Section 15. The supreme judicial court or the probate court may authorize the persons named as executors in an instrument purporting to be the last will of a person deceased, or the petitioners for administration with such will annexed, to adjust by arbitration or compromise any controversy between the persons who claim as devisees or legatees under such will and the persons entitled to the estate of the deceased under the laws regulating the descent and distribution of intestate estates, to which arbitration or compromise the persons named as executors, or the petitioners for administration with the will annexed, as the case may be, those claiming as devisees or legatees whose interests will in the opinion of the court be affected by the proposed arbitration or compromise, and those claiming the estate as intestate, shall be parties.