CascadingDropDown onchange handler

Question

Is it possible to use an jQuery change() handler with an ASP.NET AJAX CascadingDropDown? I'd like to change the value of another dropdown on the page, which is unrelated to the cascading behavior. The following never executes:

$('#<%= ddlFromCompetition.ClientID %>').change(function() {
  $('#<%= ddlToCompetition.ClientID %>').value = $('#<%= ddlFromCompetition.ClientID %>').value;
});

which produces the following at runtime:

$('#ctl00_c1_ddlFromCompetition').change(function() {
  $('#ctl00_c1_ddlToCompetition').value = $('#ctl00_c1_ddlFromCompetition').value;
});