Rambam in Geneivah 7:1 writes:
הַשּׁוֹקֵל לַחֲבֵרוֹ מִמִּשְׁקָלוֹת חֲסֵרוֹת מִן הַמִּשְׁקָל שֶׁהִסְכִּימוּ עָלָיו בְּנֵי אוֹתָהּ הַמְּדִינָה. אוֹ הַמּוֹדֵד בְּמִדָּה חֲסֵרָה מִן הַמִּדָּה שֶׁהִסְכִּימוּ עָלֶיהָ. הֲרֵי זֶה עוֹבֵר בְּלֹא תַּעֲשֶׂה שֶׁנֶּאֱמַר (ויקרא יט לה) "לֹא תַעֲשׂוּ עָוֶל בַּמִּשְׁפָּט בַּמִּדָּה בַּמִּשְׁקָל וּבַמְּשׂוּרָה":
One who weights out for his friend from weights deficient from the weights which the people of that country agreed upon, or if he measures out using a ruler deficient from the length which they agreed upon, he is in violation of a prohibition, as it says (Vayikra 19:35), "Do not do injustice in judgement, with lengths, weights, and volumes."
According to the Rambam, at least, the prohibition is based on the generally accepted measurements. So to answer your question: society in general, which, in practice, was probably the local government.