Prayer

How it Impacts

• Prayer changes God's decree by appealing to his attribute of mercy – See Bavli Taanit 23a, Yevamot 64a, Ramban Bereshit 46:15.
• Prayer changes the person and makes him/her more deserving – See R. Saadia Commentary on Bereshit 4:13, 18:25, R. Yosef Albo Sefer HaIkkarim 4:18.

This question has consequences for understanding a number of topics:

Role of a Righteous Person

• The righteous person himself prays on another's behalf – the simple reading of Bavli Berakhot 34b and Bava Batra 116a, Ramban Shemot 18:15 (see discussion in Moshe's Manifold Responsibilities), Nimmukei Yosef Bava Batra 116a. This position fits with the approach that prayer is impacting on God.
• One learns how to pray properly from the righteous person – Meiri Bava Batra 116a. See also Cassuto Shemot 18:15 (and discussion of his position in Moshe's Manifold Responsibilities). This (rationalist) position assumes that prayer is effective because it impacts on the person, and thus little is accomplished by third party intercession.