Median Voter Theorem
The median voter theorem seems to explain a few of the phenomena that occur in majoritarian voting systems. First, it may explain why politicians tend to adopt similar platforms and campaign rhetoric. In order to win the majority vote, politicians must tailor their platforms to the median voter. For example, in the United States, the Democratic and Republican candidates typically move their campaign platforms towards the middle during general elections campaigns. Just as sellers in the private market try to win over their competitor’s customers by making slight changes to better their products, so, too, do politicians deviate only slightly from their opponent’s platform so as to gain votes.
Second, the median voter theorem may explain why radical candidates or parties rarely get elected. If a politician is, for example, an extreme liberal on the very left end of the political spectrum, they will not capture nearly as many votes as the politician whose campaign platforms are more moderate. Finally, the theorem may explain why two major political parties tend to emerge in majoritarian voting systems (Duverger's law). Indeed, in the United States there are countless political parties, but only two major parties play a part in almost every major election: the Democratic and Republican parties. According to the median voter theorem third parties will rarely, if ever, win elections for same reason why extreme candidates do not tend to win. The major parties tend to co-opt the platforms of the minor parties in order to secure more votes.
(note the assumptions in the beginning of that link. A bit bold, but for mainstream economists, tractability matters more so than accuracy over all situations. To compensate, there's a weak version and a strong version. See: Explanations, first two paragraphs).