[1] = Synagoge delta155; Photius, Lexicon delta328. The headword is present active participle, masculine nominative singular, of the verb diaita/w. The more common-sense of this verb is 'living' (cf. delta 884, delta 889), but the meaning 'to arbitrate' often occurs in orators (see LSJ at web address 1), so the gloss may originate in commentary to passages such as Demosthenes 21.84 where the headword occurs. For the verb cf. delta 886; for related nouns, delta 885, delta 887, delta 888, delta 889.
[2] The the same headword but differently glossed.
[3] Or: distributing on the basis of equality.