Transcendence and Preferences

Everything in life is relative. Whether we realize it or not relative evaluation is the key to nearly every activity in our life. For instance, I'm trying to go through a weight loss routine and always want to measure how I did this week relative to last week. Similarly relative performance is in play at your work place, in school, in sports etc etc etc. I'm sure Saumya will agree that shopping too is a game in relative evaluation.

Let us consider two specific examples.The first is ranking in school. Suppose Suppandi does better than Muniyandi and Muniyandi does better than Perandi, does that imply that Suppandi has done better than Perandi? Of course the answer is yes, because of the fact that such preference orderings were computed at a given point in time when all the competitors took the test at the same time. Now assume a new test is given a week later. Is it necessary for Suppandi to do better than Perandi? Not necessarily. However transitivity of preferences would seem to suggest that such a relationship should hold.


The crux of the matter is relative measurement and it relies heavily on preference ordering. For instance consider an alternative example such as making a trip to the grocery store. The chore on hand is to buy fruits. Money or no other factor is important. The only issue is preferences. Your choice is limited to three fruits; Apples (A), Oranges (O) and Water Melons (W).

From the set {A,O,W} you choose A and O. This implies that the preference ordering could be A>O and A>W and also that O>W where the symbol ">" refers to the "preferred over" (i.e.) if A>O this means that Apples are preferred over oranges. The above ordering also implies by transitivity that A>W.

Do we adhere to the same principles on subsequent visits to the grocery store. Does your preference has to stay constant. In the case of the tests described above, we can argue that ability might not change and one test might be sufficient to ensure that the preference ordering will hold. But in the grocery store example where pure preferences play a part, is it always the case that A>W?

Now switching to a real life analogy from college football. This year is special in the sense that in the first half of the season, three teams have been ranked No. 1. BCS ranking depend heavily on transitivity. For instance given three teams A, B and C. If A beats B and B beats C, we would expect that A is better than C. But that never seems to be the case. Consider this. LSU beat South Carolina. South Carolina beat Kentucky and then Kentucky beat LSU. If it was a round robin between these three teams, then each one ends up with equal points.

Can we say that if team A beats team B and team B beats team C, team A is better than team C? Transitivity seems to suggest we can. But reality seems to be different!