Torah grants the divine power of judgment

ואלה מוסיף על הראשונים כו'. מסיני כו'.

"And these" (ve'eileh) adds to the earlier ones… from Sinai… (Rashi, Shemos 21:1).

Rashi teaches that the connecting "and" of "And these are the ordinances" joins the civil laws to the preceding Aseres HaDibros — both alike were given at Sinai.

דכתיב המשפט לאלקים הוא.

For it is written, "Judgment is God's" (Devarim 1:17).

The Torah teaches that the power of true judgment belongs to Hashem — human courts only carry out a divine faculty.

אך בקבלת התורה בסיני קבלו בנ"י אלקות כמ"ש אנכי ה' אלקיך.

But at the receiving of the Torah at Sinai, Bnei Yisrael received Godliness (Elokus), as it is written, "I am Hashem your God" (Shemos 20:2).

At Sinai Bnei Yisrael absorbed an inner divine quality, encapsulated in "Anochi Hashem Elokecha" — Hashem became "your God," dwelling within them.

ונכתב בתורה.

And it was written in the Torah.

This divine power was embedded into the Torah itself.

לכן ע"י היגיעה בתורה זוכין למצוא כח אלקי.

Therefore, through toil in the Torah, one merits to find a divine power.

Because the Elokus is invested in the Torah, laboring in Torah reveals that divine faculty within a person.

ולכן נקראו הדיינים אלהים.

Therefore the judges are called "elohim" (Shemos 22:8).

Dayanim who master Torah are titled "elohim" because they channel that divine power of judgment.

וכמ"ש אלקים נצב בעדת אל. מלשון ויתיצב ה'.

As it is written, "God stands in the assembly of God" (Tehillim 82:1) — from the language of "And Hashem stationed Himself" (Shemos 34:5).

The "standing" of God among the judges echoes Hashem "stationing Himself," signifying His presence resting upon a true court.

שהדיינים המומחין מתלבשים ברוה"ק.

For the expert judges become clothed in ruach hakodesh.

Accomplished dayanim are enveloped in a divine spirit that guides them to truth.

ולא זו בדין שבין אדם לחבירו. רק לזכות לשפוט א"ע בדרך המשפט כמ"ש חז"ל צדיקים יצ"ט שופטן.

And not only in judgment between a person and his fellow, but also to merit to judge oneself by the path of justice, as Chazal said, "The yetzer tov judges the tzaddikim."

This divine faculty of judgment is meant not only for courtroom disputes but for inner self-judgment, so a person rules himself by his yetzer tov as the tzaddikim do.

וכל זה זוכין בכח התורה.

And all this is merited by the power of the Torah.

Both right judgment of others and of oneself flow from the divine power contained in Torah.

וכמ"ש במשנה העוסק בתורה לשמה כו' ונותנת לו מלכות וממשלה וחקור דין.

As it is stated in the Mishnah: "One who engages in Torah lishmah… and it grants him kingship, dominion, and discernment in judgment" (Avos 6:1).

Learning Torah for its own sake confers the very capacities of authority and clear legal insight.

כי ע"י העסק בתורה משתנה דעת האדם להיות נמשך אחר דעת התורה וזוכה למשפט אמת:

For through engagement in Torah a person's mind is transformed to be drawn after the mind of the Torah, and he merits true judgment.

Immersion in Torah reshapes one's very da'as, aligning it with the Torah's perspective so that he can render — and live by — truthful judgment.

Summary: Because the civil laws were given at Sinai together with "Anochi Hashem Elokecha," judgment is a divine power invested in the Torah. Through toil in Torah lishmah a person's da'as is reshaped to the Torah's, so dayanim are called "elohim" and are clothed in ruach hakodesh — and one gains the power not only to judge others truthfully but to judge oneself.