def order_preserving_single_index_shift(arr, index, new_index):
    """Moves a list element to a new index while preserving order.

    Parameters
    ---------
    arr : list
        The list in which to shift an element.
    index : int
        The index of the element to shift.
    new_index : int
        The index to which to shift the element.

    Returns
    -------
    list
        The list with the element shifted.

    Example
    -------
    >>> arr = ['a', 'b', 'c', 'd']
    >>> order_preserving_single_index_shift(arr, 2, 0)
    ['c', 'a', 'b', 'd']
    >>> order_preserving_single_index_shift(arr, 2, 3)
    ['a', 'b', 'd', 'c']
    """
    if new_index == 0:
        return [arr[index]] + arr[0:index] + arr[index + 1:]
    if new_index == len(arr) - 1:
        return arr[0:index] + arr[index + 1:] + [arr[index]]
    if index < new_index:
        return arr[0:index] + arr[index + 1:new_index + 1] + [arr[index]
            ] + arr[new_index + 1:]
    if new_index <= index:
        return arr[0:new_index] + [arr[index]] + arr[new_index:index] + arr[
            index + 1:]
