I voted no
There is little hard evidence that cell phone usage leads to a higher incidence of accidents or that it leads to a higher incidence of fatalities.
Let me explain, then you can get out the pitchforks and torches. First, cell phone usage (both in cars and out) has been increasing nearly geometrically since the 90s in the United States. In that time, traffic accident rates per mile traveled have gone down slightly. Second, traffic fatalities during the same time have gone down somewhat more per mile traveled, due mostly to vastly improved safety of vehicles on the road but also significantly due to the presence of cell phones and thus much faster emergency response.
Neither fact, by itself, proves the positive proposition 'cell phone usage while driving has not cost lives', but both, together, disprove the positive proposition 'cell phone usage has significantly increased fatalities on the roads' as such an increase would be glaringly obvious in a significant increase of the fatality statistics on US roads. You would expect at least one standard deviation increase from the previous statistics, but you see a gentle downward trend instead, which is simply not compatible with the proposition that cell phone usage causes increased accidents or increased fatalities.
So, if it is obvious that cell phone usage impairs a driver compared to an 'attentive driver', what is happening?
Three theories exist:
1. Driving doesn't require that much attention. This is, mostly, true. Most drivers know when they need to be attentive (heavy traffic, adverse weather, narrow roads, etc.) and when not (open freeway, few cars, so on) and adapt appropriately. I was once on a road between Las Vegas, NV and Denver, CO, that was completely bereft of cars, hadn't seen one in hours, and I whiled away the time practicing magic. This is one reason that teenagers are disproportionately represented in cell phone usage statistics, but they are disproportionately represented in crash statistics anyway, so there is little benefit in banning teenage use of cell phones while driving anyway.
2. There are lots of other distractions. Fooling with the radio has been shown to be distracting enough to cause a wreck. I'm pretty sure one time I, personally, was rear-ended, this is what the other driver was doing. People eat, do makeup, talk with passengers, look at signs, on and on, all things that can lead to wrecks. Most of these will be nearly impossible to ban. Singling out cell phone usage and banning that will not reduce any of the other behaviors.
3. Compared to inattentive driving, there are actually worse issues, such as driving while tired, stressed, or otherwise less than optimally alert, which nearly everyone does. My morning commute is full of people who are not fully awake yet. Also, there is the issue of personality disorders. Most of my near-wrecks that happen on a constant basis (I drive 55 miles each way every day in a major city) are caused by drivers who start pulling over without looking or simply don't care. Road rage occurs at least weekly. Banning cell phones won't address any of this.
Also, please note that not only is it the case that simple statistics show that the idea that a cell phone ban would not reduce fatality rates, the fact is that the studies that do purportedly show that cell phone usage causes an increased rate of accidents are all seriously flawed. For further edification, I have added some links to a very recent time-series study showing that polities that have enacted cell phone usage bans and have seen cell phone usage drop have not seen any reduction in either accident rates or fatalities.
While I don't have it to hand, there was once a study reported in a car magazine I used to read that said, essentially, that people have a 'risk constant', and, if you make one section of a highway safer, the total fatalities do not necessarily go down; they just shift elsewhere on the same highway. If you successfully ban cell phone usage, you make my life worse, but you don't reduce the risk of travelling on the highway at all. By the principle of liberty, we must conclude that banning cell phone usage is not warranted.