Rails select_tag not holding the value rails

I'm trying to create simple dropdown mutiple dropdown from existing data I have model called dealers and it has city and state column , I'm trying to populate list of cities from state select from same through query. The issue is the select_tag :city is not holding the value, and when I hit continue button I'd want to post the value to my index in dealers controller. Can someone please correct me where I'm doing wrong, why isn't select_tag(:city) not holding the value it just resets to select city

class WelcomeController < ApplicationController
 def index
 @states= Dealer.select(:state).uniq.order('state ')  
 end  
end

 class DealersController < ApplicationController

def index  
@dealers = Dealer.dealers_by_city(params[:city])  
end

 def update_city_select
 @cities= Dealer.select(:city).uniq.where("state=?",params[:state]) 
 render :partial => "cities", :locals => { :cities => @cities }  
 end 
 end

---View---

 <%= form_tag "/dealers/index",:method => 'post',:id => 'dealer_search',:remote=> true do %>


               <%= select_tag(:state,options_for_select(@states.collect{|u|[u.state,u.state]}),
                  {prompt: "Select State",class: "span3 input-md main_select"})%><br>


                 <div id="selectcities">
                      <%= render :partial => 'dealers/cities'  %>


            <%= submit_tag "Continue",:class=>"btn btn-xlarge btn-purple"%>

<% end %>


 <script>
 jQuery(function($){
 $("#dealer_search").change(function() {
    var state = $('select#state :selected').val();

     if(state == "") state="0";

    jQuery.get('dealers/update_city_select/'+ state, function(data){

        $("#selectcities").html(data);
    })
    return false;
    })
  })
</script>

  <%= form_tag cityselect_path(:state),:method => 'post',:remote=> true do %>
   <% if !@cities.blank?%>
  <%= select_tag(:city,
           options_for_select(@cities.collect{|u|  [u.city,u.city]}),
        {prompt: "Select City",class: "span3 input-md main_select"})%>  
    <% end %>
  <% end %>


  --Routes--
  get 'dealers/update_city_select/:state', 
  :controller=>'dealers', :action => 'update_city_select', as: :cityselect