Gfyuki

In a discussion of the heifer ritual when a murder victim is found between two cities, Sotah 9:2 lists some cases when a city does not bring a heifer, including a city where a majority of the inhabitants are not Jewish and a city where there is no court. The city without a court must be a Jewish-majority one, else there would be no need to mention it here because it would already be covered by the previous case. But that, in turn, got me wondering how a Jewish city could possibly not have a court. It says עיר (city), so I assume the mishna is not talking about a tiny village that doesn't have three learned men.

At the time of the mishna, were there enough Jewish cities without a court that the mishna had to consider the case? Or is this likely to be a theoretical case, just in case a city should be lacking a court for whatever reason?

A little town hasn't Bet Din. See Sanhedrin Mishna 1.6

And how many [inhabitants] must a city have before it may have a Sanhedrin? One hundred and twenty. Rabbi Nechemiah says, two hundred and thirty, [each judge] corresponding to a chief of a group of ten.

Bartenura

מאה ועשרים - מפרש בגמרא,

1. עשרים ושלשה, סנהדרי קטנה. twenty three for the little Sanhedrin




2. ושלש שורות של עשרים ושלש עשרים ושלש יושבים לפניהם, שאם הוצרכו להוסיף על הדיינים מוסיפים מהם. Three ranges of 23 they are seeting in
   front of them, because sometime they need to add Judges




3. ועשרה בטלנים, עשרה בני אדם בטלים מכל מלאכה שיושבים תמיד בבית המדרש. ten 'chomeurs" they don't work and are all time in Bet Midrash




4. ושני סופרים לכתוב דברי המזכין ודברי המחייבין. two scribes who write the words of the accusatory and defensors




5. ושני חזנים, שמשי בית דין להלקות החייב ולהזמין בעלי הדין. Two court employees who flog the condemned and call upon the protagonists




6. ושני בעלי דינין . two protagonists




7. ושני עדים. two witnesses




8. ושני זוממין . two "zomemim" witnesses




9. ושני זוממי זוממין. two "zomeme zomemim" witnesses




10. ושני גבאים, two donation officiers




11. ושלישי לחלק הצדקה, שצדקה נגבית בשנים ומתחלקת בשלשה.a third donation officier to distribute tsedaka with them




12. ורופא אומן להקיז דם. ולבלר לט. ומלמד תינוקות. הרי מאה ועשרים: a doctor who makes bleeding therapy, a scribe and a master for children,
    = 120

The Gemara on the Mishnah you quoted says that since the verse asks for "ziknei ha'eer" (elders of the city), it means members of a Court of 23 Judges.

(See also Rambam, Hilchos Rotzeach 9:4, who says a Court of 23 Judges.)

Therefore it won't suffice to have a Court of 3 Rabbis.

The Sefer HaChinuch (Mitzvah 531) explains that the calf ceremony is for finding a murdered corpse and thus must be precided over by a Court who is empowered to judge murder cases. The minimum court for that is 23.

The requirement of 23 over 3, depends on factors having to do with the population and makeup of the city.

(The Mishnah/Gemara says we measure to the nearest city that has a court of 23; not that we just don't do the ceremony if the nearest city doesn't have a court.)

This is all in contrast to the question of whether or not the victim is found near the border or near a city with a population of idolaters.

In that case the ceremony is not carried out at all, because the wandering unknown victim should not have been wandering in a dangerous area like that alone. Therefore the victim shares some of the guilt and the people of the cities do not need to perform the eglah ceremony. (See Rambam Peirush HaMishnayos on this Mishnah.)

I hope this helps.