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Is there an election System that allows for potential seats to be empty? E.g if there are 7 seats that could potentially be filled but the people voting only want 5 to be filled.

For context: We are holding an election to a Board where there can only be 7 members + president + vice president + Quästor (But these are elected separately). In the past, we usually had less than 7 candidates for the 7 seats. so we just had a yes-no vote on each person. But now we have 10 interested candidates. Some think 7 is too much so we don't want a voting system that takes away the option to only elect 5. Or if someone does not like 4 of the 10 candidates we want them to be able to vote for the option where there would only be the 6 Board members he likes.

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    Are you asking "What are examples of existing, widely used, election systems with this property"? Because it sounds like this is something you've got the ability to decide on, which means that you could make one up if you wanted to, but hat doesn't seem to be the question? – Erik Feb 18 at 11:50
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    What is a Quästor? I tried to look it up, but it redirects to Quaestor, which is a magistrate in ancient Rome. As you, no doubt, are not that old, what is that position? – CGCampbell Feb 18 at 13:45
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    @GCCampbell actually, the hit from ancient Rome is not that far off - the function is still similar, it refers to the position of a Treasurer of an organisation and is mostly in use in Swiss German, see also this online dictionary. Their function in ancient Rome included much more than that, however. – Hulk Feb 18 at 15:35
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    @CGCampbell: further contemporary usage example: It is also a position in the European Parliament – Hulk Feb 18 at 15:45
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    If I was in your place I'd also put some thought into whether your board actually has the power to specify these kind of details of a voting system. In many organiztions that may require a change of statutes. I wouldn't wanna be accused of rigging an election. – Joooeey Feb 19 at 17:22
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There are adaptations to the Single Transferable Vote that could achieve this.

In the usual STV process, voters will rank as many or as few of the candidates as they wish, and a quota is calculated based on the number of seats available (for seven seats, this would be 1/8 of the vote plus one). When a candidate reaches this quota, they are elected, and their excess votes are redistributed to the next available preference. Where no candidates reach the quota, then the last place candidate is eliminated, and votes are redistributed to the next available preference.

If a large number of voters do not rank all the candidates, you could end up in a position where two candidates remain with two seats to be filled. Under normal STV, those two candidates would be deemed elected, whether they had technically reached the quota or not. If the possibility of empty seats is a requirement, then the requirement to reach a quota can be sustained in this case.

It is worth noting that it is very difficult to predict how many seats would be filled; for example, if every voter ranks precisely four candidates, you may still fill all seven seats, or you may fill none at all, depending on how those votes are cast (though if there are ten candidates, these extremes are less likely).

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    STV elections for student bodies often include 'RON' - ReOpen Nominations - as a candidate, allowing an explicit vote against the remaining candidates. – AakashM Feb 19 at 8:41
  • One could leave still more seats unfilled if, in addition to thus sustaining the requirement to reach a quota, one computed the quota on the basis of the number of registered electors (either in the constituency or in the whole polity) instead of on the basis of the number of people who turn out and vote. (Why might one want to do this? It makes STV more proportional, and it gives all candidates an incentive to enthuse the whole electorate and achieve high overall turnout.) – Daniel Hatton Feb 21 at 16:24
  • BTW, as I understand it, in modern implementations of STV, the number of votes transferred from a candidate with surplus votes to an as-yet-unelected candidate doesn't have to be an integer, which presumably renders the "+1"s in the formula for the quota obsolete. – Daniel Hatton Feb 21 at 16:28
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Having multiple candidates and voting yes or no on each of them is called approval voting.

Approval voting by-the-book only has one winner - the candidate with the most yes-votes. But it can easily be extended to any number of seats by also giving a seat to the runner-ups. When you don't necessarily want to fill up all seats, then don't give seats to those who do not have the approval of the assembly (more no-votes than yes-votes).

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    This wouldn't work if you liked four candidates, but wanted only three elected total (i.e. you wouldn't know who vote for strategically). – Azor Ahai -him- Feb 18 at 16:45
  • Approval is a fantastic voting method for single-member elections, because it tends to select centrists who draw support from all over the political spectrum. This quality becomes a drawback if attempting run a multi-member election, because with n seats, you end up with n centrists. The more seats that there are to be filled, the stronger the emphasis should be on proportional representation. – eclipz905 Feb 19 at 22:29
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One system I have participated in had a system in which seats can remain vacant. This is done by always including the option of "vacancy" (direct translation from Swedish).

