Hello I am working on a voting script.

So far I have this placed in a PHP while loop.

Code:
jQuery("#up a").click(function () {
    $.ajax({
    type: "POST",
    url: "vote.php?up=<? echo  $row['post_id']; ?>",
    
    }); 
});

$row['vote_count'] // Displays the number of votes
When a user clicks the button it processes the vote.php page and adds a vote to the database. How can I use jQuery to simply increment the $row['vote_count'] result by +1 without refreshing the page.