What the theorem says
A deterministic social choice function with at least three possible outcomes, onto range, and no dictator will have situations where some voter can benefit by misrepresenting their preferences.
The theorem formalizes a hard truth. Strategyproofness is not free in general voting environments.
What problem it exposes
Any voting interface invites strategic behavior if participants understand the rule and care about outcomes.
The design question is which incentives the mechanism creates, how visible they are, and whether they are acceptable for the decision context.
Where Nicolas fits
Nicolas uses quadratic costs to make stronger positions progressively more expensive. It makes intensity costly and visible even though it does not eliminate strategy.
The public record of costs and outcomes helps groups inspect the mechanism rather than treating votes as costless signals.