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.
Following what I said, I would propose something proximate to paralleled ranked-choice voting.
First, you increase the total number of representatives from 3 to 8.
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.
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.