def compute_cumulative_mean_for_raters(df_scores, rater_ids):
    """
    Compute cumulative average of given rater's scores.

    This function computes the cumulative average of scores
    assigned by the raters identified by the given list of
    ``rater_ids``. The cumulative average is computed by
    adding one rater at a time.

    Parameters
    ----------
    df_scores : pandas.DataFrame
        The data frame containing the simulated scores.
        This is usually one of the data frames returned
        by the ``simulation.dataset.Dataset.to_frame()``
        method.
    rater_ids : numpy.ndarray
        An array of simulated rater IDs whose scores want
        to compute the cumulative average over.

    Returns
    -------
    df_cumulative_mean_scores : pandas.DataFrame
        A data frame containing the cumulative average rater scores.
        It has ``len(df_scores)`` rows and ``len(rater_ids`` columns.
        Each of the columns is named ``N=n``, where n is the number of
        raters included in computing the cumulative average.
    """
    df_rater_scores = df_scores[rater_ids]
    df_cumulative_average_scores = df_rater_scores.expanding(1, axis=1).mean()
    df_cumulative_average_scores.columns = [f"N={num_raters+1}" for num_raters in range(len(rater_ids))]
    return df_cumulative_average_scores