Singapore does have a unique situation on the roads. Unlike, say, the US where drivers in some areas (e.g. quiet suburban neighbourhoods) will stop to let pedestrians cross (even if it's jaywalking) or in much of the rest of Asia where pedestrians and vehicles alike wander onto the roads and pretty much avoid each other while accepting the right of either party to be there, pedestrians wait until cars have passed before they venture onto the road, and cars won't stop if they see someone waiting to cross. But there is an exception (see point 4 below).
Singaporeans are:
1. Impatient - given a choice to proceed or to wait, they would rather proceed.
2. Kiasu - they hate being second, and want to be in front, and also prevent others from being in front.
3. Bullies - given points 1. and 2. above, drivers will take advantage of a car versus pedestrian situation.
4. Selectively rule-bound - Pedestrians DO have right of way, but only under well defined situations, like designated pedestrian crossings (zebra crossings, signalised crossings). But Singaporeans are curiously selective over which rules they follow, and which they don't. Since this is the only situation where pedestrians have right of way, and they are also kiasu and tend to bully, they then take the opportunity to turn the tables by strolling across the road casually.
So don't expect right of way unless you are at a designated crossing. If it's any comfort, drivers behave the same way towards other drivers - impatient, kiasu and bullying behaviour within the bounds of the law.
In places where drivers stop for pedestrians to cross, there is obviously a different mindset at work. Pedestrians are treated as vulnerable, and the strong (the one in the car) should help the weak. There is less impatience, and "kiasu" is an alien concept. I found it refreshing when I was in those quiet suburban neighbourhoods in the US. Try this in Singapore and you will get a confused look.