Lol I dunno why I'm still looking at this.
Ok the input for the radio button for the first option is:
<input id="PDI_answer37166779" type="radio" value="37166779" name="PDI_answer">
On the page there's a hidden field:
<input type="hidden" value="413" name="pz">
The vote button also has some JSON in it:
<a class="btn btn-primary btn-large vote-button" data-vote="{"id":8170848,"o":"0","b":"1","m":"0","at":" 20","t":77954,"v":0,"e":604800,"n":"93b0bc3dbb8a69 9bf87ed9e90814b60d"}" style="cursor
ointer;">Vote</a>
And from what I can tell the vote URL that is generated is (combined with the related JSON from that particular page view):
{"id":8170848,"o":"0","b":"1","m":"0","at":"20","t ":74472,"v":0,"e":604800,"n":"6b06da420e9913271bc8 ed630b379935"}
/vote.php?va=20&pt=0&r=1&p=8170848&a=37166779%2C&o= &t=74472&token=6b06da420e9913271bc8ed630b379935&pz =137
{"id":8170848,"o":"0","b":"1","m":"0","at":"20","t ":77954,"v":0,"e":604800,"n":"93b0bc3dbb8a699bf87e d9e90814b60d"}
"/vote.php?va=20&pt=0&r=1&p=8170848&a=37166779%2C&o= &t=77954&token=93b0bc3dbb8a699bf87ed9e90814b60d&pz =413"
So in the URL to submit a vote, looks like "p" is the poll ID, "a" is the ID of the option to vote with (37166779). "t" looks like some kind of timestamp, which is in the JSON in the tag of the vote button. No idea what "e" is but doesn't seem to change. The token is a random number for each page refresh (a nonce it's called), so one can't just submit URLs without getting a new random number each time. "pz" is the number from the hidden field.
Enough there to write a script to get a page, scrape it for the necessary values, then GET/POST or whatever to the vote.php URL.