CE
COMSCI/ECON 206 · Final FP11 Behavioral-science artifact · Zimu Zhou
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DAO Treasury Governance Lab

Who should control a shared treasury?

Explore how token-weighted voting (TWV) and square-root voting (SRV) change collective choice when one holder owns 60% of the tokens—and what happens when identity splitting becomes strategically available.

Evidence status: this Space structures self-play and peer-play reflection. It does not collect data on a server and does not establish a population-level behavioral effect. The numerical benchmark shown later comes from a separate synthetic simulation (seed 206), not from human participants.

Step 1 · Understand

One treasury, three proposals, unequal token holdings.

You are one of seven ordinary holders. Together the seven ordinary holders own 40% of the tokens; one whale owns the remaining 60%. Each actor votes for one proposal.

Token-Weighted Voting (TWV)
weight = token share

A 60% holder receives voting weight 0.600. Each ordinary holder receives about 0.057.

Square-Root Voting (SRV)
weight = √(wallet token share)

With one whale wallet, the whale receives about 0.775 while each ordinary holder receives about 0.239.

Additional information for this session: under SRV, splitting the same 60% stake across multiple wallets can increase total effective voting weight. With 8 equal whale-controlled wallets, the total SRV weight becomes √(8 × 0.60) ≈ 2.191, compared with √0.60 ≈ 0.775 for one wallet. The total stake has not changed.
Before playing, which rule seems more appropriate for this DAO treasury?

Step 2 · Vote

Round 1

Choose a proposal after seeing your own values and projected support from the other seven actors.

TWV

Your private values

Higher is better for you. Your highest-value proposal is the sincere-voting benchmark.

ProposalValue

Projected support before your vote

The other six ordinary holders split evenly between A and B; the whale supports C.

Which proposal do you vote for?

Step 3 · Compare

Same treasury. Same actors. Different aggregation rules.

The behavioral task holds the scenario fixed and changes the governance rule. Your votes may also change because the strategic environment changes.

Verified synthetic benchmark

What the separate simulation found at 60% whale ownership.

These are means from 1,000 paired synthetic valuation profiles per condition (independent uniform [0, 1), seed 206). They are computational evidence, not human-participant results.

RuleWhale walletsHolder efficiencyStake efficiencyWhale successNon-whale representation
TWV10.8990650.9910971.0000.321
SRV10.9277810.9770760.8960.417
SRV80.8990650.9910971.0000.321

Interpretation: unsplit SRV raises equal-holder efficiency and non-whale representation in this simulation, while slightly lowering stake-weighted efficiency. With 8 whale-controlled wallets, those gains disappear and the displayed metrics match TWV. “Non-whale representation” here means the winning proposal maximizes the seven ordinary holders’ aggregate synthetic valuation; it is not a protected-minority measure or proof of real-world DAO capture.

Allocation analogy boundary

This is a collective allocation problem, not a literal auction.

The scarce resource is DAO treasury funding and the proposals are competing uses of that resource. Token holdings shape decision power, but this behavioral demo has no monetary bids or payments. The project’s auction/allocation comparison should therefore be interpreted as a related allocation lens rather than as an identity between voting and auctions.

Step 4 · Reflect

What explains your choices?

This stage distinguishes the rational benchmark from possible behavioral mechanisms such as fairness preferences, strategic voting, and bounded attention to Sybil incentives.

How fair did TWV feel?
1 · very unfair5 · very fair
How fair did SRV feel?
1 · very unfair5 · very fair
After seeing the outcomes and simulation evidence, which rule do you prefer?
If you controlled the 60% whale position under SRV and wallet splitting were costless, would you split the stake across 8 wallets?
Which explanation best fits your decision?