Reply #1: this is a fascinating mathematical topic.

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mostly the math focuses on starting off with the idea that each voter gets a single vote, and how do you impose a structure on that that has various desireable properties.

but you can also change the nature of an individual's vote itself. having to distill all your preferences down to a single "this candidate or that candidate" already introduces inherent problems. my favorite solution is to let each voter rank all the candidates. then the candidate with the fewest top-ranking votes is eliminated. this then promotes the remaining candidates on everyone's list, e.g., if your #1 choice is eliminated, then your #2 choice becomes your new #1 choice, etc. the process is then repeated until a single candidate gets at least 50% of the top ranking votes.

this requires no runoff (except as needed for near-ties in certain cases) and permits people to vote for their "ideal" candidate first without "throwing away their vote". this better reflects a voter's actual preferences.

but as this article and a number of mathematicians have noted, it's impossible to satisfy any meaningful set of desireable properties with a single voting system; some of the properties are inherently at odds with each other.