In the case of single seats, like the "Quästor" role cited in the question, there would be a vote sheet listing all candidates for the seat and another option for "vacancy". Each voter gets one vote. The option/candidate that receives the most votes is elected to the seat. If vacancy is elected, then the seat remains open.

For a multi-seat vote, like the 7 seats at the board cited in the question, there would also be a vote sheet listing all candidates for the seat with the additional option of "vacancy". Each voter gets to mark 0 to 7 of these candidates (i.e. up to the number of seats), including vacancy. If a person only likes 4 of these candidates, then these 4 candidates would get a check plus vacancy.

Then the same procedure would ensue where all candidates with the most votes and more than vacancy would be elected (up to the number of available seats).

In this particular system, ties were solved by chance, for example by coin flips.

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What I've seen in similar situations is to first vote about the size of the board and then elect the members. The choices of the voters in the first vote were, of course, informed by their knowledge of the likely candidates for the second vote.

This assumes that the electorate which fills the seats has the right to adjust the size, but since you're asking about voting systems I presume there is such freedom.

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It's not clear how this vote is being taken. This wouldn't work very well if it was a large, asynchronous vote, but if it was feasible, you could hold elections for each open seat in turn with a "no candidate" option.

At each election, the candidate with the most votes is seated. Then if "no candidate" wins, that seat is left open.

This is somewhat like STV, but may be more accessible (depending on who gets to vote).

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    It’s not clear how, because OP is asking how. – WGroleau Feb 18 at 22:48
  • @WGroleau Well, sure, but you could do this at a big meeting of 100 people, but you couldn't do it by mailing out ballots or a voting link and giving people a week to vote. – Azor Ahai -him- Feb 19 at 0:09
  • Of course you can, if the system is designed for it. For example, the system CplDavidson mentioned. – WGroleau Feb 19 at 7:32
  • @Wgr I'm not talking about Cpl's idea, I'm talking about mine. If the election is done in a big lecture hall, this idea is much easier than doing seven weeks of elections where each election is open for a week. – Azor Ahai -him- Feb 19 at 15:07
  • The question wasn’t whether it’s easy. The question is whether a system exists. – WGroleau Feb 19 at 16:47
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Depending on the reason for limiting the number of seats to be filled:

  • If you want to take only people everybody approves of:

    • For each candidate, hold a vote. If the candidate does not get a majority (or any threshold you want — but you should set this in advance), they are eliminated. Count the number of positive votes.

    • If the number of remaining candidates is below the maximum number of seats, you're done. Otherwise keep the candidates with the most positive votes. You may have issues with ties.

  • If you want to limit to a preset number of people whatever happens:

    • Change the max number of seats
    • Then apply method above
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You could use Single Transferable Vote with an additional option (like a candidate) of "Vacancy", then if "Vacancy" was "elected", the remaining seats would be left vacant.

  • This enables voters to indicate their preferences for all candidates, including those to whom they would prefer a vacant seat (they can still fill in all remaining candidates after "Vacancy").
  • Voters can also vote for a small number of candidates (for example, if they don't know most of the candidates) without indicating that that is the number of seats that they want filled. (e.g. They might want 5 seats, but only vote for two candidates (and not vote for "Vacancy"). They then are not voting to limit the number of seats, although they can't express their preference for 5 either.)

However, this (and probably any single vote for candidates) does not allow people to actually vote on how many people they think should be on the board. e.g. Someone might prefer a board of four (because they think more that than results in slow decision-making, etc.) even if they are not their first four preferences. Another option would be a separate vote on how many people should be on the board. There are a few options for that, using ranked voting systems, and each will lead to different voting strategies and a different outcome. e.g. STV or Condorcet are relatively strategy-free. DeBorda promotes compromise (and so the outcome is likely to be one of the middle options), but encourages strategic voting (e.g. someone who wants a board of 5, but expects that most people will vote for 4, could vote for 7 insincerely, to tip the balance more towards 5.)

I think the latter (separate vote) makes sense if the expected reason for voting for a smaller board is related to the practicality of managing a large board, rather than considering some particular candidates as unqualified or worst than no board member.

You could do both. Then the "Vacancy" option could cause the size of the board to be reduced from that chosen in the vote on the size. Then people could use the vote on the board size to vote on what size they prefer in principle, and use the "Vacancy" option for opposing candidates that the voter considers unqualified (or objectionable), etc.

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