How to write a PHP ternary operator

A Ternary is not a good solution for what you want. It will not be readable in your code, and there are much better solutions available.

Why not use an array lookup "map" or "dictionary", like so:

$vocations = array(
    1 => "Sorcerer",
    2 => "Druid",
    3 => "Paladin",
    ...
);

echo $vocations[$result->vocation];

A ternary for this application would end up looking like this:

echo($result->group_id == 1 ? "Player" : ($result->group_id == 2 ? "Gamemaster" : ($result->group_id == 3 ? "God" : "unknown")));

Why is this bad? Because - as a single long line, you would get no valid debugging information if something were to go wrong here, the length makes it difficult to read, plus the nesting of the multiple ternaries just feels odd.

A Standard Ternary is simple, easy to read, and would look like this:

$value = ($condition) ? 'Truthy Value' : 'Falsey Value';

or

echo ($some_condition) ? 'The condition is true!' : 'The condition is false.';

A ternary is really just a convenient / shorter way to write a simple if else statement. The above sample ternary is the same as:

if ($some_condition) {
    echo 'The condition is true!';
} else {
    echo 'The condition is false!';
}

However, a ternary for a complex logic quickly becomes unreadable, and is no longer worth the brevity.

echo($result->group_id == 1 ? "Player" : ($result->group_id == 2 ? "Gamemaster" : ($result->group_id == 3 ? "God" : "unknown")));

Even with some attentive formatting to spread it over multiple lines, it's not very clear:

echo($result->group_id == 1 
    ? "Player" 
    : ($result->group_id == 2 
        ? "Gamemaster" 
        : ($result->group_id == 3 
            ? "God" 
            : "unknown")));

Since this would be a common task I would suggest wrapping a switch/case inside of a function call.

function getVocationName($vocation){
    switch($vocation){
        case 1: return "Sorcerer";
        case 2: return 'Druid';
        case 3: return 'Paladin';
        case 4: return 'Knight';
        case 5: return 'Master Sorcerer';
        case 6: return 'Elder Druid';
        case 7: return 'Royal Paladin';
        default: return 'Elite Knight';
    }
}

echo getVocationName($result->vocation);