The magento custom sorting functionality is not working

Question

I am creating a Magento module to add a sorting option of a bestseller on the category page. For doing so I have to override few classes in the core. In the beginning, I have created config.xml file. It is as below

<config>
    <modules>
        <Example_Catalog>
            <version>0.1.0</version>
        </Example_Catalog>
    </modules>
    <global>
        <blocks>
            <catalog>
                <rewrite>
                    <product_list_toolbar>Example_Catalog_Block_Product_List_Toolbar</product_list_toolbar>
                </rewrite>
            </catalog>
        </blocks>
        <models>
            <catalog>
                <rewrite>
                    <config>Example_Catalog_Model_Config</config>
                </rewrite>
            </catalog>
            <catalog_resource>
                <rewrite>
                    <product_collection>Example_Catalog_Model_Resource_Product_Collection</product_collection>
                </rewrite>
            </catalog_resource>
        </models>
    </global>
</config>

As per the config file, the overriding of toolbar under blocks class is as below

class Example_Catalog_Block_Product_List_Toolbar extends Mage_Catalog_Block_Product_List_Toolbar
{
    public function setCollection($collection)
    {
        parent::setCollection($collection);
        if ($this->getCurrentOrder()) { 
            if($this->getCurrentOrder() == 'qty_ordered') {
                $this->getCollection()->getSelect()
                     ->joinLeft(
                            array('sfoi' => $collection->getResource()->getTable('sales/order_item')),
                             'e.entity_id = sfoi.product_id',
                             array('qty_ordered' => 'SUM(sfoi.qty_ordered)')
                         )
                     ->group('e.entity_id')
                     ->order('qty_ordered ' . $this->getCurrentDirection());

            } else {
                $this->getCollection()
                     ->setOrder($this->getCurrentOrder(), $this->getCurrentDirection())->getSelect();
            }
        }

        return $this;
    }
}

for adding the option in the sorting drop-down, in the category page, in the config.php file is as below

<?php class Example_Catalog_Model_Config extends Mage_Catalog_Model_Config
{
    public function getAttributeUsedForSortByArray()
    {
        return array_merge(
            parent::getAttributeUsedForSortByArray(),
            array('qty_ordered' => Mage::helper('catalog')->__('Sold quantity'))
        );
    }
}

The overriding of collection class in collection.php file is as below

<?php
class Example_Catalog_Model_Resource_Product_Collection extends Mage_Catalog_Model_Resource_Product_Collection
{
    protected function _getSelectCountSql($select = null, $resetLeftJoins = true)
    {
       $this->_renderFilters();
       $countSelect = (is_null($select)) ?
           $this->_getClearSelect() :
           $this->_buildClearSelect($select);

       if(count($countSelect->getPart(Zend_Db_Select::GROUP)) > 0) {
           $countSelect->reset(Zend_Db_Select::GROUP);
       }

       $countSelect->columns('COUNT(DISTINCT e.entity_id)');
       if ($resetLeftJoins) {
           $countSelect->resetJoinLeft();
       }
       return $countSelect;
    }
}

The module has been created and I can see the option in the drop-down, but when I click on the Sold quantity option, the Toolbar class that I have overridden has been loaded. But the setCollection method under the toolbar class in not being called at all and the default sorting is happening. Kindly let me know what should I do to make this work properly.