When Benjamin Netanyahu “won” a recent Israeli election, his Likud party actually won 30 of 120 seats in Parliament. Because this was a plurality, they would have the first shot at forming a “government” (called an administration in the U.S.) by forming a coalition with other parties. So it was really a coalition that won the election, a coalition that is formed after the election.
Parliamentary systems often lead to governing coalitions. At least the principle of majority rule is preserved even though it was through a plurality that the majority was achieved.
In two-party systems, one party will inevitably win a majority outright. The U.S. has had a two-party system. But elections are usually by plurality. Gubernatorial elections for example are by plurality. That can easily lead to a candidate who is less acceptable to the majority being elected. That is apparently what happened in Maine in 2014.
How can this happen? Voters are allowed to vote for only one candidate, so they vote for the candidate the approve of the most. But with three or more candidates, the electorate can be split so that no candidate gets a majority. The candidate with the largest plurality wins. If the candidate who came in second was acceptable to many of the people who voted for the candidate who came in third, he or she might have had a majority of the votes.
The problem is not that voting is binary: we either approve or disapprove of the candidates. The problem is that voters can only approve of one candidate. They are forced to disapprove of all the other candidates. This is a flaw.
The solution is called “approval voting”. Each candidate is either approved or disapproved as before but voters can approve of any number of candidates and disapprove of any number of candidates. As always, the votes for each candidate are tallied and the candidate with the most votes wins.
Approval voting is a much superior system that avoids plurality elections when there are more than two candidates. It is simple and can easily be implemented now.