linguistic:paraphrasing
Left-right spectrum

Soon after Arrow published his theorem, Duncan Black showed his own remarkable result, the median voter theorem. The theorem proves that if voters and candidates are arranged on a left-right spectrum, Arrow's conditions are all fully compatible, and all will be met by any rule satisfying Condorcet's majority-rule principle.

More formally, Black's theorem assumes preferences are single-peaked: a voter's happiness with a candidate goes up and then down as the candidate moves along some spectrum. For example, in a group of friends choosing a volume setting for music, each friend would likely have their own ideal volume; as the volume gets progressively too loud or too quiet, they would be increasingly dissatisfied. If the domain is restricted to profiles where every individual has a single-peaked preference with respect to the linear ordering, then social preferences are acyclic. In this situation, Condorcet methods satisfy a wide variety of highly-desirable properties, including being fully spoilerproof.

The rule does not fully generalize from the political spectrum to the political compass, a result related to the McKelvey-Schofield Chaos Theorem. However, a well-defined Condorcet winner does exist if the distribution of voters is rotationally symmetric or otherwise has a uniquely-defined median. In most realistic situations, where voters' opinions follow a roughly- normal distribution or can be accurately summarized by one or two dimensions, Condorcet cycles are rare (though not unheard of).