What is the difference between this.click() and $(this).click() ?

Answer 1

$(this) contains a jQuery wrapper (with lots of functions) whereas this is solely the DOM object.

Answer 2

The fact that counter is going up gave me the clue that there is a link between checked attribute, which you are using, and firing the click event manually.

I searched Google for 'jquery checkbox click event raise' and found this link, where author faces the exact same problem and the workaround he used.

http://www.bennadel.com/blog/1525-jQuery-s-Event-Triggering-Order-Of-Default-Behavior-And-triggerHandler-.htm

On a side note, I think you can simplify your code further:

$j('input[type=checkbox].vote_item').click( 
function() 
{
    var maxNumberOfChoices = 5;

    //get number of checked checkboxes. 
    var currentCheckedCount = $j('input[type=checkbox].vote_item :checked');

    if(currentCheckedCount > maxNumberOfChoices)
    {
        //It's useful if you show how many choices user can make. :)
        alert('You can only select maximum ' + maxNumberOfChoices + ' checkboxes.');
        return false;
    }

    return true;
});

Answer 3

this.click() calls the browser DOM method click().

$(this).click() calls the jQuery method click(), which does more than just call the browser method: see the implementation of the function trigger for details.