<li>
    <select name="names" id="names">
    <option value="">Constituency</option>
    <!-- populates the drop down with names -->
    <?php foreach ($cons as $constituency): ?>
    <option value="<?php htmlout($constituency['ids']); ?>">
    <?php htmlout($constituency['names']); ?>
    </option>
    <?php endforeach; ?>
    <?php if (isset($selectError)): ?>
    <p><?php htmlout($selectError); ?></p>
    <?php endif; ?>
    </select>
    </li>

    <li><input type="hidden" name="action" value="search"></li>
    <li><input type="submit" value="SEARCH" class="button search" id="jsbutton" disabled="disabled"></li>

$(document).ready(function() {

    if ($('#names').val() = '')
    {
        $('#jsbutton').attr('disabled', 'disabled');
    }
    else
    {
        $('#jsbutton').removeAttr('disabled');
    }
    });

try
      {
        $cons_result = $pdo->query("SELECT id, name
                               FROM constituency
                               ORDER BY name");
      }
      catch (PDOException $e)
      {
        $error = 'Error fetching constituencies from database!' . $e->getMessage();
        include 'error.html.php';
        exit();
      }


      foreach ($cons_result as $rows)
      {
        $cons[] = array('ids' => $rows['id'], 'names' => $rows['name']);
      }

      include 'searchform.html.php';
    }

$(document).ready(function() {
     $("#names").change(function () {
          var str = "";
          if ($("#names option:selected").val()=='')
            {

                $('#jsbutton').attr('disabled', 'disabled');
            }
            else
            {

                $('#jsbutton').removeAttr('disabled');
            }
        });
});

<select id="names">
    <option value=0>Please Select</option>
    <?php ($cons as $constituency) {...} ?>
</select>
<input id="jsbutton" type="submit" disabled />

$(function(){
    $('#names').change(function(e) {
        if ($(this).prop("selectedIndex") === 0)
        {
            $('#jsbutton').prop('disabled', true);
        }
        else
        {
            $('#jsbutton').prop('disabled', false);
        }
    });
});

$(document).ready(function() {
    $('#names').change(function() {
        if ($('#names').val() == '')
        {
            $('#jsbutton').attr('disabled', 'disabled');
        }
        else
        {
            $('#jsbutton').removeAttr('disabled');
        }
    }
});

<li>
<select name="names" id="names" onChange='editButton(this.value);'>
<option value="">Constituency</option>
<!-- populates the drop down with names -->
<?php foreach ($cons as $constituency): ?>
<option value="<?php htmlout($constituency['ids']); ?>">
<?php htmlout($constituency['names']); ?>
</option>
<?php endforeach; ?>
<?php if (isset($selectError)): ?>
<p><?php htmlout($selectError); ?></p>
<?php endif; ?>
</select>
</li>

<li><input type="hidden" name="action" value="search"></li>
<li><input type="submit" value="SEARCH" class="button search" id="jsbutton" disabled="disabled"></li>

<script type='text/javascript'>
function editButton(value){
if (value == '')
    {
        $('#jsbutton').attr('disabled', 'disabled');
    }
    else
    {
        $('#jsbutton').removeAttr('disabled');
    }
}
</script>

$('#names').val() =='' instead of $('#names').val() = ''