Workaround for lack of paper-dropdown

polymerHelper.coffee

bindPaperMenuButton = (selector = "paper-menu-button", unbindTargets = true) ->
  ###
  # Use a paper-menu-button and make the
  # .dropdown-label gain the selected value
  #
  # Reference:
  # https://github.com/polymerelements/paper-menu-button
  # https://elements.polymer-project.org/elements/paper-menu-button
  ###
  for dropdown in $(selector)
    menu = $(dropdown).find("paper-menu")
    if unbindTargets
      $(menu).unbind()
    do relabelSelectedItem = (target = menu, activeDropdown = dropdown) ->
      # A menu item has been selected!
      selectText = $(target).polymerSelected(null, true)
      # console.log("iron-select fired! We fetched '#{selectText}'")
      labelSpan = $(activeDropdown).find(".dropdown-label")
      $(labelSpan).text(selectText)
      $(target).polymerSelected()
    $(menu).on "iron-select", ->
      relabelSelectedItem this, dropdown
  false


jQuery.fn.polymerSelected = (setSelected = undefined, attrLookup = "attrForSelected") ->
  ###
  # See
  # https://elements.polymer-project.org/elements/paper-menu
  # https://elements.polymer-project.org/elements/paper-radio-group
  #
  # @param attrLookup is based on
  # https://elements.polymer-project.org/elements/iron-selector?active=Polymer.IronSelectableBehavior
  ###
  unless attrLookup is true
    attr = $(this).attr(attrLookup)
  else
    # If we pass the flag true, we get the label instead
    attr = true
  if setSelected?
    if not isBool(setSelected)
      try
        $(this).get(0).select(setSelected)
      catch e
        return false
    else
      $(this).parent().children().removeAttribute("aria-selected")
      $(this).parent().children().removeAttribute("active")
      $(this).parent().children().removeClass("iron-selected")
      $(this).prop("selected",setSelected)
      $(this).prop("active",setSelected)
      $(this).prop("aria-selected",setSelected)
      if setSelected is true
        $(this).addClass("iron-selected")
  else
    val = undefined
    try
      val = $(this).get(0).selected
      if isNumber(val) and not isNull(attr)
        itemSelector = $(this).find("paper-item")[toInt(val)]
        unless attr is true
          val = $(itemSelector).attr(attr)
        else
          # Fetch the label
          val = $(itemSelector).text()
    catch e
      return false
    if val is "null" or not val?
      val = undefined
    val


isEmpty = (str) -> not str or str.length is 0

isBlank = (str) -> not str or /^\s*$/.test(str)

isNull = (str) ->
  try
    if isEmpty(str) or isBlank(str) or not str?
      unless str is false or str is 0 then return true
  false

isNumber = (n) -> not isNaN(parseFloat(n)) and isFinite(n)

bindPaperMenuButton()

polymerHelper.js

// Generated by CoffeeScript 1.9.3
(function() {
  var bindPaperMenuButton, isBlank, isEmpty, isNull, isNumber;

  bindPaperMenuButton = function(selector, unbindTargets) {
    var dropdown, i, len, menu, ref, relabelSelectedItem;
    if (selector == null) {
      selector = "paper-menu-button";
    }
    if (unbindTargets == null) {
      unbindTargets = true;
    }

    /*
     * Use a paper-menu-button and make the
     * .dropdown-label gain the selected value
     *
     * Reference:
     * https://github.com/polymerelements/paper-menu-button
     * https://elements.polymer-project.org/elements/paper-menu-button
     */
    ref = $(selector);
    for (i = 0, len = ref.length; i < len; i++) {
      dropdown = ref[i];
      menu = $(dropdown).find("paper-menu");
      if (unbindTargets) {
        $(menu).unbind();
      }
      (relabelSelectedItem = function(target, activeDropdown) {
        var labelSpan, selectText;
        selectText = $(target).polymerSelected(null, true);
        labelSpan = $(activeDropdown).find(".dropdown-label");
        $(labelSpan).text(selectText);
        return $(target).polymerSelected();
      })(menu, dropdown);
      $(menu).on("iron-select", function() {
        return relabelSelectedItem(this, dropdown);
      });
    }
    return false;
  };

  jQuery.fn.polymerSelected = function(setSelected, attrLookup) {
    var attr, e, itemSelector, val;
    if (setSelected == null) {
      setSelected = void 0;
    }
    if (attrLookup == null) {
      attrLookup = "attrForSelected";
    }

    /*
     * See
     * https://elements.polymer-project.org/elements/paper-menu
     * https://elements.polymer-project.org/elements/paper-radio-group
     *
     * @param attrLookup is based on
     * https://elements.polymer-project.org/elements/iron-selector?active=Polymer.IronSelectableBehavior
     */
    if (attrLookup !== true) {
      attr = $(this).attr(attrLookup);
    } else {
      attr = true;
    }
    if (setSelected != null) {
      if (!isBool(setSelected)) {
        try {
          return $(this).get(0).select(setSelected);
        } catch (_error) {
          e = _error;
          return false;
        }
      } else {
        $(this).parent().children().removeAttribute("aria-selected");
        $(this).parent().children().removeAttribute("active");
        $(this).parent().children().removeClass("iron-selected");
        $(this).prop("selected", setSelected);
        $(this).prop("active", setSelected);
        $(this).prop("aria-selected", setSelected);
        if (setSelected === true) {
          return $(this).addClass("iron-selected");
        }
      }
    } else {
      val = void 0;
      try {
        val = $(this).get(0).selected;
        if (isNumber(val) && !isNull(attr)) {
          itemSelector = $(this).find("paper-item")[toInt(val)];
          if (attr !== true) {
            val = $(itemSelector).attr(attr);
          } else {
            val = $(itemSelector).text();
          }
        }
      } catch (_error) {
        e = _error;
        return false;
      }
      if (val === "null" || (val == null)) {
        val = void 0;
      }
      return val;
    }
  };

  isEmpty = function(str) {
    return !str || str.length === 0;
  };

  isBlank = function(str) {
    return !str || /^\s*$/.test(str);
  };

  isNull = function(str) {
    try {
      if (isEmpty(str) || isBlank(str) || (str == null)) {
        if (!(str === false || str === 0)) {
          return true;
        }
      }
    } catch (_error) {}
    return false;
  };

  isNumber = function(n) {
    return !isNaN(parseFloat(n)) && isFinite(n);
  };

  bindPaperMenuButton();

}).call(this);

sample.html

<!-- Sample HTML from SSARHerps.org -->
            <paper-menu-button>
              <paper-button class="dropdown-trigger"><iron-icon icon="icons:filter-list"></iron-icon><span id="filter-what" class="dropdown-label"></span></paper-button>
              <paper-menu label="Group" data-column="linnean_order" class="cndb-filter dropdown-content" id="linnean-order" name="type" attrForSelected="data-type" selected="0">
                <paper-item data-type="any">All</paper-item>
                <paper-item data-type="squamata">Non-Snake Lizards</paper-item>
                <paper-item data-type="serpentes">Snakes</paper-item>
                <paper-item data-type="testudines">Turtles</paper-item>
                <paper-item data-type="crocodylia">Crocodiles &amp; Alligators</paper-item>
                <paper-item data-type="caudata">Salamanders</paper-item>
                <paper-item data-type="anura">Frogs</paper-item>
                <paper-item data-type="gymnophiona">Caecilians</paper-item>
              </paper-menu>
            </paper-menu-button>