|יא וַיִּשְׁלַח יְהוָה אֶת-יְרֻבַּעַל וְאֶת-בְּדָן, וְאֶת-יִפְתָּח וְאֶת-שְׁמוּאֵל; וַיַּצֵּל אֶתְכֶם מִיַּד אֹיְבֵיכֶם, מִסָּבִיב, וַתֵּשְׁבוּ, בֶּטַח.||11 And the LORD sent Jerubbaal, and Bedan, and Jephthah, and Samuel, and delivered you out of the hand of your enemies on every side, and ye dwelt in safety.|
But who in the world is this fellow? We see no mention of him in sefer Shofetim, which given its chronological pattern of shofet after shofet after shofet, would not seem to have any space for a gap, and an additional judge.
All the meforshim -- Targum, Rashi, Mahari Kara, Radak, Metzudat David, Ralbag, Malbim -- identify Bedan as Shimshon. They all get it from the gemara (Rosh Hashanah 25a - b), which has:
ואומר (שמואל א יב) ויאמר שמואל אל העם ה' אשר עשה את משה ואת אהרן ואומר (שמואל א יב) וישלח ה' את ירובעל ואת בדן ואת יפתח ואת שמואל ירובעל זה גדעון ולמה נקרא שמו ירובעל שעשה מריבה עם הבעל בדן זה שמשון ולמה נקרא שמו בדן דאתי מדן יפתח כמשמעו
דף כה, ב גמרא ואומר (תהילים צט) משה ואהרן בכהניו ושמואל בקוראי שמו שקל הכתוב שלשה קלי עולם כשלשה חמורי עולם לומר לך ירובעל בדורו כמשה בדורו בדן בדורו כאהרן בדורו יפתח בדורו כשמואל בדורו ללמדך שאפילו קל שבקלין ונתמנה פרנס על הצבור הרי הוא כאביר שבאבירים
The purported connection is bedan as ba from dan, and Shimshon was the shofet from the tribe of Dan. But the influence of this explanation is almost surely the closed-canon approach. That is, if you have a Biblical figure otherwise unidentified as famous, and all of a sudden brought to brief prominence, conflate them with another famous Biblical figure. Thus, the eved Avraham who went to pick up Rivka was surely Eliezer, Shifra and Puah were Yocheved and Miriam, and the two anonymous spies Yehoshua sent in last week's haftarah were Calev and Pinchas. So too, Bedan is the famous Shimshon. Radak notes an irregularity, that the chronologically later Shimshon is then placed after Yiftach in the pasuk, but he answers that the order is based on their greatness. (I would also add that Yerubaal is one of two names for the same individual, namely Gideon, so saying that Shimshon had two names, though not mentioned elsewhere explicitly in the text, is slightly plausible.)
There is another possibility. The LXX (Septuagint, an early Greek translation), the Syriac translation, and the Arabic translation all have Barak instead of Bedan. (I would point out a slight irregularity that we might have expected Devorah rather than her lackey.) We can treat the evidence from these sources in one of two ways. We could note that each of these is a translation of a Hebrew original, and even in our own Targum, Bedan was "translated" to another shofet, namely Shimshon. We cannot know that some other tradition (perhaps based on a closed-canon approach) did not develop that Bedan was Barak, and that this is what these translations are doing. If it is translation rather than mere transcription, then these sources are much less relevant.
On the other hand, we could presume that these are transcriptions of the Hebrew, rather than translations. They would then reflect a variant girsa. Even so, the variant girsa could reflect an error, but still, we would be faced with variant versions of the text. We would think it likely that this reflects a variant girsa because both בדן and ברק begin with a bet; there is orthographic similarity between the daled and the resh; and similarly between the long nun sofit and the kuf. If so, scribal error could produce either variant from the other.
Even if we are dealing with a scribal error creating a variant, my assumption is that our Masoretic text is the correct one. This is not just because I like defending our tradition. Rather, there is a principle of lectio difficilior, the rule of the difficult word being more likely to be original. Of course, some corruptions will make the text insensible, but the idea behind it is as follows: Which is more likely, to change a text from an otherwise unknown shofet into a famous one, or vice versa? Bedan would seem like an error, so a scribe would be less likely to write it; but in a confusing source text, a scribe is quite likely to arrive at Barak, believe it to make sense, and maintain it.
They key behind lectio difficilior, when I use it at least, is that there is an obvious and immediately apparent difficulty with one of the choices over the other, but on closer scrutiny and consideration, one can make a compelling case for the other choice.
And here is my compelling case. It is not true that we do not know Bedan from elsewhere. The name is found in I Divrei Hayamim 7:
Now the next shofet in the list, Yiftach, was the son of a Gilead, and a descendant of the famous Gilead, and lived in Gilead in Menasheh's portion. And the shofet previous to him was Yair, of Gilead, and perhaps his thirty sons as well.
Without bothering to work out the chronology of Divrei Hayamim, perhaps there was another shofet from Gilead wedged in there, either the one in Divrei Hayamim or someone bearing that name, since we see that names sometimes recur within families (such as Gilead).
If so, we might adopt a quasi-open canon approach. It is only- quasi since we do find this person (or this name) elsewhere in Tanach. But we can assume that it is not someone who was named explicitly in sefer Shofetim as a judge.
To Shmuel's audience, who lived at that time, Bedan would indeed be famous. But he was left on the cutting room floor of sefer Shofetim, so later generations did not know what to do with this reference. If so, Bedan gets sudden significance, hidden until now. It has a plausibility which is not immediately apparent. And thus I would favor it in a contest against Barak.
I will leave off with a nice parallel. In sefer Yechezkel, we have the following:
Note the krei and ketiv for Daniel, as Danel. It turns out that Danel was a famous figure in the Ancient Near East as a wise and righteous king. (See here.) So we have in this pasuk three famous gentile figures, renowned for their righteousness. It is only a later reader who has no clue who Danel is, and substitutes Daniel in its place. The open-canon approach in this case is almost certainly correct.