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When a community elects leaders (a board of trustees, moderators, officers, etc), that community must first determine a voting scheme. There are lots of different voting schemes out there, and they can support electing one or more than one person. For example, my congregation elects its board of trustees using first past the post, choosing the top N finishers where N is the number of seats. Most government elections in the US also use first past the post. On the other hand, Stack Exchange uses a form of single transferable vote (preference ballot where you rank all or your top N choices) to elect community moderators, whether choosing one or several, and I've been told of a local school board that elects its members this way.

This question is not about which voting scheme is "best"; that's subjective and context-dependent. But I found myself thinking about voting dynamics recently, particularly with STV systems, and I realized that STV was really designed for electing one candidate (it's a single transferable vote, not a collection of votes, after all), and that got me wondering if the properties of such elections are different if you're electing multiple candidates.

So my question is: how does the number of candidates inform the choice of voting scheme for elections? Does this really not matter, and you should choose STV or FPtP or drawing names from a hat or whatever based on the other properties of those systems, or do voting systems behave differently with different numbers of open positions? I understand that there is a whole field of sociology and/or game theory about voting systems; are there studies that address this question and, if so, what do they say?

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    Tagging: I was aiming for "moderator-selection" as the closest match to this, and it came out as a synonym of "moderators". Tagging improvements welcome! This doesn't feel quite right to me. – Monica Cellio May 12 '15 at 3:27
  • I'm not sure this is on-topic, though I think it is. Let's find out! (One could argue that it belongs on a site about game theory or the like, but I'm asking it in a community-building context.) – Monica Cellio May 12 '15 at 3:28
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    STV is actually not designed for single elections; it works best when there's a reasonable chance for even small minorities to have one representative, which is more likely to occur when electing multiple representatives at the same time. This is also where it has the strongest advantage over simply electing each representative in a separate race, as minority representation can be accumulated much more efficiently, rather than needing a critical mass in any given race to have a chance. – Nathan Tuggy May 12 '15 at 18:13
  • @NathanTuggy interesting. Outside of SE, the places I've seen it have been to produce a single winner -- Hugo awards, for example. – Monica Cellio May 12 '15 at 18:33
  • Yeah, its advantages are much less significant with low numbers of available positions; the Wikipedia article suggests it really kicks in with maybe four or more. – Nathan Tuggy May 12 '15 at 18:43
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While I think there are a lot of advantages to STV, it's not for everyone. In particular:

  • It requires a more complicated ballot to allow voters to rank preferences.
  • Votes can't be quickly counted by hand except in trivial situations.
  • The algorithm is a bit of a black box for those unwilling or unable to analyze it.

In most situations, something like Meek STV is overkill because the results are often the same as plurality voting.* For organizations that use paper ballots, count them by hand, and hope to announce results shortly after the ballots are collected, I'd recommend a traditional method despite their flaws.

However, organizations comfortable with electronic voting will find most of the disadvantages dissolve and might as well move to more sophisticated methods. OpaVote, the service Stack Exchange uses to count election results, recommends:

  • For electing one candidate, we recommend instant runoff voting for most organizations. If the members of your organization are comfortable with a more complicated counting system, then we recommend Condorcet voting.
  • For electing more than one candidate, we recommend Scottish STV for most organizations. If the members of your organization are comfortable with a more complicated counting system, then we recommend Meek STV.

An exception to the above, if there are only two candidates in the election, then use plurality voting because there is no benefit to using a ranked method.

For an organization born out of programmer culture, such as Stack Overflow, the choice is obvious. For less technical groups, there's not much cost to using a simpler method at least to start. It's really not hard to change counting systems once you get over the hurdle of moving to electronic balloting.

Finally, I should note that many organizations I've been a part of hold pro forma elections that are rarely contested. Sometimes members take turns holding officer positions. Sometimes it's difficult to recruit volunteers to hold office. Sometimes candidates are pre-vetted by a trusted committee. Complicated election systems run counter to the goal of these votes. They are designed for members to participate in the selection with an escape valve for the improbable situation when the presumed winner proves unacceptable at the eleventh hour. In these cases, voice voting suffices.


Footnote:

* [citation needed] but I base this claim on experience announcing Stack Exchange election results. When you look at the first round of an election (example: Stack Overflow на русском Moderator Election 2015) the candidates with the N longest bars are often the N people who have won in the final round.

  • Jon, i have to strenuously disagree that Condorcet is more complicated to count or to understand than STV. STV has all sorts of contrivances (like second-choice votes don't count at all in determining voter support of a candidate until the first choice is eliminated) and pathologies as was demonstrated in Burlington Vermont in 2009. For Condorcet it's simple: "If a more voters mark their ballots preferring Candidate A to Candidate B than vise versa, then Candidate B is not elected." for multi-winner elections, add the words: "... before Candidate A." Who can argue with that?? – robert bristow-johnson Mar 15 '16 at 1:03
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Actually, this problem is exactly the reason first-past-the-post voting systems get so much flak. Anyone who votes for the winning candidate gives up the chance to provide any input on who should be the runner-up. Obviously that's not an issue if you're electing only one person, but in an election for multiple positions, it means a significant amount of information about the preferences of the electorate is lost.

Single transferable voting was developed to solve exactly that problem: it's called "transferable" because anyone who votes for the winner only has to spend part of their vote to do so, and the rest is transfered over to their second-choice candidate. (And then if that candidate is elected, the remainder is transfered to their third choice, and so on.) The "single" simply means that each person gets one vote - though that may not be such a meaningful statement, now that votes can be subdivided into arbitrary pieces.

The goal of STV, according to the Wikipedia article, is to enable proportional representation: each party or interest block gets a number of representatives in the final set of winners that is roughly similar to the fraction of voters that support it. One can argue about whether it actually achieves that goal (and I'm sure there's a whole body of research on that, which I'm not personally familiar with), but given the design goal, if you want your election to achieve proportional representation as well as possible, STV is probably the system to go with.

(Thanks to Nathan Tuggy for bringing up some of these ideas in the comments.)

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