No submit button value is serialized since the form was not submitted using a button.
Since you only have a single button in your form, the simplest solution is to remove its
name
attribute, and move the value to a hidden input.
<form class="upVote" action="../inc/handlers/up-vote.php" method="post">
<input type="hidden" name="plus" value="foo" />
<button type="submit">button</button>
</form>