Let's talk about voting and different voting systems. Not voter eligibility, not voting districts, campaign finance reform, not terms or term limits or that (those are all important, but another topic) but just the basic nuts and bolts as to how the voting works on a functional level.
Let's keep the following questions in the back of our heads.
1. Is it "better" if the majority of voters get their preferred candidate or the majority of voters get an acceptable candidate?
2. Do different "levels" of election (Federal, State, Local) have to operate the same way?
So let's look at some ways of voting.
1. Winner take all, first past the post.
Each eligible voter gets 1 and only 1 vote. At the end all the votes are counted and the person with the most votes wins.
Example: Bill and Ted run for President. Bill gets 48% of the vote and Ted gets 52% of the vote. Ted becomes President, Bill gets nothing.
Upside: The greatest number of people get their preferred choice. This is probably the easiest to administrator
on a procedural level. (This is a bit of conjecture but I get the vague idea that this is the system that "feels" the fairest to most people.")
Downside: Inevitably leads to a two party system. Near impossible for third parties to get involved. Leads to election being determined mostly by people voting against a candidate instead of for one. Winning by a sliver is as good as a landslide. Third party candidates tend to siphon votes off of other candidates they are closer to so there is tendency to "split" elections for one political or ideological stripe.
2. The Alternative Vote / Ranked Voting.
Each voter can rank their preferred candidates in any order.
Example: Let's say there's a major election where there are 4 candidates with at least some chance of winning, two major party candidates and two third party candidates. The two major party candidates are pretty close in most polls, both the of the third party candidates are polling in the low single digits.
So most people cast a primary vote for one of the two major party candidates, maybe with secondary choices.
Most of the third party voters cast a primary vote for their preferred third party candidate but cast a secondary vote for whichever of the major party candidates they like better.
Come election night and, as predicted, neither of the two third party candidates received that many votes so the votes they got go to whichever major candidate the the voters put as their second choice.
This is why this type of voting is sometimes called "Instant Runoff."
Pros: People can vote their conscious instead of being forced to vote strategically. Major candidates cannot ignore third party voters. No fear of splitting a side and winning the election for "the other side."
3. The Electoral College.
Ehhhh each person casts a vote and then some behind the scenes magic happens and then a bunch of separate non-elected special people who we don't know actually are the ones who vote, aren't required to actually follow the popular vote, and often don't. Electoral College members are allowed to punch those normal plebeian voters in the dick and sleep with their wives on their wedding nights (I might have made that last part up.) Has a 7% failure rate.
Scenario: You go vote. Or not it doesn't really matter. You drink until the pain stops. If you don't live in about a half dozen states at most you literally don't matter on any level.
Upsides: Every four years the government has to pretend it cares about Ohio.
Downsides: It basically goes against the idea of democracy. It doesn't do any of the things that people think it does (protect small states, protect rural areas). It literally means that certain people's votes don't count as much as others. It's why Ohio, Virginia, Pennsylvania and Florida are the only states that decide elections. You could theoretically win the election without cheating with only 22% of the vote in a two candidate election. It's just awful.
4. Consolation Prize Voting.
The runners up in the election get other positions.
Scenario: Okay let's say in your country the three most powerful single elected positions are... Prime Minister, Vice Prime Minister, and Head of the Grand Committee (the Congress or Parliament or whatever).
Bill, Ted, and Steve are running for Prime Minister. Ted gets the most votes, Steve the second most, and Bill the thirst most. So Ted becomes Prime Minister, Steve becomes Vice Prime Minister, and Bill becomes Head of the Grand Committee.
This was, in a way, originally how the American Presidential Elections worked. Originally the Vice President was just the runner up in the Presidential election. This didn't work out and was changed in 1804 via Constitutional Amendment.
Upside: It would literally be impossible for a single party to gain control of the government unless it was pretty much the only popular party. You have to admit it would be fun to watch. A potentially good leader that a large percentage but not quite majority of people think would make a good leader doesn't get wasted.
Downside: Literally nothing would ever get done. The skills each of these three positions requires might not be the same.