bˈækstɚ pɹɪfˈɜːd nˌɑːt tə dᵻskɹˈaɪb hɪz ˈoʊn dʒuːdˈɪʃəl fɪlˈɑːsəfi, bˌʌt ɐ nˈaɪntiːnhˈʌndɹɪd nˈaɪnti θɹˈiː ˈɑːɹɾɪkəl ɪnðə lˌɑːs ˈændʒəlɪs tˈaɪmz dᵻskɹˈaɪbd hˌɪm æz hˈævɪŋ æn "ɪmˈɜːdʒɪŋ ɹˌɛpjuːtˈeɪʃən ɐmˌʌŋ kˈoːɹt əbzˈɜːvɚz æz kˈɔːʃəs, kənsˈɜːvətˌɪv ænd kˈɑːmpɪtənt".
Baxter preferred not to describe his own judicial philosophy, but a 1993 article in the Los Angeles Times described him as having an "emerging reputation among court observers as cautious, conservative and competent".