This is getting a bit crazy. I have been trying the code for hours now and no luck:
I had the same problem and the decision is in the connected libraries
I include in head tag this css
code.jquery.com/mobile/1.0a4.1/jquery.mobile-1.0a4.1.min.css
and this
code.jquery.com/mobile/1.0a4.1/jquery.mobile-1.0a4.1.min.js
and all works well!
looks like a direct copy paste from the link did you include jquery and jquery mobile ?
If you look at the source of the web page you can see it's in a form tag:
<form action="#" method="get">
So Adding this between the form tags would get the desired results: Live Example Link
<form action="#" method="get">
<div data-role="fieldcontain">
<label for="select-choice-1" class="select">Choose shipping method:</label>
<select name="select-choice-1" id="select-choice-1">
<option value="standard">Standard: 7 day</option>
<option value="rush">Rush: 3 days</option>
<option value="express">Express: next day</option>
<option value="overnight">Overnight</option>
</select>
</div>
</form>
Another problem it could be:
Try adding this tag to the dropdown: Live Example Link
data-native-menu="false"
I had this issue recently, and the accepted answer did not fix it for me. In the process of creating a question on it, I figured out the solution:
When using both jQuery UI and jQuery Mobile, UI must come before Mobile in your list of scripts.
I had this:
<script src="https://code.jquery.com/mobile/1.4.5/jquery.mobile-1.4.5.min.js"></script>
<script src="https://code.jquery.com/ui/1.11.4/jquery-ui.js"></script>
Which resulted in UI having precedence over my form elements, especially noticeable in select menus. I switched these statements, and the menus were enhanced by Mobile properly.