You can use the below function that will look for the first selected element in your list, and will scroll the select box to it.

Make sure you call the function when you already have the selections loaded, usually on window.onload event, but if you're populating the selections with ajax call, the function needs to be called respectively (once the selections are already in place)

// this is how you call the function, using the ID ("s") in your example:
window.onload = function(){
 scrollToSelected( "s" )
}

function scrollToSelected( select_id ) {
  var select = document.getElementById( select_id );
  var opts = select.getElementsByTagName('option');
  for ( var j = opts.length -1; j > 0; --j ) {
    if ( opts.item(j).selected == true ) {
      select.scrollTop = j * opts.item(j).offsetHeight;
      return;
    } 
  }
}

With the following line you can set the exact scroll position:

select.scrollTop = j * opts.item(j).offsetHeight;

... the above will attempt to scroll until the selected will be in the top of the list.

Thanks for your advice.

It seems that I cannot post code in a comment, so I will need to put this here. What seems to work is height: 20px; in the CSS for the option tag and the following Javascript:

 var select = document.getElementById(select_id);
    if (!select) console.error("no " + select_id);
    var opts = select.getElementsByTagName('option');
    var j = select.selectedIndex;
    if (j == -1) return;
    select.scrollTop = j * 20;

I'm getting 0 for the option's offsetHeight but hard coding a value as above seems to work.