JSFiddle - React, Tailwind, and code Playground

HTML

<base href="https://polygit.org/*+:master/paper-dropdown-menu+:fix-light-flex/components/">
<link rel="import" href="polymer/polymer.html">
<link rel="import" href="paper-dropdown-menu/paper-dropdown-menu.html">
<link rel="import" href="paper-dropdown-menu/paper-dropdown-menu-light.html">
<link rel="import" href="paper-item/paper-item.html">
<link rel="import" href="paper-menu/paper-menu.html">

<style is="custom-style">
  paper-dropdown-menu,
  paper-dropdown-menu-light {
    --paper-font-subhead: {
      font-size: 40px;
      font-family: monospace;
    }
  }
</style>
<div>
  <div class="row">
    <div>
      pdm
    </div>
    <paper-dropdown-menu no-label-float>
      <paper-menu class="dropdown-content" selected="0">
        <paper-item>Foo</paper-item>
        <paper-item>Bar</paper-item>
      </paper-menu>
    </paper-dropdown-menu>
  </div>

  <div class="row">
    <div>
      pdm light patched
    </div>
    <paper-dropdown-menu-light no-label-float>
      <paper-menu class="dropdown-content" selected="0">
        <paper-item>Foo</paper-item>
        <paper-item>Bar</paper-item>
      </paper-menu>
    </paper-dropdown-menu-light>
  </div>
  
  <div class="row second">
    <div>
      pdm (flex)
    </div>
    <paper-dropdown-menu no-label-float>
      <paper-menu class="dropdown-content" selected="0">
        <paper-item>Foo</paper-item>
        <paper-item>Bar</paper-item>
      </paper-menu>
    </paper-dropdown-menu>
  </div>

  <div class="row second">
    <div>
      pdm-light patched (flex)
    </div>
    <paper-dropdown-menu-light no-label-float>
      <paper-menu class="dropdown-content" selected="0">
        <paper-item>Foo</paper-item>
        <paper-item>Bar</paper-item>
      </paper-menu>
    </paper-dropdown-menu-light>
  </div>

</div>

CSS

body {
  min-width: 800px;
}

body > div {
  display: flex;
  flex-direction: column;
}

div.row {
  display: flex;
  flex-direction: row;
}

div.row :first-child {
  flex-shrink: 0;
  flex-basis: 300px;
}

div.row.second :last-child {
  flex: 1;
}

JavaScript

Polymer({
  is: 'x-foo',
  properties: {},
  ready: function() {},
});