Can you win an election with fewer than half the votes?

Yes, under plurality voting it is allowed. Each voter marks one name, and the candidate who polls more than any other wins. Nobody is required to reach a majority. The leading candidate is elected whether or not they have more than half the votes, and in its single-seat form the system is sometimes called "first-past-the-post".

Here is how odd that can get, using an illustrative example. Imagine Tennessee voting on where to put its capital. The population is split between four cities, and every voter wants the capital as close to home as possible. If each voter simply picks their own city, Memphis is chosen, because it has the most votes at 42%. Yet 58% of the voters preferred Memphis least.

A different result was within reach. If everyone who voted for Chattanooga or Knoxville had voted for Nashville instead, Nashville would have won with 58%. That would only have been the third choice for those voters, but by voting for their own first choices they ended up with their fourth choice, Memphis.

Plurality voting is among the simplest of all electoral systems for voters and for the people counting the ballots. It spread throughout the English-speaking world with the British Empire, including most of the United States, although more countries now use some form of proportional representation than use plurality or a runoff.