That's a good starting short lecture.
It's something everyone should look into. Some will get further than others.
A giant caveat is that mathematical impossibility in an idealised setting isn't quite the same as real world implementations.
A smaller scales the US first-past-the-post system worked tolerably well for some time.
Tweaked proportional does much better, pitfalls are rare and "real world" untidiness can address that well enough to reap the other benefits.
The subject of the video you linked is mainly Arrow's impossibility theorem which is covered early in a number of applied math | discrete math courses.
Plurality-rule methods like first-past-the-post and ranked-choice (instant-runoff) voting are highly sensitive to spoilers, [..]
By contrast, majority-rule (Condorcet) methods of ranked voting uniquely minimize the number of spoiled elections by restricting them to rare situations called cyclic ties.
Under some idealized models of voter behavior (e.g. Black's left-right spectrum), spoiler effects can disappear entirely for these methods.
https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore...The focus on no system being perfect distracts from bigger issues; which systems suck less than others, which systems result in better representation, which systems can doom spiral, etc.
