Simple AJAX poll voting system with Laravel

Question

I'm creating a simple poll voting script with Laravel, so far so good... but I get stuck when rendering the appropiate view without reloading the page. It's a simple problem, but I can't get it to work:

This is my route/controller code:

Route::post('poll/vote', function() {
    $poll = Poll::findOrFail(Input::get('id'));

    $pollOption = PollOption::findOrFail(Input::get('option_id'));
    $pollOption->increment('votes');

    $cookie = Cookie::make('poll_vote_' . $poll->id, true); //User voted on this poll, create a cookie
    $view = View::make('includes.poll', ['poll' => $poll])->render();

    $response = Response::json(['view' => $view]);
    $response->headers->setCookie($cookie);
    return $response;
});

The jQuery (AJAX), which is not so importants because it works perfectly:

$('.poll-option').click(function(e) {
    e.preventDefault();
    var form = $(this).parents('form'),
        url = form.attr('action');

    $.ajax({
        type: 'POST',
        url: url,
        data: form.serialize(),
        dataType: 'json'
    }).done(function(view) {
        $('#poll .content').html(view['poll']).find('.loading').remove();
    }).fail(function() {
        alert('Er is iets fout gegaan tijdens het antwoorden van de poll');
    });
});

And then there's my view

<div class="question">{{{ $poll->question }}}</div>
@if(Cookie::has('poll_vote_' . $poll->id))
    <ul class="list small votes">
    @foreach($poll->options as $option)
        <li>
            <span class="light">{{ $option->getVotePercentage() }}</span> {{{ $option->title }}}
            <div class="percentage-bar-container">
                <div class="percentage-bar" style="width: {{ $option->getVotePercentage() }}"></div>
            </div>
        </li>
    @endforeach
    </ul>
@else
    <ul class="list small options">
    {{ Form::open(['url' => 'poll/vote']) }}
        {{ Form::hidden('id', $poll->id) }}
        @foreach($poll->options as $option)
            <li>{{ Form::radio('option_id', $option->id, null, ['class' => 'poll-option']) }} {{{ $option->title }}}</li>
        @endforeach
    {{ Form::close() }}
    </ul>
@endif

In the view I check whether the cookie is set. If so, then display the votes (results), otherwise display the options that can be voted on. Now if a user votes on an option, the view still shows the options because the page isn't refreshed (so the Cookie isn't set yet). How can I fix this problem or create a workaround?

Thanks in advance!