Method comparison

Quadratic voting vs ranked-choice voting

Ranked-choice voting asks participants to order options, while quadratic voting asks how strongly they support or oppose each option under a finite voice budget. The right choice depends on whether the decision needs preference order or preference intensity.

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

What ranked-choice voting reveals

Ranked-choice voting records an order of preference, so it is useful when the group needs to know which option each participant prefers first, second, third, and so on.

That order can be valuable, but it does not directly say whether a participant barely prefers one option or cares intensely about the difference.

What quadratic voting reveals

Quadratic voting records costly intensity by letting participants allocate support or opposition across alternatives, while stronger positions become progressively more expensive.

In Nicolas, the decision record includes aggregate support, shifted-softmax outcome probabilities, and gross quadratic costs.

How to choose

Use ranked-choice voting when the main goal is to aggregate ordinal rankings into a winner or ordering.

Use Nicolas when the decision needs intensity-aware signals, explicit accounting, delegation, and a transparent record of how strongly participants care.

Use cases

Where this decision model helps

Ranked-choice fit

Candidate-style choices where ordering preferences is the key input.

Quadratic voting fit

Multi-alternative decisions where strength of support or opposition matters.

Nicolas fit

Governance or team decisions that need delegation and transparent cost accounting.

FAQ

Is ranked-choice voting intensity-aware?

Not directly. Ranked-choice voting records order, but it usually does not measure how strongly a participant prefers one option over another.

Can quadratic voting rank options?

Quadratic voting can produce aggregate support and outcome probabilities. Ordinal ranking solves a different problem.

Where does Nicolas fit?

Use Nicolas when preference intensity, opposition, delegation, and transparent accounting carry more weight than ranked ballots alone.