In its discussion of the commandment to judge monetary cases, Sefer HaChinukh explains the judicial obligation to investigate claims and decide according to valid testimony and evidence. It supplies the broader ethical and legal setting for the burden of proof.
מִצְוָה שֶׁיִּשְׁפֹּט בְּצֶדֶק – לִשְׁפֹּט בְּצֶדֶק, שֶׁנֶּאֱמַר (ויקרא יט טו) בְּצֶדֶק תִּשְׁפֹּט עֲמִיתֶךָ, וּבָא הַפֵּרוּשׁ שֶׁנִּצְטַוּוּ הַדַּיָּנִין לְהַשְׁווֹת בַּעֲלֵי הָרִיב, כְּלוֹמַר, שֶׁלֹּא יְכַבֵּד הַדַּיָּן אֶחָד מִבַּעֲלֵי הַדִּין יוֹתֵר מִן הָאַחֵר, וְכֵן אָמְרוּ בַּסִּפְרָא (קדושים ד ד) שֶׁלֹּא יְהֵא אֶחָד מְדַבֵּר כָּל צָרְכּוֹ, וְאֶחָד אוֹמֵר לוֹ קַצֵּר דְּבָרֶיךָ. וְכֵן בְּפֶרֶק שְׁבוּעַת הָעֵדוּת (שבועות ל א), תָּנוּ רַבָּנַן בְּצֶדֶק תִּשְׁפֹּט עֲמִיתֶךָ, שֶׁלֹּא יְהֵא אֶחָד עוֹמֵד וְאֶחָד יוֹשֵׁב, אֶחָד מְדַבֵּר כָּל צָרְכּוֹ וְאֶחָד אוֹמֵר לוֹ קַצֵּר דְּבָרֶיךָ. וְכֵן בִּכְלַל מִצְוָה זוֹ, שֶׁכָּל אִישׁ שֶׁהוּא חָכָם בְּדִינֵי הַתּוֹרָה וְיָשָׁר בִּדְרָכָיו, שֶׁהוּא מְצֻוֶּה שֶׁיָּדִין דִּין תּוֹרָה בֵּין בַּעֲלֵי הָרִיב אִם יֵשׁ כֹּחַ בְּיָדוֹ, וַאֲפִלּוּ יָחִיד יָכוֹל לָדוּן מִדִּין תּוֹרָה, וּכְמוֹ שֶׁאָמְרוּ זִכְרוֹנָם לִבְרָכָה (סנהדרין ג, א) אֶחָד דָּן אֶת חֲבֵרוֹ דִּין תּוֹרָה, שֶׁנֶּאֱמַר בְּצֶדֶק תִּשְׁפֹּט עֲמִיתֶךָ. וַחֲכָמִים הִזְהִירוּ (אבות ד ח), שֶׁלֹּא יְהֵא אָדָם דָּן יְחִידִי. וְעוֹד יֵשׁ בִּכְלַל מִצְוָה זוֹ, שֶׁרָאוּי לְכָל אָדָם לָדוּן אֶת חֲבֵרוֹ לְכַף זְכוּת וְלֹא יְפָרֵשׁ מַעֲשָׂיו וּדְבָרָיו אֶלָּא לְטוֹב. שֹׁרֶשׁ הַמִּצְוָה נִגְלֶה הוּא, כִּי בְּהַשְׁוָיַת הַדִּין יִתְיַשֵּׁב הָעוֹלָם, וְאִם יְכַבֵּד הַדַּיָּן אֶת הָאֶחָד מִבַּעֲלֵי הַדִּין עַל הָאַחֵר יִפְחַד בַּעַל הָרִיב מִלְּהַגִּיד כָּל טַעֲנוֹתָיו לְפָנָיו, וּמִתּוֹךְ כָּךְ יֵצֵא הַמִּשְׁפָּט מְעֻקָּל. וּבְמָה שֶׁאָמַרְנוּ שֶׁמִּצְוָה עַל הֶחָכָם בְּדִבְרֵי תּוֹרָה וְהוּא אִישׁ יָשָׁר לָדוּן בֵּין הַחוֹלְקִים, שֶׁזֶּהוּ בִּכְלַל הַמִּצְוָה, כְּמוֹ כֵן, גַּם בָּזֶה תּוֹעֶלֶת, כִּי הֶחָכָם וְהַיָּשָׁר, יָדִין דִּין אֱמֶת. וְאִם הוּא הַיּוֹדֵעַ לֹא יִרְצֶה לִשְׁפֹּט יִשְׁפְּטוּם שְׁאָר בְּנֵי אָדָם שֶׁאֵינָם חֲכָמִים וְיַטּוּ הַדִּין עַל הָאֶחָד מִבַּעֲלֵי הַדִּין בְּלִי יְדִיעָה. גַּם בְּמָה שֶׁאָמַרְנוּ שֶׁכָּל אָדָם חַיָּב לָדוּן חֲבֵרוֹ לְכַף זְכוּת, שֶׁהוּא בִּכְלַל הַמִּצְוָה, יִהְיֶה סִבָּה לִהְיוֹת בֵּין אֲנָשִׁים שָׁלוֹם וְרֵעוּת, וְנִמְצָא שֶׁעִקַּר כָּל כַּוָּנַת הַמִּצְוָה לְהוֹעִיל בְּיִשּׁוּב בְּנֵי אָדָם עִם יֹשֶׁר הַדִּין וְלָתֵת בֵּינֵיהֶם שָׁלוֹם עִם סִלּוּק הַחֲשָׁד אִישׁ בְּאִישׁ.
The commandment to judge with righteousness: To judge with righteousness, as it is stated (Leviticus 19:15), “you shall judge your people with righteousness.” And the explanation of it comes that the judges were commanded to treat the parties to the dispute equally - meaning to say that the judge not honor one of the litigants more than the other. And so they said in Sifra, Kedoshim, Chapter 4:4 that one not speak all that he needs, and [the judge] say to the other, “Speak briefly.” And so [too,] in the chapter [entitled] Shevuot HaEdut (Shevuot 30a), “Our Rabbis learned, ‘“You shall judge your people with righteousness” — that it not be that one stand and one sit; one not speak all that he needs, and [the judge] say to the other, “Speak briefly.”’” And so [too,] included in this commandment is that every man that is wise in the laws of the Torah and righteous in his ways is commanded to judge the law of the Torah between parties of a dispute, if he has the power in his hand [to do so]. And even an individual can judge from Torah writ — and like they, may their memory be blessed, said (Sanhedrin 3a), “One can judge his fellow from Torah writ, as it is stated, ‘You shall judge your people with righteousness.’” But the Sages warned (Mishnah Avot 4:8), that a man not judge alone. And also included in this commandment is that it is fit for every person to judge his fellow favorably, and only to understand his deeds and his words favorably. The root of the commandment is revealed to all — as with equitability in judgment, the world is civilized. But if a judge honors one of the litigants over the other, the [latter] disputant will fear to say all of his claims in front of him. And from this, the judgment will come out twisted. And about that which we said that it is a commandment upon one wise in words of Torah — and he be a righteous man — to judge those who disagree, that this is included in the commandment as well; there is benefit in this as well, as he will judge a true judgment. But if this one that knows does not want to judge, other people who are not wise will judge them, and they will slant the judgment towards one of the litigants without knowing. Also about that which we said that every person is obligated to judge his fellow favorably — that it is included in the commandment — is a cause for there to be peace and amity among people. And [so] it comes out that the essence of the whole intent of the commandment is to help in the civilization of people with righteousness of judgment, and to bring peace among them with the removal of suspicion of one man towards another.