Various different single-winner methods are proposed as improvements. There's little or no consensus on standards for evaluating them. Defining some of those standards & criteria, and telling how the methods do by them, with initial special attention to a few of the best methods, is the purpose of these articles.
Why are single-winner methods important? What government does, what it allows or doesn't allow, those things affect every material aspect of our world. Even a bird in a tree in the most remote forest is affected by that. So it becomes important how public wishes translate to government policy--typically, but not necessarily, via the election of candidates for office, and by voting by those candidates in their legislatures.
What's wrong with the Plurality method? The lesser-of-2-evils problem. Voters know that if they vote for their favorite, that will often prevent them from being able to help a more winnable compromise (the "lesser-evil"), who may be the only candidate who could beat someone whom they despise more. So they have to completely abandon their favorite. I believe that most agree that that is the main problem that dramatizes why we need better single-winner voting systems. Many of the criteria that I describe later are for measuring compliance with that standard.
Here are the topics covered in these articles: