MD Settings: Search page, switching paper-dropdown-menu to native select.

chrome/browser/resources/settings/search_page/search_page.html

 <link rel="import" href="chrome://resources/html/polymer.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/neon-animation/neon-animatable.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-button/paper-button.html">
-<link rel="import" href="chrome://resources/polymer/v1_0/paper-dropdown-menu/paper-dropdown-menu-light.html">
-<link rel="import" href="chrome://resources/polymer/v1_0/paper-listbox/paper-listbox.html">
 <link rel="import" href="/route.html">
 <link rel="import" href="/search_engines_page/search_engines_page.html">
 <link rel="import" href="/search_engines_page/search_engines_browser_proxy.html">
 <link rel="import" href="/settings_page/settings_animated_pages.html">
 <link rel="import" href="/settings_page/settings_subpage.html">
 <link rel="import" href="/settings_shared_css.html">
+<link rel="import" href="/select_css.html">
 
 <dom-module id="settings-search-page">
   <template>
-    <style include="settings-shared">
-    </style>
+    <style include="settings-shared select"></style>
     <settings-animated-pages id="pages" section="search">
       <neon-animatable route-path="default">
         <div class="settings-box first">
           <p class="start">$i18n{searchExplanation}</p>
-          <paper-dropdown-menu-light vertical-align="auto" no-label-float>
-            <paper-listbox class="dropdown-content"
-                selected="[[getSelectedSearchEngineIndex_(searchEngines_)]]"
-                on-iron-select="onIronSelect_">
+          <div>
+            <select on-change="onChange_">
               <template is="dom-repeat" items="[[searchEngines_]]">
-                <button class="dropdown-item" role="option">
+                <option class="dropdown-item" role="option" selected$="[[item.default]]">

[dpapad, 2016/09/29 19:16:23]

We can probably remove both the class and the role now. I believe that the class
was only used for styling and the role should just work given the existence of
<option>

                   [[item.name]]
-                </button>
+                </option>
               </template>
-            </paper-listbox>
-          </paper-dropdown-menu-light>
+            </select>
+            <span class="select-underline"></span>
+          </div>
         </div>
         <div id="subpage-trigger" class="settings-box">
           <paper-button on-tap="onManageSearchEnginesTap_"
               class="primary-button">
             $i18n{searchEnginesManage}
           </paper-button>
         </div>
       </neon-animatable>
       <template is="dom-if" route-path="/searchEngines">
         <settings-subpage
             associated-control="[[$$('#subpage-trigger')]]"
             page-title="$i18n{searchEnginesManage}">
           <settings-search-engines-page></settings-search-engines-page>
         </settings-subpage>
       </template>
     </settings-animated-pages>
   </template>
   <script src="search_page.js"></script>
 </dom-module>