是否存在在数组之间进行选择的方法，该数组具有特定位置的最高值

the roadblock: using multiple nested arrays and wanting to select the array with the largest int in a specific position; in the selected array change another specific position's value.

psuedo code might look like this:

$array1 = array(2, 23, 7);
$array2 = array(2, 21, 7);

$Mutt = array($L, $P, $O, $array1)
$Jeff = array($L, $P, $O, $array2)

find array with max [3][1] {
('selected' [1]++)
}

in real life this might look like: Mutt ($Mutt) has the worked the most days this month ($Mutt [3][1]), he has earned an additional 'personal day' ($Mutt [1]).

I have tried to find a solution to this. I may be too new to understand how to word my search correctly, but I am having no luck.

I hope I have undestood well what you want:

Your arrays:

$array1 = array(2, 23, 7);
$array2 = array(2, 21, 7);

$Mutt = array($L, $P, $O, $array1);
$Jeff = array($L, $P, $O, $array2);

Creating a new array $people which contains $Mutt and $Jeff (passed by reference).

$people=array(&$Mutt,&$Jeff);

Creating function findMaxIndex, which returns the index for which $people[that index] is the array with maximum value at the position that we want.

Its arguments are:

$arr, the array which contains the arrays we want to compare (in this case, $people)
$pos1 and $pos2, which are the indexes we want to compare

So... we will compare

$arr[0][$pos1][$pos2]
$arr[1][$pos1][$pos2]
...
$arr[count($arr)-1][$pos1][$pos2]

This function works like this:

It creates the array $max, where $max[0] is the index of $arr with the maximum value (among the arrays we have examined until that moment), and $max[1] is that value.
It iterates through all $arr
If it finds that current value ($arr[$i][$pos1][$pos2]) is greater than the maximum value, $max is updated and becomes array($i,$arr[$i][$pos1][$pos2]).
Finally, it returns $max[0], which is the index for which $people[that index] is the array with maximum value at the position that we want.

The function is:

function findMaxIndex($arr,$pos1,$pos2){
    $max=array(0,$arr[0][$pos1][$pos2]);
    for($i=1;$i<count($arr);$i++){
        if($arr[$i][$pos1][$pos2]>$max[1]){
            $max=array($i,$arr[$i][$pos1][$pos2]);
        }
    }
    return $max[0];
}

Then we call the function...

$maxIndex=findMaxIndex($people,3,1);

... which gives 0, so the array with maximum value is $people[0] ($Mutt)

Finally, we increase that array:

$people[$maxIndex][1]++;

$Mutt and $Jeff are modified too because we passed them by reference.

In short,

$array1 = array(2, 23, 7);
$array2 = array(2, 21, 7);
$Mutt = array($L, $P, $O, $array1);
$Jeff = array($L, $P, $O, $array2);
$people=array(&$Mutt,&$Jeff);
function findMaxIndex($arr,$pos1,$pos2){
    $max=array(0,$arr[0][$pos1][$pos2]);
    for($i=1;$i<count($arr);$i++){
        if($arr[$i][$pos1][$pos2]>$max[1]){
            $max=array($i,$arr[$i][$pos1][$pos2]);
        }
    }
    return $max[0];
}
$maxIndex=findMaxIndex($people,3,1);//gives `0` -> Max is `$people[0]`
$people[$maxIndex][1]++;

==============================================

And if you want multiple indexes in case of tie (changes in bold):

Your arrays:

$array1 = array(2, 23, 7);
$array2 = array(2, 21, 7);

$Mutt = array($L, $P, $O, $array1);
$Jeff = array($L, $P, $O, $array2);

Creating a new array $people which contains $Mutt and $Jeff

$people=array(&$Mutt,&$Jeff);

Creating function findMaxIndex, which returns the array which contains the indexes for which $people[that index] is the array with maximum value at the position that we want.