Method comparison

Quadratic voting vs cumulative voting

Cumulative voting lets participants concentrate a fixed number of votes, while quadratic voting lets people concentrate support only as each additional unit of intensity becomes progressively more expensive.

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 cumulative voting reveals

Cumulative voting gives each voter multiple votes that can be spread across options or concentrated on one option, which can reveal more intensity than a single binary vote.

The cost of concentrating votes is usually linear, so moving another vote to the same option is not progressively harder.

What quadratic voting changes

Quadratic voting makes intensity convex. A vote vector costs the sum of squared intensities, which lets participants express strong conviction while making concentration increasingly costly.

Nicolas applies that rule to positive and negative vote intensities, then reports aggregate support, quadratic costs, and outcome probabilities.

How to choose

Use cumulative voting when a simple fixed-point allocation method is enough and the group does not need a convex cost rule.

Use Nicolas when intensity must be measurable, costly, and tied to a transparent decision record.

Use cases

Where this decision model helps

Cumulative voting fit

Simple vote allocation where fixed points are easy for participants to understand.

Quadratic voting fit

Decisions where extra intensity needs a progressively higher cost.

Nicolas fit

Group decisions needing delegation, signed intensity, and outcome probabilities.

FAQ

Is cumulative voting the same as quadratic voting?

No. Both let participants concentrate influence, but quadratic voting uses squared costs while cumulative voting usually allocates a fixed number of equal votes.

Why do squared costs matter?

Squared costs make very strong positions possible but expensive, which can reveal conviction without making concentration free.

Can Nicolas be used like cumulative voting?

Nicolas can support prioritization-like decisions, but its rule is quadratic rather than a simple fixed-point allocation.