Siew Kum Hong's article in Today "Voting must be seen to be secret" appears to suggest that while votes are secret, serialised ballot slips, recording of serial numbers and allocated voting lanes (perhaps in tandem?) create the impression that they are not secret. And this fear had in the past caused his civil servant friend to vote against her conscience (presumably this means for the PAP).
Is the vote secret? There are two ways to look at it.
First, I think it is safe to assume that your INDIVIDUAL vote is secret. Your ballot slip (with serial numbers) get put in a box together with (probably) hundreds others. The boxes are unsealed and counted on polling night, with agents from both parties present. Theoretically, there's a tiny window of opportunity for someone present who knows your serial number to look out for your number, but this is not realistic. Now, after the results are out, the ballots get sealed in the boxes again and put with the Courts for 6 months, after which they are incinerated. So in these 6 months, someone could conceivably take out the boxes and sift out your ballot slip (assuming again he knows your serial number, which I believe most voters themselves would not remember unless they were planning to buy 4D). For this to happen, however, we would also need some level of corruption in the system (may be a low-level guard to take the box out; or at a higher level, some court/government official to authorize access to the boxes. It just seems like too much trouble in any case. If I wanted to know how person A voted, I could ask his friends, his family (or even person A himself) and probably get a pretty clear idea.
However, it is well known that politicians know how specific precincts or smaller parts of estates (possibly a block?) have voted, since each group is allocated a voting lane (and hence their votes go into the same box). So conceivably, an observant counting agent could tell what percentage of Blk 123X voted. So, your COLLECTIVE vote is not secret.
So why not get rid of serial numbers and voting lanes and make voting more fuss (and fear) free for all? The simple answer is that it is not in the interests of the ruling party. Why? Amongst the voters would be some who (a) would vote for the Opposition but are fearful that their vote may be found out and it would impact their job, HDB application etc; and (b) some who would vote PAP but want to make a statement against this not-so-seemingly-secret voting process. Everyone else -- lets call them group (c) -- is indifferent to the voting procedure, as long as the number in group (a) outnumbers those in group (b), it is in the interests of the PAP to maintain the status quo. Doing anything else simply benefits the Opposition.
Unfair? Probably. But why would they want to do otherwise? Hence, it fell to Opposition figure such as Low Thai Khiang to use their air time assure everyone that their vote was secret (or secret enough, anyway).