Setting object property to the result of a sort without sorting

I have an array of objects, each with a property called sort_order that I need to change based on another property score but the catch is I can't actually change the order of the array which means no Array.sort().

Basically I want this:

function compare(a,b){
    return b.score - a.score;
}
scores.sort(compare);

but instead of actually sorting I want to set a.sort_order and b.sort_order accordingly.