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Quadratic Voting Explained

Quadratic Voting Explained​

Introduction​

Traditional voting models (one-person-one-vote) treat every vote equally, but can unintentionally empower majority interests and underrepresent passionate minorities. Quadratic Voting (QV) is an alternative system that balances equality and intensity of preference, allowing participants to cast multiple votes for an option at an increasing cost.

1. What Is Quadratic Voting?​

  • Core Idea: Voters purchase voting credits to express how strongly they feel about options. The cost of casting n votes is n² credits.

  • Formula:

    Cost=(Number of Votes)2\text{Cost} = (\text{Number of Votes})^2

    For example:

    • 1 vote costs 1 credit
    • 2 votes cost 4 credits
    • 3 votes cost 9 credits

2. Why Use Quadratic Voting?​

  • Reflects Intensity: Allows voters to show stronger preference where they care most.
  • Prevents Monopoly: Quadratic cost discourages extreme vote-buying by making additional votes progressively expensive.
  • Promotes Fairness: Balances between one-person-one-vote equality and weighted-voting nuance.

3. Mechanics of Quadratic Voting​

  1. Allocate Credits: Each member receives a fixed number of voting credits (e.g., 100).
  2. Cast Votes: Members distribute credits across proposals; paying n² credits to cast n votes on a single proposal.
  3. Tallying: The total votes on each proposal determine its priority; costs are only for allocation, not deducted from community funds.

4. Scenario: Tribal DAO Project Funding​

Context: The Tribal DAO must choose between three community proposals:

  1. Water Restoration
  2. Digital Learning Hub
  3. Traditional Garden Revival

One-Person–One-Vote Scenario:

  • Each member casts one vote for their top choice:

    • Member A votes for Garden Revival
    • Member B votes for Digital Learning Hub
    • Member C votes for Garden Revival

  • Results:

    • Garden Revival: 2 votes
    • Digital Learning Hub: 1 vote
    • Water Restoration: 0 votes

  • Winner: Garden Revival (majority decision but ignores preference intensity)

Quadratic Voting Scenario:

  1. Credit Distribution: Each member receives 25 voting credits.

  2. Member A (Gardening Enthusiast):

    • Spends 9 credits to cast 3 votes for Garden Revival (cost = 3² = 9).
    • Spends 16 credits to cast 4 votes for Water Restoration (cost = 4² = 16).

  3. Member B (Tech Advocate):

    • Spends 16 credits to cast 4 votes for Digital Learning Hub (cost = 4² = 16).
    • Spends 9 credits to cast 3 votes for Water Restoration (cost = 3² = 9).

  4. Member C (Balanced):

    • Spends 4 credits to cast 2 votes each on all three proposals (cost = 2² = 4 per proposal; total = 12).

  5. Results:

    • Garden Revival: 3 (A) + 2 (C) = 5 votes
    • Water Restoration: 4 (A) + 3 (B) + 2 (C) = 9 votes
    • Digital Learning Hub: 4 (B) + 2 (C) = 6 votes
  • Winner: Water Restoration (reflects both breadth and intensity of preference)

5. Benefits for a Tribal DAO​

  • Cultural Respect: Members can express stronger cultural ties (e.g., elders vote more on traditional projects) without overpowering all voices.
  • Resource Allocation: Ensures projects with highest collective passion receive priority funding.
  • Transparency: On-chain credit allocation and vote costs are publicly auditable, reinforcing trust.

6. Quadratic Voting with Two Options​

  • Applicability: QV can be used even when choices are binary (e.g., Support vs Against a proposal). It still lets members express intensity of preference.

Example Scenario:

  1. Credits: Each member has 25 voting credits.

  2. Member X (Strong Supporter):

    • Spends 16 credits to cast 4 votes for Support (cost = 4² = 16).

  3. Member Y (Moderate Supporter):

    • Spends 4 credits to cast 2 votes for Support (cost = 2² = 4).

  4. Member Z (Opposed):

    • Spends 9 credits to cast 3 votes for Against (cost = 3² = 9).

Results:

  • Support: 4 + 2 = 6 votes
  • Against: 3 votes

Interpretation:

  • Even with only two options, QV distinguishes strong from moderate support, ensuring the outcome reflects the intensity of members' convictions.

7. Credit Spending Flexibility​

  • Voters are never required to spend all their credits in a quadratic voting round. They can spend none, some, or all.

  • Flexible Allocation: Each member starts with a fixed number of credits (e.g., 25) and chooses how to distribute them across options.

  • Strategic Considerations:

    • Care Intensity: Allocate more credits to issues you care about deeply.
    • Breadth vs. Depth: Spread small vote allocations across multiple proposals to signal moderate interest.
    • Conservation: If you're indifferent on certain items, you may opt to spend few or no credits on them.

  • Unused Credits Expire: Unspent credits simply expire at the end of the voting round and do not carry over.

  • Rationale: Forcing full credit expenditure dilutes genuine preferences; allowing flexibility ensures votes reflect true intensity.

Conclusion​

Quadratic Voting empowers a Tribal DAO to balance equitable participation with the intensity of community preferences. By adopting QV, Matou DAO can ensure that both majority interests and deeply held cultural priorities are fairly represented in decision-making.