization Dynamics
[G’25]
Minority Rights
[GG’24 🏆]
Blockchains are Permissionless
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🡪
No Trust in Miners
Collusion-Robust Mechanisms
🡪
Blockchains: A Soft Intro
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Total Blockchain Market Cap
Blockchain Market Cap Partition
$6T
$4T
$2T
$0
‘14 ’15 ‘16 ’17 ‘18 ‘19 ‘20 ‘21 ‘22 ‘23 ‘24 ‘25
‘14 ’15 ‘16 ’17 ‘18 ‘19 ‘20 ‘21 ‘22 ‘23 ‘24 ‘25
100%
75%
50%
25%
0%
Bitcoin
Ethereum
Stablecoins
Other
Blockchains: Why?
Why not traditional transaction systems?
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“Competition among service providers within the platform and free entry imply no entity can profitably affect the level of fees paid by users.”
Huberman, Leshno & Moallemi, REStud ‘21
“Competition among service providers within the platform and free entry imply no entity can profitably affect the level of fees paid by users.”
Huberman, Leshno & Moallemi, REStud ‘21
But it comes with its own set of challenges…
Cost to Send USD Internationally
$44 via International Wire Transfer
$12 via USDC on Ethereum, ’21 avg
$1 via USDC on Ethereum, Sep ’24 avg
<$0.01 via USDC on Base L2,Sep’24 avg
[a16z crypto, State of Crypto 2024 Report]
Blockchains: Technical Primer
Users
Miners
Block
Block
Transaction
Blockchain
Block
Block
A Random Miner is Given Temporary Monopoly Power
Block
Reward
Fees
To prevent Sybil Attacks, the random choice depends on a finite resource
In Bitcoin, transactions allow payments. In Ethereum, they are Turing-Complete and can encode any logic.
Transaction Fees
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Users
Block
Miner
TX
TX
TX
Max size:
2 TXs
Max Eth
Block
Source: mempool.jhoenicke.de
Pending TXs
Date
Bitcoin’s Transaction Fee Mechanism
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EIP-1559: Ethereum’s New TFM
Goal 3: Understand whether burning matters
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Tip
Base
Tip
Base
Ethereum fees before and after EIP-1559 [LLNZZZ CCS’22]
TX
New Block of Size 2
Base Fee
A total of >4m ETH were burned since EIP-1559
Transaction Fee Mechanisms (TFMs)�
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The foundational open problem of TFMs:
Existence of a simple for users, miner non-manipulable, and robust to collusion TFM?
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No deterministic mechanism satisfies all desiderata.
A gap in welfare exists for randomized mechanisms.
[Gafni & Yaish EC’24, Minor revision at Games and Economic Behavior]
1st and 2nd price auctions
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1st-price auction
2nd-price auction
Pays its own bid
We focus on single-item auctions in the talk.
The paper characterizes the multi-item setting.
Highest bidder wins
Pays second highest bid
Highest bidder wins
Simple for Users ✅
Robust to Miner manipulation ✅
Pays set price (1.5)
Ok, bidder 1, just say you’re willing to pay 1.5, and I’ll cash you back 1
1.5
1
The true value for bidder 1
Bidder 1’s payment
Miner’s transfer
Arbitrary winner above a set price
Problem?
Hint: Bad price discovery, which motivates collusion
Some Notations…
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The Desiderata
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”Myerson’s Lemma” [Myerson ‘81] :
UIC <=> monotone allocation, payment uniquely determined by allocation.
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No revenue…
What if we only have Global-SCP?
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Less burn, same value.
Bidder and Miner can balance using transfers.
Adding UIC and MIC into the mix…
Our characterization of Global-SCP:
Constant burn, highest-bidder allocated if and only if higher than the burn.
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Achieving all together is impossible.
With UIC:
Second-price auctions with a reserve that is burned.
With MIC:
“Generalized first-price” auctions
A slightly generalized EIP-1559/Bitcoin Mechanism!
Randomized Mechanisms
So far, we discussed only deterministic mechanisms.
We always assumed a specific bidder is allocated.
What if we allow a random choice of who is allocated?
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General Randomized Mechanisms
Proof-sketch: We have 0 revenue with a single bidder (burn=payment).
