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At my work we need to elect three representatives among four separate departments.

  • There is a max of one representative per department.
  • Any member of a department can run as a candidate.
  • There is no limit on potential candidates per department.
  • All employees can vote for any candidate, regardless of department.

How can we conduct an election like this that is fair to all candidates and departments?


EDIT


Regarding some questions and comments, I add some information.

  • In the past, this was not a problem, because there were never more than three volunteers.
  • Members are not expected to follow a department line, even though they likely favor their own.
  • All aspects of this scenario have long been decided and I agree that it is weird. At this time, we can not change the number of seats as it also depends on others administrative sectors.
  • Each department is roughly the same size. Two are slightly bigger than the other two.
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    The setup seems rather weird. Surely it makes more sense to just elect a 4th representative and let each department be represented. No electoral system is completely fair-- they all have positive and negative attributes-- but it seems unlikely that the workers in whatever department fails to elect a representative are going to consider the outcome fair. – Justin Cave Apr 12 at 15:57
  • I agree on everything here. – POC Apr 12 at 15:59
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    What happens if only people from 2 departments are willing to be candidates? Does one of the seats go unfilled? – Barmar Apr 12 at 22:43
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    To get a good answer you'll have to provide more information about what are the goals of the system. There are a lot of voting systems to choose from and various criteria of "fairness" that can be adopted. Unfortunately, all voting algorithms fail on some criterion or another (although some fail on more counts than others) so to pick one you have to choose which are the criteria that are more important for your situation and which are the ones you can live without. It is also important to know the relative size of each department as that could be a distorting factor to guard against. – Rad80 Apr 13 at 7:53
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    Also: do you expect voters to vote along department lines? – Rad80 Apr 13 at 7:55
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Probably the most easily understandable method is approval voting. Each person can vote "yes" or "no" on each candidate individually. Then, you order from most votes to least, and take individuals if someone from their department has not already been elected.

Depending on how complicated you can get with your voters, you could expand to score voting, where each voter scores each candidate on some scale, and the sum of scores ranks them.

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    Approval does not result in proportional representation, though, which is often considered desirable for electing multiple representatives. en.m.wikipedia.org/wiki/Sequential_proportional_approval_voting – endolith Apr 13 at 10:07
  • One department still won't be represented. – henning -- reinstate Monica Apr 13 at 11:37
  • @henning--reinstateMonica The OP didn't ask about that (but I agree it's silly). – Azor Ahai -him- Apr 13 at 14:34
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    @endolith (1) I have a hard time considering "proportional representation" in an three-person committee without parties (or where "parties" are capped at one each anyway); (2) You have to recall this is a workplace election not full of political nerds (most likely). Even if there's 200 constituents, 80 voting might be a good turnout. My point is getting too complex might just be alienating and confusing - although if you put it in as an answer, I'd happily upvote it – Azor Ahai -him- Apr 13 at 14:58
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Don't elect them all at once.

Our department has four different, equally sized groups, governed by a committee of three people. (It needs to be odd so that votes are never tied.) However the elections are staggered so that we only elect one person at a time, and the department just tries to vote on who they think is the best candidate.

There can be a little politicking, but the committee membership rotates pretty equally among all of the groups, on average.

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  • Could you be a little bit more specific on why, we should not elect them all at once? Thank you! – POC Apr 13 at 18:32
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    By having staggered elections different groups are not competing against each other at the same time. If the current committee has a member from group A and B, the faculty will (as a whole) tend to chose someone from C or D because there is a recognition of a desire for balance. Even if all faculty in group A vote as a block it's not enough to elect a second candidate to the committee. (BTW, we run several rounds of secret ballots until a candidate gets a majority.) – Kieran Mullen Apr 13 at 21:13
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The electoral criterion you proposed seems very odd to me and can potentially lead to a wildly un-representative outcome no matter how you design it.

For this reason, I would recommend the following changes.

1) Increase the number of seats to at least 4.

Given that there are 4 departments (constituencies), the bare minimum of representative should be 4, otherwise, at least one department will always be deprived of representation. That's just basic math.

But ideally, the number of representatives should be higher, because we don't know how many people there are within each department. The result would be wildly disproportional if both department A and B get one representative, despite that department A has ten times the number of employees as department B.

Therefore, the number of representatives that each department returns should be as follows:

Number of representatives in a department = Number of employees in a department / A fixed quota of voters for each representative.

For example, if you have 100 employees in a department, and you want 20 voters per representative, then the number of representatives should be 5.

2) Voters should only vote within their constituency.

It makes no sense that voters from one department can vote for candidates in another department because it messes up the incentive mechanism for electoral accountability.

For example, a candidate in department A can win an election by receiving a huge amount of votes from department B, despite that such candidate received a very low amount of votes in department A. In this scenario, the employees in department A are essentially deprived of their voice because their representative is accountable to voters in another department.

The solution is as follows: You either make people only vote within their constituency, or you abolish the constituencies altogether and make everyone vote in a single constituency combining the four departments.

My recommendation:

Following what I said, I would propose something proximate to paralleled ranked-choice voting.

  1. First, you increase the total number of representatives from 3 to 8.

  2. Second, each department (constituency) elects 1 representative using either instant-runoff system or approval voting system. This ensures strong local representation so each department is guaranteed at least one voice.

  3. Third, the four departments collectively elect 4 representatives using single-transferrable vote system. These four representatives are accountable to everyone across the four departments, which ensures that at least half of the total 8 representatives are looking out for collective interest, rather than just their own departments.

The key here is that the number of constituencies candidates (those elected within the department) should be equal to those elected across all departments. For instance, if you want to make each department elect 2 representatives instead of one, it is best to increase the collectively elected representatives from 4 to 8 as well.

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Only three representatives over four departments? Weird...

At any rate, some variant of ranked choice voting is likely best for your purposes: you can put as many candidates as you like on the ballot, and the least popular will drop off naturally without feeling like they've been excluded.

The example they give on Ballotpedia is for a single-winner race; if you search around you can find modifications for multiple-winner races.

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    This is why I hate FairVote for co-opting the term "Ranked Choice Voting (RCV)" to mean Instant Runoff Voting (IRV). There are dozens of ranked voting methods, and discussing them has gotten significantly harder in the last 5 years thanks to their efforts. The most common multi-winner ordinal voting method is called "Single Transferable Vote (STV)". To add insult to injury, the multi-winner STV is a decent system for achieving proportional representation, while the more famous single-winner IRV fails miserably in common election scenarios – eclipz905 Apr 12 at 21:02
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    This does not address the department issue at all. Moreover there are several "ranked choice" voting algorithms and the one described in the link is not one of the best. -1. – Rad80 Apr 13 at 7:42
  • @Rad80: True enough; I was just putting the RCV option out there. – Ted Wrigley Apr 13 at 14:53
  • @Rad80 I don't quite undestand your comment. This is, afaik, one of two answers to mention RCV - which by definition is a better than "first past the post" systems to elect a multiple of representatives from possibly minority subsets. That is why they were concieved. I hope you voted down all the other answers that were lacking the same items on your list? – Stian Yttervik Apr 14 at 12:27
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Elect 1 representative from each department. Final electees draw straws (or other fair/random choice mechanism) to choose which 3 serve.

If these positions are not lifetime appointments, you can set up a rotation such that each department is only unrepresented for 1 term in 4.

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