JSFiddle - React, Tailwind, and code Playground

HTML

<script>Polymer = {dom: 'shadow'};</script>
<base href="https://polygit.org/*+:master/components/">
<link rel="import" href="polymer/polymer.html">
<link rel="import" href="paper-dropdown-menu/paper-dropdown-menu.html">
<link rel="import" href="paper-item/paper-item.html">
<link rel="import" href="paper-listbox/paper-listbox.html">
<link rel="import" href="paper-menu/paper-menu.html">

<dom-module id="x-foo">
  <template>
    <style>
      :host {
        display: flex;
        flex-direction: column;
      }
      :host > paper-menu, paper-listbox {
        height: 200px;
        overflow: scroll;
      }
    </style>
    <h4>regular paper-menu</h4>
    <paper-menu>
      <template is="dom-repeat" items="{{items}}">
        <paper-item>Item [[item]]</paper-item>
      </template> 
    </paper-menu>
    
    <h4>paper-listbox inside a paper-dropdown-menu</h4>
    <paper-dropdown-menu>
      <paper-listbox class="dropdown-content">
        <template is="dom-repeat" items="{{items}}">
          <paper-item>Item [[item]]</paper-item>
        </template> 
      </paper-listbox>
    </paper-dropdown-menu>
    
    <h4>native select</h4>
    <select size="10">
      <template is="dom-repeat" items="{{items}}">
        <option>Item [[item]]</option>
      </template> 
    </select>
  </template>
</dom-module>

<x-foo></x-foo>

JavaScript

Polymer({
  is: 'x-foo',
  properties: {
    items: {
      type: Array,
      value: function() {
        var arr = [];
        for (var i = 0; i < 50; i++)
          arr.push(i);
        return arr;
      }
    }
  },
});