From a macro collective perspective, the Manila traffic situation is really a simple issue. What we call the "mess" that is Manila traffic is no more than an emergent property; a collective outcome of the idiotic behaviour of the system's individual elements -- Idiotic Filipino Drivers. Tell-tale signs of a truly idiotic driver is a traffic negotiation style characterised by frequent rapid acceleration followed by hard braking, and awkward squeezing into tight spots. All are hallmarks of a habitual failure to anticipate, empathise, and foresee.
These are aspects that, when understood a bit more deeply, hold the keys to a successful conquest of Pinoy-style road traffic; thus,
(1) Keep tabs on what is going on behind you. It is a good driving habit to glance at your rear view mirrors every now and then. Usually, agressive drivers stick out like an attention-deficited kid in a class of well-behaved students. The more you are aware of and anticipate their movements, the less chance of you getting caught in a surprise cut in once these morons catch up with you.
(2) Do not signal your intentions when planning to shift lanes. The Philippines is a nation of takers, not givers. The moment a neighbouring motorist senses your intention to move into her lane, she will speed up and close the gap you are planning to fill. Empathy for the typical Pinoy condition reduces the ill-manners of surrounding motorists to nothing more than a sporting challenge -- like how the experienced tennis player applies an intuitive understanding of the physics of moving objects to evaluate the best way to whack an approaching ball back across the net.
(3) Continuously evaluate the situation four or five cars ahead of you, or as far ahead as your line of sight allows. Most Filipino drivers are morons lacking in foresight. They will often attempt to get ahead by swerving into a lane without realising there is a jeepney ahead in that lane stopping to disgorge a load of passengers onto the pavement. Use your far keener anticipation faculties to hem in cars behind jeepneys so that their drivers' malicious intentions to cut back into your lane ahead of you are thwarted.
Apply a bit of driving class.
Don't involve your passengers in the driving process. I've seen entire families involved in hand signalling surrounding motorists as their vehicle squeezes from one lane to the other. I've also seen passengers (in some really pathetic cases, the drivers' dates) getting out of the car to assist the driver squeeze into a tight parking spot. Uncool, to say the least.