You want to do some AJAX!
Using something called the XMLHTTPRequest object, you can request data from a different location. Using the same concept, you can send data to a php page behind the scenes.
Set up your php page to receive your "form data". Using the XMLHTTPRequest object, you can have your javascript send a URL encoded with your data to your PHP page. When your PHP has processed the data, have it return a success value to your XMLHTTPRequest object. Depending on the value, you can execute some javascript to tell your user his vote was received.
There's a little more to this than I have time for, but check out the following link:
http://developer.apple.com/internet/webcontent/xmlhttpreq.html
I found the following book, quite useful: AJAX HACKS: Tips & Tools for Creating Responsive Web Sites (O'Reilly)
http://www.oreilly.com/catalog/ajaxhks/
The Data Analyst
http://www.squidoo.com/thedataanalyst