Mechanism guide

Quadratic costs and stronger votes

The core idea in Nicolas is simple. Participants can express stronger support or opposition because the cost rises with the square of vote intensity, creating a finite tradeoff instead of unlimited enthusiasm.

Start a decisionSee the mechanism

Nicolas mechanism signals

These concepts follow the mathematical contract used by the app.

Convex cost

cost = c * sum a_ij^2

Voice budget

sum a_ij^2 <= B

Outcome rule

shifted softmax over support

The cost formula

For a vote vector across alternatives, Nicolas computes spend as the sum of squared intensities, so a value of 2 costs 4 voice credits while a value of 3 costs 9.

The sign determines whether the vote supports or opposes an alternative. Magnitude determines spend, so positive and negative votes are symmetric in cost.

Why the cost is convex

A convex cost lets participants show deep conviction while making concentration progressively harder. It measures intensity instead of simply handing out equal dots.

The finite voice budget also creates opportunity cost. Spending more on one alternative leaves fewer credits for support or opposition elsewhere.

What Nicolas shows

Nicolas displays the submitted intensities, aggregate support, quadratic costs, delegation context, and outcome probabilities for a decision.

The cost display does not claim money movement, because voice credits are part of the decision model rather than a payment flow.

Use cases

Where this decision model helps

Participant education

Help voters understand why a stronger vote spends disproportionately more credits.

Decision design

Pick a voice budget that lets participants express meaningful intensity without unlimited concentration.

Method comparison

Explain why quadratic voting differs from dot voting, approval voting, and cumulative voting.

FAQ

What is the quadratic voting cost formula?

Nicolas computes spend as the sum of squared vote intensities across alternatives, bounded by the participant's available voice budget.

Does a negative vote cost less?

No. Because cost depends on magnitude, a vote of -2 and a vote of +2 both cost 4 voice credits.

Are voice credits money?

No. Voice credits are decision credits inside the voting mechanism, not a payment or money movement.

Keep reading

Continue with adjacent concepts and practical Nicolas workflows.

Quadratic voting calculatorTry the squared-cost formula interactively.Quadratic voting vs cumulative votingCompare squared costs with fixed vote allocation.