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Fairness ?

11 Nov

Sometimes, the way we think is purely gated by how a given problem or issue is presented to us. If we take time to wonder how we all fit into a complex network of society, it is just amazing how it would look for an outsider to envision the way we operate. In order for a complex society to thrive, I guess some amount of fairness needs to be distributed across it. If not, there will only be chaos. This is not to say that the world is a fair place. But, on a macroscopic scale, I believe fairness prevails. This brings up the important question, what does the term “fairness” really mean? I believe that fairness is a context dependent issue which has different meanings in different contexts. Also that, being fair to everyone is impossible. So, where is the trade-off? This blog is an attempt to characterize a queuing problem for different facets of fairness, just to see how fairness is influenced by various schemes. If you think about it, all schemes discussed below do acheive fairness of some sort. If you think otherwise, it is probably because you did not do a lot of thinking..:)

Assume a parking lot with “m” columns (c1,c2,c3,..cM) and 1 row. The 1 row being the one through which people exit a parking lot (c1 is closest to exit). Each of the m-columns join with the exit-row only once. Let us assume for this problem that no new cars are entering the parking lot and that all cars are trying to exit the parking lot. Also, assume that the exit row is already filled up with cars trying to exit. Now, the question is, what strategies can be used make the process of exiting fairly?

In approach1, the condition is that you cant exit from a column until the ongoing traffic in the row exits out of the parking lot. So, if you are in c1, you will not get to the exit until there is no ongoing traffic in the exit row. This would mean the person in column c1 will get to go only till all cars from c2 through cM have left. Now, let us consider that at each junction point, each person in the column will only wait for one oncoming car to pass through and then gets the right of way. This would mean that a car in column 1 will get to go out for every 1 car out of all the remaining columns. But, this would be unfair across the different columns since car in column 1 gets 50% chance of getting out and the car in column 2 will get 25% of chancing of getting out and so on. If you want to establish fairness, one can say that a car in column 1 should wait for, let us say 4 cars before it can go out. This would distribute fairness across the different columns.

Looking at the above notion of fairness, an engineering mind could add that, why not build more than 1 exit from the parking lot. This would simplify the problem not only by the number of exits, but also distribute some of the exponential delay factors in the problem. A business person’s perspective would be to assign a cost based on the “unfairness” associated with a car to exit from a given parking lot. So, someone who pays more could get out much easily. A statistician could argue that, if the arrival distribution of people who want to take the car out of the parking lot is such that the low cost folks populate first and if there is a varying degree of cost distribution, then the distribution of cost wouldnt make sense. He might also add that, having a seperate parking lot to serve high cost customers and low-cost customers could be a good idea. A socio-economic point of view would be to avoid having a parking lot and offer a shuttle service to transport people to a different place where parking is distributed enough that they can all go out easily. Even if the parking lot is cramped up as in approach1, we can assume that the passengers in the car are uniformly distributed in terms of the positions in the parking lot and hence can get out fairly in shorter time span. Here, the size of the shuttle and its frequency of operation would decide the number of people transported. Also, the fairness of populating the shuttle would depend upon the arrival order, which sounds fair as well.

The list of take aways from this problem are, being fair to someone would not mean that you are being fair to everyone else, Being fair to everyone would mean that it is not an efficient system, in some cases money could buy you fairness, if you try to limit fairness to a small group of individuals it is usually quite successful. The discussion above is just glorified common sense. It is just that I wanted to glorify it my own way since I had “some” time at my disposal…:)

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5 Comments

Posted by on November 11, 2005 in From AM-KICKING blog

 

5 responses to “Fairness ?

  1. Survivor

    November 12, 2005 at 8:01 pm

    Mindframes,
    As usual..Somehow, most of your blogs are linked to probability of which I understand very little. I was initially overwhelmed, but reading it twice, understood all about fairness in a parking lot..
    So, what you are trying to say is that it is fair not to be fair with everyone all the time. Am I right?
    In all fairness,you must have had “lots” of time at your disposal to have come up with the scheme.:-)

     
  2. BrainWaves

    November 14, 2005 at 10:27 pm

    In real world it is implicitly understood that people closer to exit will get out sooner and those rows are filled up by people who come early (investing their time) or who pay more (investing their money) or who must get out early (handicaps, family cars etc).
    So, people in other rows know that it is fair (though we crib) that they are not getting out soon.

    The question comes when their is lawlessness. For example, in India drivers cross the yellow line to get “unfair” advantage and in turn screw up the entire system.

    I have more theories on why Fairness (objective) for all in a bigger picture is possible. But collecting all those thoughts now is like assimilating a 5 dimensional problem or picture. So I will leave it later

     
  3. IamwhatIam

    November 15, 2005 at 1:02 am

    Wow, A complicated blog. I had read it a couple of times to visualize the parking lot. Interesting thing is that you are trying to solve fairness like one would approach a math problem. But there are somethings in life that cannot be solved like a problem because there is no predictable outcome. One of them I think is fairness. If someone asks me “Are you a fair person”, I would say “well, that depends”. Let us say a parking lot adopts your technique to be fair to everyone. Then the guy who is supposed to go after you in the parking lot goes before you, what do you do? If you remain calm to maintain fairness, what will the guy after you do? Will he wait for you to go or will he think it is actually his turn and leave?. If this goes on you will never be able to get out of the parking lot.

    How often one is unfair or is treated unfairly depends on many external factors. Some of which are population, Monetary status etc. For the same reason there is more unfairness in a populous & poor country like India than a rich country like US. In India where the vehicle to parking spot ratio is high one has to be unfair in parking to get the last table for dinner at the restaurant. When it comes to basic needs in life fairness is a long way behind

     
  4. BrainWaves

    November 15, 2005 at 1:36 am

    In the current context, if you are letting someone who should’nt go then it is not because you want to be “Fair” but because you(or anyone) thinks it is too insignificant to fight over.

    Fairness, if defined without any boundries are meaningless.

    Will we call the Airline which charges 3X amount for first class and providing additional service as Unfair even though it discriminates between rich and poor (relatively)?

    I do agree there is another angle of exploitations which is UNFAIR.

     
  5. Mindframes

    November 15, 2005 at 4:28 am

    I agree to “IamWhatIam” and “brainwaves” that fairness is context based, but I disagree to the statement that fairness is not quantifiable. I think fairness is different from “ethics”. For example, Judiciary system is to enforce fairness (there could be exceptions). Traffic laws are to enforce fairness. Similarly, most of our actions in the society is not just controlled by the society itself but by a whole lot of rules governing it (which probably arised out of societal unfairness). One could be ethically unfair inspite of “rules” and they usually face consequences. Anyway, if you think of the blog the next time you enter a parking lot, I have achieved what I wanted to achieve..:)

     

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