Not always. I recall twice that I didn’t let an aggressive jackass on the right merge in front of me, forcing said jackass to exit onto an off-ramp that he didn’t intend to do.
Oh, wait. I guess that makes me the more aggressive jackass! 
Why, yes. Yes it does.
In fact, I have always noticed that, even in bumper-to-bumper traffic (and in fact, especially in bumper-to-bumper traffic), most drivers are pretty good about zipper merging.
ETA: This is true, even where an on-ramp lane merges, where technically the merging on-ramp traffic doesn’t have the right-of-way at all – specifically where the freeway traffic is bumper-to-bumper so they’re all already going slow anyway. On-ramps in areas of heavy traffic commonly are metered these days, which helps make it easier.
Major Feelgud’s last activity was in 2004. I doubt the good Major will see this.
Since this thread has been resurrected, I gotta say: this is a good joke.
cough HOWEVER–
The answer is perfectly obvious–it’s the policeman.
Reason: POTUS would be in Marine One in such a situation, not in a car. So that’s actually an impostor. The ambulance is actually going to the fire at the orphanage. Therefore, it needs to yield to the fire truck. The EMTs can’t do their thing until the fire is out. Eight seconds, or however long it takes for a car to clear an intersection, probably isn’t going to make any significant difference at a fire, but it very well might at an armed robbery.
Therefore the policeman has the right of way.
In Thailand, the larger vehicle always has the right of way. Always. Sad but true.
This has to be the single most contentious traffic question I’ve ever encountered. Zipper-mergers and immediate-mergers fight hammer and tongs over this on almost every social media venue I’ve ever been a part of. And both sides are just incredulous that the other side could possibly be serious about their partisanship.
I’m always a little amazed at how enraged people can become just discussing this.
But what happened to the missing dollar?
The car with the zombie in it, of course.
There is one exception. Many of our two lane entrance ramps go to a single lane before the highway merge. These are metered, and when the metering lights are on there is no problem, since only one car goes at a time. When off though it is possible that two cars hit the single lane at the same time. For the most part people are reasonable and stay in the right lane in this situation, but I should research what the law says, if anything.
Some have 24 hour a day carpool lanes on the left, and I’d suspect they have priority.
As for Lib’s joke, the clear answer is the car with the biggest bumpers.
Whoever has the largest caliber gun in Florida.
Phu Cat
Makes me nuts in Colorado. We do have good signage on the highways, but whatever lane ends is willy nilly with no thought of the road design.
IMHO. The right lane should always have the ROW over overtaking/passing vehicles that made the choice to pass.
I was reading this thread without noticing it was a zombie until I came across the line “throw a disk in the Mavica,” which is when I felt like I had time-traveled. It’s been a looooong time since I’ve seen someone inserting a 3.5" floppy into a digital camera.
Which one is the merging lane? 
Here’s what no one will ever explain to me. Zippers start at the bottom of the jacket and end at the top. If you zipper-merge, you inevitably “zip up” the road to the point where the lanes are separate. In order to reset, someone has to jump up to the “head” of the the now-empty, ending lane. In other words, someone has to continue to the merge point.
The alternative is to continue 'til the merge point and merge there. That requires people to skip ahead. Anyone who tries to “wait their tun” would be bringing the merging lane to a halt.
So how can people zipper-merge and also merge at the merge point at the same time?
Zipper merge is just an analogy, and somewhat inexact. Imagine the ‘slider’ is staying still and is the merge point and you are pushing the two rows of teeth into the slider, to get the zipped rows extruding out the other side.
dqa may have found a rule/law covering this matter, but this thread illustrates that knowing a rule of the road is of little value in many instances. Frankly, if two drivers want the lane in between them, the lane belongs to the stupider driver, because the smarter one will get the hell out of the way of someone insisting on occupying a lane. That’s a dangerous situation and no rule/law is going to be of much help. Driving is largely a matter of working and playing well with others. Being smart and safe is a lot better than being right and dead.
I believe this section does not apply to the situation in the OP. This section would apply only on a roadway with three or more lanes going in the same direction. e.g. You’re in the outside lane, another car is in the inside lane and you both are moving to a center lane. Presumably the thinking is that the driver in the right-most lane has a better view to the left prior to moving left.
Also, I don’t believe you’ll find any traffic statute that gives a driver the exclusive right-of-way in any situation - it will designate which driver must yield. (At least that’s the way it was 20 years ago when I studied traffic law.) There’s a message in that wording.
I still haven’t found a (Texas) statute that covers the original question specifically. I can’t even remember how it was enforced back in my time. Then again I can’t remember what I did yesterday.
Then that requires me to stay parallel to “my” spot, waiting for us to approach the merge point. The car ahead of me is gone, so there’s empty space there now. If I zipper, I can’t move up. If I move up, I’m “cutting.” The important point here is my lane is moving faster because it has less cars. There’s no way to fix that. Either I stall or I cheat. Which is it?
If you move up, you are defeating the efficiency of the zipper maneuver; people behind you will eventually have to brake to let you in.
But the zippering only happens at the merge point. Say you are on the right of the merge. If there is a steady stream of cars on the left, trying to force yourself in with the car in front of you is obnoxious. One car at a time makes life easier. However if for some reason there is space in front of the car on the left, it is silly to wait for him to merge. In that case two at a time makes sense. The same is true of the complementary situation. So moving up reduces surprises at the merge point.