Saturday, July 10, 2010

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.

5 comments:

  1. Aditya.....i understand what u r trying to say...for ur information there is a system currently in place in the Indian Political system...however, its different from what u have suggested and i think its better than what u have suggested...just go through the elction procudre used for the election of the president of India...a single transferable vote system

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  2. @Ojha: Thanks for viewing the blog....will follow your advice and find out about the other system...

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  3. the system of multiple votes do make you think that something is fishy. But the method what you suggest also has it share of grey areas.
    look at it this way, out of 6 people, 3 people do not want D as their leader but only 1 is actually opposed to C.
    But in your method, its D who gets elected and not C. I hope i got my number right, and also hope you see what i am trying to point at

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  4. @Bags:
    I know that there are problems with the system that I've tried to illustrate. My point was simply to show that by tweaking the procedure slightly, we might end up with results that are, in my opinion, better. Of course, in such a context, better or worst comes down to utility functions(management jargon).

    As has been pointed out in the first comment, there are much better ways to conduct elections of this nature. However, they come with attached complexity in execution and counting.

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  5. The flaw that you have pointed out could have been due to the fact that too few candidates are competing for too many seats (i.e. only 13 candidates for 10 seats). I seriously doubt if this system can work in an optimal manner under these conditions.

    On a slightly different note, maybe we can vote in the manner in which we bid for various courses. Basically allot say 1000 points to all the students and let them split the points the way they deem fit among the various candidates. Sum the points for all the candidates and you can have the ranking that you were looking for.

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