公 (gōng): This character means “public,” “common,” or “fair.” It's the same character used in words like 公园 (gōngyuán - public park) and 公司 (gōngsī - public company).
道 (dào): This character means “way,” “path,” or “principle.” It carries a philosophical weight, as seen in the word 道家 (Dàojiā - Daoism). Here, it combines with 公 to mean “the principle of fairness.”
杯 (bēi): This simply means “cup” or “pitcher.”
When combined, 公道 (gōngdào) means “fairness,” “justice,” or “impartiality.” Therefore, 公道杯 (gōngdàobēi) literally translates to the “fairness cup,” a name that perfectly encapsulates its function and the philosophy behind its use.