Although you requested shorter, sometimes I think clearer is better. Most of the other answers include extra arrays or triples, which are totally fine and 100% valid, but I don't think the intent of the code is that obvious. For me, I would keep the if and just use and -- for incrementing and decrementing. I think the "business rules" are pretty obvious and the code reads cleanly.

Again, not exactly what you asked for, just my two cents.

if ('up' === $vote) {
    $voteModel['up']++;
    $voteModel['down']--;
} else {
    $voteModel['up']--;
    $voteModel['down']++;
}

Solution 1:

$arg = $vote === 'up' ? [1,-1] : [-1,1];
$voteModel['up'] += $arg[0];
$voteModel['down'] += $arg[1];

Solution 2:

$voteModel['up'] += ($vote === 'up' ? 1 : -1);
$voteModel['down'] += ($vote !== 'up' ? 1 : -1);

Solution 3 (if "up" in $voteModel is index 1 and "down" is index 0):

$voteModel[$vote==='up']++;
$voteModel[$vote==='down']--;

Solution 3b (if we want to preserve the associated key):

$arr = ['down','up'];
$voteModel[$arr[$vote==='up']]++;
$voteModel[$arr[$vote==='down']]--;