* Ensure that your changes are made to the Mint-X theme. You need access to the theme selector. Click on the Linux button (bottom left hand corner) and click on Settings. In the right hand menu pane click on Appearance (with the jacket and tie icon). This shows the theme selector when you pick the first tab, Style (which is the default tab). When you click on a theme it is immediately selected. There is no need to logout, reboot, or anything else. On selecting a theme the theme config files are read and processed. Therefore when you edit the theme files, use the selector to pick any theme *other* than Mint-X, then click on Mint-X again to pick up your changes.
* As root, edit the theme files. These are found under /usr/share/themes, so for Mint-X the directory is /usr/share/themes/Mint-X. There are sub-directories for gtk-2.0 and gtk-3.0. My edits were done to gtk-2.0. The file there is called gtkrc. Make a backup copy of the file first. Ensure your file contains the following:
GtkScrollbar::has-backward-stepper = 1
GtkScrollbar::has-forward-stepper = 1
GtkScrollbar::stepper_size = 18
GtkScrollbar::min-slider-length = 30
GtkScrollbar::slider-width = 18
GtkScrollbar::trough-border = 1
GtkScrollbar::activate-slider = 1
The crucial line turns out to be:
GtkScrollbar::stepper-size = 18
Without that line, no scroll bar arrows.
I found this tip on Linux Questions at http://www.linuxquestions.org/questions/linux-mint-84/question-how-to-enable-scrollbar-arrow-buttons-in-linux-mint-v17-3-a-4175580868/.