No System is PerfectDr. Kenneth Arrow won a Nobel Prize for proving, in essence, that there's no such thing as a perfect voting system. What this means is that every voting system has flaws, and every voting system has strengths and weaknesses. This also means that for any voting system, it's possible to manufacture particular examples where a candidate wins who common sense suggests should not win.
The best voting system for a particular situation depends on what you value and what you are trying to accomplish, and not surprisingly, some people differ greatly in their assessments of this.
For example, plurality voting -- the most common voting system in the United States, in which the highest vote-getter wins, even if it's withs less than a majority -- only measures the amount of intense, core support a candidate has. Breadth of support is irrelevant.
On the other hand, another system, called Condorcet, only measures breadth of support and ignores how strong the support is. A Condorcet winner may not be the favorite candidate of any voter, but the person would have to compare favorably in head-to-head matchups with each of the other candidates.
Instant runoff voting is actually a compromise between these two extremes: it requires sufficient core support to avoid elimination and enough broad support to win a majority of the votes.
This is all to say that different voting systems achieve different goals, and since there are many possible goals that we seek to achieve through voting systems, it's not surprising that no one system is perfect for all of them.
For example, what you look for in a mayor of a city might be quite different than from what you want in a treasurer for a private organization. And that might be different than what you want in trying to pick a time that members of a committee can meet at. In each of these cases, you could use a voting system to pick the mayor, treasurer or meeting time, but you might not seek the same qualities in each, so you might select different voting systems.
The rest of this page describes alternatives to single winner systems and contains some links to additional information about them. It is not an exhaustive discussion of the strengths, weaknesses and suitabilities of these systems.
[ Review alternative voting systems ]