I was able to find a workaround that's almost good enough to be called a solution. It is possible to emulate a scroll wheel while holding down both the left and the right mouse button. They have to pressed simultaneously, but this should be easy enough on a laptop that allows you to press both of them with a single finger. Follow these steps to make it work.
- Open a terminal (Ctrl-Alt-T) and type "sudo apt-get install gpointing-device-settings". Enter your password when asked. gpointing-device-settings
- There should be a new utility called "Pointing devices". Since I use Gnome Classic, it's located under Applications -> System Tools -> Preferences, but you should be able to search for it in Unity.
- Select "Use middle button emulation" and select a short timeout, unless your laptop already has three buttons. This will trigger the "middle button" whenever you press both buttons at once.
- Select "Use wheel emulation" as well as vertical/horizontal scrolling to your liking.
- Select button 3. This tells the system to use the "middle button" you just created for scrolling.
- Adjust the timeout and inertia sliders for wheel emulation to the settings you find optimal.
If it takes to long for the "scrolling mode" to activate, you need to reduce the timeout. On the other hand, if scrolling is activated instead of middle clicking, you need to increase it. Select a value that suits you. I keep this one slightly to the left of the middle.
The inertia slider adjusts the scrolling speed. The more inertia, the slower your scrolling will be. For me, this slider is very close to the left end, and has to be adjusted very carefully.
That's it. Whenever you hold down both buttons, you should be able to scroll using the touchpad. As an added bonus you will get the middle button, which is good for a lot of things such as pasting text in the terminal and opening websites in new tabs.