Consider an election voting process where people need to elect a representative among n number of candidates.
Is there an approach to determine the most favorable option? Voting just a single person may not be favorable because even if the winner secures say 25% of the total votes, he still maybe actually rejected by 75% of the people.
On
If you define "fairness" in a fairly sensible way you get the famous result https://en.wikipedia.org/wiki/Arrows_impossibility_theorem
Instant-runoff voting (aka the alternate vote) as opposed to first past the post voting (i.e. your method, aka FPTP) fixes this problem. Unfortunately, the USA isn't going to adopt this method any time soon.
You might also be interested in this list of voting methods and the voting criteria they fulfill. Neither the alternate vote nor FPTP voting produce a Condorcet winner, and if you're interested in that, you might want to look into the Kemeny-Young method.