Without (P1), miner would create a shill bidder.
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General Randomized Mechanisms
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Takeaways
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Emergence of Data-Sharing Protocols
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🡪
Exclusivity Attacks
🡪
Robust Protocols
�A growing interest in building shared models…
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Building Shared Models
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Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Model
Federated Learning
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Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Model
Model
Model
Federated Learning
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Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Local Gradients 1
Local Gradients 2
Local Gradients 3
+
+
3
Updated Model
Federated Learning
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Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Model
Free-Riding is a threat!
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Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Model
Model
Model
Free-Riding is a threat!
74
Coordinator Server
Client 1
Client 2
Client 3
Local Data 1
Local Data 2
Local Data 3
Local Gradients 1
Local Gradients 2
Local Gradients 3
+
2
Updated Model
Free-Riding is a threat!
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Client 1
Client 2
Client 3
Updated Model
Updated Model
Coordinator Server
Local Data 1
Local Data 2
Local Data 3
Updated Model
Local Gradients 3
Free-Riding is a threat!
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“For Federated Learning, incentive mechanism design for honest participation is an important practical research question […] particularly relevant in the cross-silo setting, where participants may at the same time be business competitors.“
[Kairouz et al., “Advances and Open Problems in Federated Learning” 2021]
A General Concept:�Exclusivity Attacks
where all other agents report truthfully and accept the model,
can an attacker launch a successful exclusivity attack?
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Example: The one-shot function SUM
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20
10
+
=
30
Example: The one-shot function SUM
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30
30
A successful attack on one-shot SUM
80
20
10
+
=
A successful attack on one-shot SUM
81
30
A failed attack on one-shot MAX
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20
10
,
)=
max(
A failed attack on one-shot MAX
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??
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We consider a long-term interaction
Continuous Protocol:
Conditionally Vulnerable
Universally vulnerable
Linear Regression in d features
(d-LR)
k-Center Clustering
Yes
Yes
No
Periodic Protocol: d-LR, k-Center are not vulnerable.
Formal model – Continuous Protocol
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A failed attack on continuous MAX
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Ledger update:
120
Ledger update:
90
Nature
Agent 1
Agent 2
Ledger
True update:
90
User update:
90
Ledger update:
90
User update:
120
Ledger update:
120
True update:
90<X<120
User update:
90<X<120
Ledger update:
120
Ledger update:
120
Observed history, Strategy and Vulnerability
87
Ledger update:
120
Ledger update:
90
Nature
Agent 1
Agent 2
Ledger
True update:
90
User update:
90
Ledger update:
90
User update:
120
Ledger update:
120
True update:
90<X<120
User update:
90<X<120
Ledger update:
120
Ledger update:
120
Observed History: All the messages agent j sees.
Update Strategy: Mapping from observed histories to user updates.
Truthful: a user updates U iff the user received true update U
Observed history, Strategy and Vulnerability
88
Ledger update:
120
Ledger update:
90
Nature
Agent 1
Agent 2
Ledger
True update:
90
User update:
90
Ledger update:
90
User update:
120
Ledger update:
120
True update:
90<X<120
User update:
90<X<120
Ledger update:
120
Ledger update:
120
Observed history, Strategy and Vulnerability
89
Ledger update:
120
Ledger update:
90
Nature
Agent 1
Agent 2
Ledger
True update:
90
User update:
90
Ledger update:
90
User update:
120
Ledger update:
120
True update:
90<X<120
User update:
90<X<120
Ledger update:
120
Ledger update:
120
Linear regression
90
Challenge for the Attacker:
How to ‘reverse’ effects of fake points submitted?
A temporary omission conditional attack
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A Universal Attack
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A Universal Attack
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Example of a universal attack on �Linear Regression with one feature.
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Truthful
Universal Attack
Example of a universal attack on �Linear Regression with two features.
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Takeaways
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Looking Forward…
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UNISWAP Foundation Fellowship!
Robust TFM Design
Blockchains Beyond TFMs
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Incentives & Economics of AI
Fair Allocation: Theory to Practice
Thanks for listening!�
Email: yotam.gafni@gmail.com
Website: https://www.yotamgafni.com