Elections at B

When the Academic Coucil Elections were conducted last term, I had a feeling that something was wrong, though I couldn't quite put my finger on it. So, today morning, I decided to try and work out what it was that was bothering me.

To those of you who aren't aware of Academic Council, it is an elected council at my institute, which acts an interface between the students and the institute. Last term, 5 people stood up for elections. 4 were to be elected finally. The election was held in the procedure below:

1) Each student has the right to vote.

2) Each student was given a piece of paper to write. He/She was expected to write exactly 4 names (Any deviations from this were discarded in the counting phase). These bits of paper were then put into the ballot box(the standard secret ballot procedure)

3) Simple counting ensued and results announced

Now, please stop reading for a while and think if everything seems OK. Did we, through this process, really end up choosing most preferred candidates? The answer to this question, in my opinion, is NO.

My reasoning for the claim is that we did not take the internal preferences of each student into account. I believe that each student internally sets up ranking for each of the candidates. For example, if A,B,C,D and E were standing for elections, I would have my own assessment and ranking as C>B>A>E>D. Hence, based on this, I would cast 'a vote each' for C,B,A and E. But surely, 'a vote each' has not really taken my internal preferences into account.

As an illustration, let me make it a bit simple. Let us assume that 4 people are standing for elections. There are only 3 elected seats, hence, only 3 out of the 4 will finally be chosen.

Let me also assume that there are 6 people voting. Let their votes be

P1: A B C

P2: A D C

P3: D A C

P4: A D B

P5: A B C

P6: A B C

Now, based on this, you can swiftly see that A has 6 votes, B has 4, C has 5 and D has 3. So, A B and C are elected. But now a question arises. Note C; this candidate has been only the third best preference of 5 of them and not all preferred by a sixth. Do you really think it is right for him to get elected? This is an issue which will always crop up if internal preferences are not asked for.

Now, suppose I take the internal preferences(I'm assuming it is the same order in which the student has voted i.e. for P1, A>B>C>D). I decide to attach a ranking to the preferences. For example, for P1's choices A>B>C>D, let us give 3 points(votes) to A, 2 to B, 1 to C and 0 to D.

If I were to do this for all the 6 and add up points for each candidate, then I'm in for a small surprise.

This time, A has 17 pts, B has 7, C has 5 and D has 7. And now A B and D will be elected.

This particular solution of A B and D being elected seems like a more optimal solution to me than choosing A B and C. The reason I say this is, since we took internal preferences into account, we have ended up by maximising the group's overall utility.

I welcome any other viewpoints. I have not factored many other real life factors such as regionalism, students making internal preferences without even having an inkling of each candidate's agenda, human errors in casting and counting. These factors are important because, I think, it makes the election more of a popularity contest instead of the utility maximisation mechanism. However, for the moment, I'm neglecting these facors.