Let me ask you a seemingly simple question: In an election with more than two candidates, if one candidate always wins against any other candidate in a head to head battle, should they be considered the winner?
This is known as a Condorcet winner, and it has caused a major paradoxical issue in today's voting systems. Largely because a Condorcet winner does not always exist. Anyone who has ever played a three-way game of Rock Paper Scissors should recognize the possibility of a no-win condition. But many people instinctively believe that any voting system should always choose the Condorcet winner if one does exist.
I was shown a wonderful article recently showing the flaws in different voting systems, and how ranked voting can have wildly different results depending on what system you use to count the tallies. http://www.ams.org/publicoutreach/feature-column/fcarc-voting-decision
Additionally, all of these ranked voting systems introduce a measure of strategic voting, which always pushes voting toward a two party system where voters vote against the candidate they hate, instead of for the candidate they want.
Cardinal voting is often proposed as a solution to this problem, because it preserves independence of irrelevant factors, which many ranked systems do not. there is no penalty for voting up your favorite candidate, so this feels like a more fair system for finding a popular candidate.
Interestingly, none of the four most popular ranked voting methods today choose the Condorcet winner, or the winner who would win against any other candidate in a head to head battle, when using the proposed sample ballots in the linked article. Nor does cardinal voting under most conditions. and even more interesting, not all ballot conditions produce a Condorcet winner
This proposes an interesting philosophical dilemma. If crafting a voting system that always chooses the Condorcet winner if one exists is impossible, how important is it to always choose the Condorcet winner? Should this be our primary concern, or should we focus more on the most popular winner overall? This is a largely undecided philosophical dilemma, so all opinions are welcome in addition to facts and figures.