What quadratic voting computes
Each participant allocates support or opposition across alternatives, and the vote vector costs the sum of squared intensities. Moving from 1 to 2 votes costs four times as much as a single vote, while moving from 2 to 3 costs nine times as much.
The convex cost makes intensity visible while discouraging a single participant from spending all influence cheaply, so the output shows both supporter count and aggregate strength of preference.
How Nicolas extends the mechanism
Nicolas supports real-valued vote intensities, positive and negative support, explicit voice budgets, liquid delegation, and transparent quadratic cost accounting.
Outcome probabilities are computed from aggregate support with a shifted softmax, which keeps the numerical calculation stable even when alternatives receive very different levels of support.
Where it fits
Quadratic voting is useful when a group needs to know both direction and strength of preference across budget priorities, product roadmaps, governance proposals, community funding, research agendas, or internal policy choices.
It is less appropriate when the group needs a legally binding election, secret-ballot guarantees, or a simple majority rule decision with no need to measure intensity.