...Well, if the answer is "yes", or maybe you want a drop-down arrow that appears the same in each browser (including the old ones), here there is an easy trick. For these browser, it is easy to set the same background image for the drop-down in order to have the same arrow. The appearance rules are set to none to reset browsers default ones, if you want to have the same aspect for each arrow, you should keep them in place. The background rules in the examples are set with SVG inline images that represent different arrows. They are positioned 98% from left to keep some margin to the right border (you can easily modify the position as you wish).