I thinks find to solve this problem i have test in ie, FF, chrome and Edge.
HTML
<select id="selecttest">
    <option value="1">one</option>
    <option value="2">two</option>
    <option value="3">free</option>
    <option value="4">four</option>
    <option value="5">five</option>
    <option value="6">six</option>
    <option value="7">seven</option>
    <option value="8">height</option>
    <option value="9">nine</option>
    <option value="10">ten</option>
    <option value="11">eleven</option>
    <option value="12">twelve</option>
    <option value="13">thirdteen</option>
</select>
<input type="button" value="testing" id="MyButton"/>
JQUERY
$('#MyButton').on("click",function(){
    $("#selecttest").attr("size", 8);
    $("#selecttest").css("position","fixed");
    $('#MyButton').css("margin-left", $("#selecttest").width() + 5);});
$('#selecttest').on("change",function(){
    $("#selecttest").attr("size", 1);});
jsfiddle test this