Voting systems are so central to the operation of any sort of representative government, but almost every one currently in use is provably severely flawed. I will write primarily about American systems, but the same flaws are present in virtually every nation that holds elections.
Before we can talk about what's wrong with the current system, we need to talk about what the purpose of voting is. In an abstract sense, a voting system is any function that takes the voters' opinions as input, and outputs a list of one or more of the candidates as winners. A successful voting system, then, does this in a way that makes the voters as happy as possible with the selection of winners. Note that the underlying assumption to this whole discussion is that democracy is the ideal form of governance; while this can be disputed, I'll work within that framework for this article.
The first problem with plurality voting, our current system, is that it does not listen well to the voters' preferences. Voters are likely to have an opinion on every candidate, and plurality voting fails by limiting the amount of information they can give to just naming one single candidate. If voters cannot express themselves fully, it is impossible to be sure of picking the best winner - no matter how smart the tallying system is.
As an example of this, suppose there are three candidates - Alice, Bob, and Charlie. 25% of the population prefers Alice, likes Bob, and hates Charlie. 35% of the population prefers Bob, dislikes Alice, and hates Charlie. 40% prefer Charlie, but also like Alice and Bob. Under plurality voting, Charlie wins even though only 40% can tolerate him. Bob only has 5% fewer "first choices" than Charlie, and everyone likes him, but he's sent home.
Another problem with plurality voting is that it encourages voters to lie about their preferences. If two candidates have the backing of major political parties, then anyone who votes for a third party candidate is effectively voting for the candidate they like the least out of the top two. A good voting system should encourage people to vote honestly, and deal with any resulting issues intelligently.
This issue leads into another - the fact that plurality voting tends to reduce the number of viewpoints available for voters to choose from. Specifically, plurality voting will nudge nations toward a one- or two-party system. This is known as Duverger's Law. With fewer options, it becomes less likely that an excellent candidate will even be in the race. The consequences are more far-reaching than just who wins, though - fewer candidates mean fewer viewpoints get exposure, making it more likely that good but unconventional ideas get ignored.
These are some, but not all, of the problems with traditional voting systems. At the least, I hope you will agree that our current system is flawed and we should consider other options. Many alternative, better systems have been invented - you may have heard of terms like instant runoff voting or Borda count. I argue that the best solutions to these problems are range voting and its simplification, approval voting.
When trying to create a good voting system, we ought to make sure that the voters can express themselves fully. A single check mark is an inferior option because voters likely have an opionion about most or all of the candidates. Ranking each possible pairing of candidates is a reasonable solution, but hardly concise. It also does not match our intuitive understanding of preference - it allows for illogical preferences such as saying that you want Alice to beat Bob, Bob to beat Charlie, and Charlie to beat Alice. Simply ranking the whole list of candidates seems better, but this still an oversimplification of our true mental picture of the relative merits of each candidate. It has been proven that ranked methods will always lead to some of the problems with plurality voting - this is known as Arrow's impossibility theorem.
Probably the best way to concisely represent one's opinions in an election is to give each candidate a rating - say, a number between 0 and 99. This captures views on all candidates very accurately, while being short enough to be entered into a voting machine. The tallying system is then natural - the results are averaged, and the candidate with the highest average wins. It is also easily adaptable to allow for elections with multiple winners; just take the top two or three. Range voting also avoids Arrow's impossibility theorem because it is not a ranked system.
In the end, the strongest argument for range voting is how well it selects a winner that makes the voters happy. The way we can measure how much a voting system will tend to produce inferior candidates is a quantity called Bayesian Regret (BR). If a system almost always picks the best winner given the voters' preferences, it will have a BR near zero. If a system fails to select a good winner, it will have a high BR value.
Mathematician Warren D. Smith has made computer models of various voting systems in many different simulated elections, in order to test which was most effective by measuring the average Bayesian Regret of each. Results were tabulated separately for both honest voters, and those voting strategically. The results of the analysis put range voting on top, in every category. If all voters are honest, range voting is nearly perfect in selecting the best winner. If all voters cast their votes strategically, giving only 0s or 100s, then range voting becomes "approval voting", which is still superior to any other tested system under strategic voting. The results of the study are published online.
In short, assuming five-candidate elections, we would gain more as a society by switching from plurality voting to range voting, than we would lose by starting to choose winners at random! But the true consequences are even greater, because of Duverger's law; elections so diverse hardly happen under a plurality system.
The real criticisms of range voting are few, and the main one is that a relatively small but loyal group of supporters could elect someone that no one else voted negatively for because they have not heard of them. This is fixable by requiring a minimum percentage of voters (a quorum) to have an opinion on a given candidate in order for them to win, treating empty votes as 50s, or by more sophisticated and accurate mathematical techniques.
With all the reasons that range voting is superior to what we have, yielding far superior results and allowing for a much more diverse and less hegemonic power structure, I hope you will support it as I do.