Select menu text-overflow fade

Question

(This is for particular styling of the option Select menu, not the overall styling/incapabilities of styling select menus)

I'm wondering how I can fade the text out on the overflow of the selected option in a select menu. For example, in the JSFiddle, where "Mercedes" is cut at the moment, it would fade out to the edge using a CSS gradient background style.

This is a similar answer, but I can't seem to get to work on select menu, maybe it's not possible?

     <div class="selectbox">
      <select>
        <option value="volvo">Volvo</option>
        <option value="saab">Saab</option>
        <option value="mercedes">Mercedes</option>
        <option value="audi">Audi</option>
      </select>
    </div>

CSS:

.selectbox {
    border: 1px solid #ccc;
    width: 50px;
    border-radius: 3px;
            background: #fafafa no-repeat 90% 50%;

}
.selectbox select:after {
    content: '';
    position: absolute;
    top: 0;
    right: 0;
    width: 30%;
    height: 100%;
  position: absolute;
  right: 0;
  bottom: 0;
  width: 100%;
  height: 50%;
  background: -webkit-linear-gradient(left, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 1) 100%);
  background-image: -moz-linear-gradient(left, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 1) 100%);
  background-image: -o-linear-gradient(left, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 1) 100%);
  background-image: linear-gradient(left, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 1) 100%);
  background-image: -ms-linear-gradient(left, rgba(255, 255, 255, 0) 0%, rgba(255, 255, 255, 1) 100%);    pointer-events: none;
  }

.selectbox select {
    padding: 5px 8px;
    width: 100%;
    border: none;
    box-shadow: none;
    background: transparent;
    background-image: none;
    -webkit-appearance: none;
        background: #fafafa no-repeat 90% 50%;


}

.selectbox select:focus {
    outline: none;
}

Here's the attempt on: https://jsfiddle.net/nick_1002/7y5uezs5/

Any help is greatly appreciated :)