There has been a lot of theoretical work on voting, starting with Kenneth Arrow's proof that it's impossible for any consistent vote counting procedure to satisfy a short list of desirable criteria he provided. Over the years since then, people have proposed a variety of counting procedures that make different trade-offs among them. The LFS uses a variant of the preferential voting system to allow members to rank candidates because nominees must get more votes than NOTA to win. This approach means we don't have run-off votes if there isn't a single winner in the first round of voting.
Voting isn't a great way to solve problems, but it may be the best we have in situations in which people want to work together and choices must be made about how to proceed. This is often the case when people want to cooperate (volunteer groups, owner's associations, or standards organizations). There are some actions that work best when performed in concert, so people often agree to follow a group's decisions. (With some limits on what the group's purview is, or the right to withdraw if the decisions are unacceptable.)
Wikipedia has several articles on different vote counting procedures: Borda count, Condorcet (and variants) and several others. Each system makes a different trade-off, some ensuring that the winner is hated by the fewest electors, other that the winner is preferred by more electors over each opponent, preferred more strongly by the most voters, and so on.
The other aspect of electoral systems is that for many purposes, we prefer to elect representatives who will spend more time discussing issues in detail and make a proposal for all to consider or decide among the alternatives themselves. Most voters, most of the time aren't willing to pay much attention. (Economists have shown why it is irrational for voters to become informed if the electorate is large, and why narrow interests control the issues that pertain to them.) In organizations at all scales most of the time, most people have better things to do with their time and attention.
There are as many ways to select representative panels as to count votes. Representatives in the US Congress are chosen by a majority in a single district. Senators are chosen in the same way, even though there are two of them. The problem that PR addresses is that if 51% of the people in each district vote Orange, and 49% vote Purple, then no Purple Legislators are elected. PR counts votes over larger districts, and selects winners in proportion to the votes cast. In elections for corporate Boards of Directors, any voter can usually cast all their votes for a single candidate, ensuring that someone who owns 20% of the shares can select a Director (one of five seats) even if everyone else votes for the same slate of 5. (If it were congressional seats, each representative for the larger group would win with 80% of the vote.) Many European countries' parliaments are selected using Proportional Representation (PR), so the representatives are chosen in proportion to the sum of the electors' votes. (Notice that PR also defuses the pressures for gerrymandering.)
The choice of vote counting mechanism and how multiple representatives are chosen has a large effect on the make-up of the elected body. The American approach naturally limits the power of third parties. Since the only people who get elected have more than 50% of the votes, parties that can't at least occasionally surpass that mark won't ever hold office. That naturally leads to a two party system. If any party has significantly less than half the electorate as its base, then it can increase its chances of being elected by joining with another group. If a faction isn't within the margin of power of its party, the party can ignore their demands without hurting their chance of being elected, so the faction can increase its influence by threatening to join a different party that will pay more attention to their voter's wishes. Sometimes, a faction can't credibly threaten to bolt the party (because of historical interactions with the other party, for instance) and so their influence will wane.
In PR systems, there is often a floor: parties with less than 5% of the vote (for example) don't get a seat. Any faction larger than that can get a seat, and be part of the decision-making body. As long as the voting rules in the representative body allow their voice to be effective, that's enough to keep the factions alive, and ensure that they continue to distinguish their positions from their rivals.
All of this has an effect on how interest groups organize and persist. Most of the time, single-issue groups can't get elected to general legislatures. Most voters have too many distinct interests to allow one interest to represent them. Even with the lower floor in PR systems, groups representing e.g. labor have to take a position on most of the major issues, and hope to attract voters who match their position on more issues than their rivals. In the American system, single-issue groups find they have to be allied with one major party or the other (think of the NRA, the NAACP, either side of the abortion question, labor, etc.).
Since I'm a libertarian, I'm always a minority and my vote is of no interest to the major parties. For a long time, the Libertarian Party had a stated goal of being the margin of victory between the major party candidates in as many local elections as possible. The theory was that at that point, the weaker party would have a reason to try to co-opt some platform planks in order to gain converts. Every time they do that, that party would be moving closer to libertarian positions, which is useful given that libertarians aren't going to be elected in numbers anytime soon.
Years ago, I had an idea for a different way of organizing representative bodies that would fundamentally change the dynamic. It ought to energize all the minor factions, and could make it possible for representative bodies to reach decisions that matched the voters' views much more often by ensuring that elected representatives don't have to be a compromise between positions on a large number of issues. There is, of course, an argument to be made that satisfying more voters more often will lead to the government constantly robbing different minorities in order to pay off constantly changing majorities. I think the right response to that is to try the mechanism out in voluntary organizations rather than governmental bodies.
I call my proposal "dynamically transferable proxies". The idea is that representatives aren't elected, they merely carry proxies from voters who currently back them. A representative's vote in the forum is the sum of the individuals they currently represent. Voters can choose new representatives as often as they want. A proxy-holder can transitively assign all the proxies they currently hold to any other representative. Voters and assigners can revoke their assignments anytime they like as well.
In order to have productive negotiations about what alternatives to consider, those currently representing the largest constituencies should have a place (virtual, if necessary) to talk. I think it makes sense to choose a number (20, 100, 435) and enable that number of the largest proxy-holders to convene. If they agree on an agenda, and set particular times to discuss specific issues, the voters can dynamically switch their proxies to people or groups that best represent them on that topic. If gun control is on the agenda, then the NRA will have some number of proxies from their dedicated members, and Handgun Control, Inc. will have proxies from their constituents. More importantly, everyone else, somewhere in the middle, will assign their proxy to someone who can articulate a reasonable compromise, or someone who can plausibly claim to be willing to listen to arguments. Major parties can attempt to form coalitions, but voters can defect, one issue at a time.
In this context, some people would aim to be representatives, but many more would find a niche as proxy-holders who would notify constituents when an upcoming agenda item affects them, and commit to assign the proxy to someone who would represent their views effectively. (That's the right role for the NRA and the right-to-life/choice groups. They don't need to be present on the floor 99% of the time, but when contentious issues are being discussed, it would be better to separate representatives of extremists from representatives of moderates.)
I think this approach could have a moderating effect on politics. But I don't think there's any point in trying to promote it as a replacement for currently existing governments. OTOH, connectivity has increased enough that it might make sense for some groups. Some of the criteria for a good fit include: highly-connected constituency, broad range of issues to make decisions about, and a need to make collective decisions. I think it would work as well for a voluntary group as for a political subdivision.
I have been an officer of a couple of volunteer organizations, but the range of issues hasn't been wide enough for this kind of process to be worthwhile. I've occasionally fantasized that this would be the right way to run a large colony once we start exploring space or a starship. What organizations would it make sense for? Does 2nd Life have a representative governing body?
Thanks to Dan Reeves (currently at Yahoo) for encouraging me to write this idea up.