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Say in an election there are predefined categories users can be assigned to. Of the people who are assigned to a certain category, other users can vote for them. To compute the results, the following rules have to be adhered to:

  1. Highest voted user in category wins
  2. If 1 user have same 5 vote count for 1 category and 8 vote for 2 category then he/she will be elected for category 2.
  3. If 1 user have same 5 vote count for 1 category and 5 vote for 2 category then the winner selection will be On Hold
  4. If two or more users in a same category has the same votes, then goes on hold

So, for example: the table lists the positions and for each position it gives the name of the user and the votes they received.

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For this, the winners should be as follows:

  • Position 1: User 1
  • Position 2: User 3
  • Position 3: User 2 (User 3 loses because of rule 2 and wins in position 2)
  • Position 4: User 5 and User 6 are both kept on hold (rule #4)
  • Position 5: User 4 on hold (rule #3)
  • Position 6: User 4 on hold (rule #3)

I have tried solving this using the Hungarian algorithm to no avail. It works quite well, after some modifications, for this problem. But doesn't live up to the following case:

enter image description here

In this case, the results are as follows:

  • Position 1: User 1
  • Position 2: User 2
  • Position 3: EMPTY (User 1 and 2 loses due to rule 2)
  • Position 4: EMPTY (User 1 and 2 loses due to rule 2)
  • Position 5: EMPTY (User 1 and 2 loses due to rule 2)

Basically, no user can be assigned to more than one position.


Any help solving this would be extremely helpful.

Thank you

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