I was searching through technorati for posts about Singapore when I came across this article on the fare hikes that went through. The author took down some figures from Today articles to calculate the actual fare increase and concluded that the increase is more than the reported 2.4% and request for people to correct his maths if it is wrong, and if so he will pull it out. I just love mathematical challenges (perhaps physics majors/graduates really enjoy pain).

The author, Yuhui, started by quoting the average fare and increase reported as 80 cents and 2 cents respectively. He then proceed to say that 2 cents is actually 2.5% of 80 cents. (It should be 1.92 cents for 2.4% so I'm giving Today the benefit of the doubt). After that, he factor the average fare and increase for cash paying commuters to be 80 cents and 10 cents respectively for a 12.5% increase himself.

Now up to this point we can see that Yuhui contradicted himself. He assumed that the average fare increase of 2 cents reported excludes the 10 cents for cash paying commuters which is a wrong assumption. If we work out the increase for each fare individually for EZ link users, we can find that the average increase for EZ link users would definitely be lower than 2.4% hence the 2 cents have to include the cash paying commuters. Examples for air-con service below.

$0.63-$0.64=>1.59% increase $0.83-$0.85=>2.41% increase
$1.03-$1.05=>1.94% increase $1.13-$1.15=>1.77% increase
$1.23-$1.25=>1.62% increase $1.33-$1.35=>1.50% increase
$1.43-$1.45=>1.40% increase $1.53-$1.55=>1.31% increase

He claimed the following when I post a comment to doubt his methodology.

At 8:43 AM, Yuhui said...

I am assuming from the older Today article that all of the different fares that you mentioned have already been worked out to give the average of 80 cents. If this assumption is wrong, then either Today is vague in their wording or did not do their calculations correctly.

Then why he does not assume the average increase is worked out from all of the different fares but segregate the cash paying fares out? And why is Today at fault for an erroneous assumption he made?

Yuhui proceed to further his argument in the article by calculating the "actual" fare increase by assuming the average fare of 80 cents for all the 3.4 million commuter trips daily to come out with the shocking conclusion of 3.09% increase yada yada yada~~ But we know that all those calculations are wrong as his assumption was proven incorrect above.

I shall briefly describe my suggested method to calculate the fare increase below. (Warning, it can get technical so I suggest that you skip it if you are not mathematically inclined.)

To calculate the actual increase we will need to have the detail breakdown of the number of commuters paying each fare rate and also the number of transfer information too. Given that the public is unlikely to obtain such information, we can only work by assuming a certain distribution (Gaussian, Poisson or uniform etc) for the number of fare stages commuters ride in. From the assumed distribution calculate the total fare and the fare increase for, say, EZ-link payers on the air-con services. Repeat the calculation for non-aircon services, cash paying commuters, commuters who transferred from MRT, child/student/concession card holders with all the different possible permutations. Note that you will have to make a lot of logical estimations on the numbers like number of child/student commuters who pay cash and EZ link etc. After that you can safely estimate the actual increase in fare.

Have your brain suffer from a cramp yet? And no, I won't go through this calculation, I know I'm free but I'm not that bored, unless I want to publish a 10 page paper on it.

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Updated (2/6/05): Yuhui's reply:

Actually the two-cent average increase for EZ-Link cardholers that I mentioned is my own figure based on the stated fare increases (1-2 or 3 cents). Today did not mention (nor do I recall it mentioning) such an average increase.

Therefore, my average two-cent increase does not include the 10-cent increase for cash-paying commuters.

Also, in the real world, you can't pay with less than a cent, i.e. there are no fractions of a cent that you can use physically to pay for goods or services, which is why I rounded the number up to two cents. If the transport companies round the number down, i.e. to one cent, then I will have to do some recalculations.

Funny how different figures can be obtained from the same exact source I got from him. (Note: 3 cents for MRT only, 1-2 cents for buses which is the focus of this discussion) Somehow we didn't manage to connect as I wonder when the problem of fractions of a cent came out. All in all, I lost my respect for a writer I once thought who could produce some decent articles.

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Tagged: singapore fare public transport