I am finding when I style elements (specifically, with background: transparent), the arrow is missing in Safari on iOS. Have any of you experienced this or know why it's hiding the browser chrome? Can I use conditional statements to apply CSS just for Safari on iOS (without JS)?

The device is running iOS 6.1.2.

here is a screenshot on Safari in iOS (iPad2):

Here is a screenshot on Safari (desktop, Windows 7, same for all other desktop browsers):

CSS:

select.choose_state,
select.choose_state option {
    background: transparent;
}
select.choose_state {
    border: 1px solid #000;
    -webkit-appearance: none;
    -webkit-border-radius: 0px;
    outline: none;

    float: right;
    position: relative;
    top: 35px;
    margin-right: 15px;
    font-size: 1.4em;
}

HTML:

<select name="state_select" id="state_select" class="choose_state" size="1">[...]</select>