JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://netdna.bootstrapcdn.com/twitter-bootstrap/2.3.0/css/bootstrap-combined.min.css">
<script src="http://netdna.bootstrapcdn.com/twitter-bootstrap/2.3.0/js/bootstrap.min.js"></script>
<script src="http://silviomoreto.github.com/bootstrap-select/javascripts/bootstrap-select.js"></script>
<link rel="stylesheet" href="http://silviomoreto.github.com/bootstrap-select/stylesheets/bootstrap-select.css">
<select id="chose_something" class="selectpicker span6" multiple>
      <option value="1">Mustard</option>
      <option value="2" selected="selected">Ketchup</option>
      <option value="3">Relish</option>
</select>

<select id="chose_something_other" class="span3">
      <option value="1">Mustard</option>
      <option value="2" selected="selected">Ketchup</option>
      <option value="3">Relish</option>
</select>

<button type="button" id="chose_something_else">choose</button>

JavaScript

$('.selectpicker').selectpicker();

$("#chose_something_else").on('click', function(){
    $("#chose_something").val('3');
    $("#chose_something_other").val('3');
});