Best How To :

There are a number of problems in your code, but the one that causes the actual problems you're having is the fact that your function pie does not increment the values you fetched from the DB, that's done outside of the function, but the incremented values aren't used there:

function pie()
{
    //this query was already performed, pass the result resource to this function, don't re-run the query
    $data = mysql_query("SELECT * FROM votes") or die(mysql_error()); //google or die must die
    $result = mysql_fetch_array($data);//mysql is deprecated
    //array keys need to be quoted
    $total  = $result[partijA] + $result[partijB] + $result[partijC] +      $result[partijD];
    $one    = round(360 * $result[partijA] / $total);
    $two    = round(360 * $result[partijB] / $total);
    $per1   = round($result[partijA] / $total * 100);
    $per2   = round($result[partijB] / $total * 100);
    $per3   = round($result[partijC] / $total * 100);
    $per4   = round($result[partijD] / $total * 100);
    //functions return, they don't echo
    echo "<img src=vote_pie.php?one=" . $one . "&two=" . $two . "><br/>";
    Echo "<font color=000000>Partij A</font> = $result[partijA] votes = $per1 <br /> 
         <font color=000000>Partij B</font> = $result[partijB] votes = $per2 <br />
         <font color=000000>Partij C</font> = $result[partijC] votes =  $per3 <br /> 
         <font color=000000>Partij D</font> = $result[partijD] votes = $per4 <br />";
}

I've taken the liberty of adding some comments to point out several issues with the code.

Just remove the code that queries and increments outside of the pie function, and have your function do all of the work. Pass it the values it needs (ie $_GET, and have it return the result, instead of echoing it).
I'd rewrite the function to take arguments like so (not going into not using mysql at this point):

function getPie(array $params, $connection)
{
    //added limit 1, seeing as you're only processing the first result
    $result = mysql_query($connection, 'SELECT * from votes LIMIT 1');
    $row = mysql_fetch_assoc($result);
    if (isset($params['a'])) {
        $row['partijA'] += 1;
    } else if (isset($params['b'])) {
        $row['partijB'] += 1;
    } //add more else's for all parties
    $percentages = [];//array
    foreach ($row as $key => $val) {
        $percentages[$key] = round(($val/$total) * 100);
    }
    $total = array_sum($row);//total of all votes
    $markup = '<img src=vote_pie.php?one=' .
      $percentages['partijA']*360 . '&two=' . $percentages['partijB']*360 . '><br>';
    foreach ($percentages as $k => $perc) {
        $markup .= '<font color=000000>Partij ' . str_replace('partij', $k) . '</font> = '.
            $row[$key] . ' votes = ' . $perc . '<br>';
    }
    return $markup;
}

Then call this function like so:

if ($_GET) {//if a get form was submitted
    echo getPie($_GET, $db);//where $db holds the mysql resource
}

That's just a quick-fix, though... there's still a long way to go...

What I changed:

A quick canter through the actual changes I've made:

• Passing arguments to the function: the function now takes 2 arguments, an array (the $_GET values in this case), and the db connection to use.
• Loops instead of repetition: instead of repeating round($resutl['key']/total*100), I've used a loop, so I only have to write this statement once, and have it applied to all values
• use an array for the percentages: Instead of assigning the percentage for each party to a new variable, I've opted to use an array instead. This keeps data that belongs together, well... together
• Loops to create markup: Though I find stringing together markup bad practice, I've noticed most of the HTML is actually identical, so instead of hard-coding everything, I simply iterate over either the $row or $percentages array (they both have the same keys), and fill in the specific values. This also means that I can safely add a party without having to change the code that creates markup