Not too sure if the event was properly bind. It might be,
showTab( select.val() );
happens once at the start/load of the page and then never occurs again. Debugging would have made it clear.
Since you want this behaviour on every selection option change, you can try in other way to verify.
Something like following should do:
<form>
<p>
<select id="dropdown" name="dropdown" onchange="showTab();">
<option value="Pub-Chains" selected="selected"> Pub Chains </option>
<option value="Councils">Councils </option>
<option value="Property">Property </option>
<option value="Various">Various </option>
<option value="Universitys">Universitys </option>
</select>
</p>
<div id="Pubs-Chains">
<div id="Councils">
<div id="Property">
<div id="Various">
</form>
JS:
<script>
function showTab( ) {
var select = $( '#dropdown' );
$( 'div' ).not( select.val()).hide();
$( name ).show();
}
</script>