What the theorem says
Voters with single-peaked preferences along one dimension give majority rule a stable winner, the alternative preferred by the median voter.
This is a positive result because it identifies a domain restriction where majority voting can behave coherently.
Why the assumptions matter
Many real decisions are not one-dimensional, since a workplace policy, budget allocation, or governance proposal can affect participants across several dimensions at once.
Preferences can be multidimensional, and intensity can vary widely. In those cases, a simple median position may not capture the decision problem.
Where Nicolas fits
Nicolas is built for multi-alternative decisions where participants may care at different intensities, so it reveals costly support and opposition across named alternatives rather than trying to find the median voter.