How a Machlokes in Halacha is resolved?

Question

How does accepted Halacha come to be when there is a dispute?

More specifically - we notice different approaches in terms of practice: when it comes certain mitzvot: to how to put up a mezuzah, we take a hybrid approach. When it comes to shofar - we listen to a hundred blasts to fulfill various opinions., Zecher and Zeicher by parshas Zachor. However, when it comes to other mitzvot, we don’t find all Jews trying to fulfill all opinions in Halacha - e.g. Rabbeinu Taam tefilin, parshas Zachor in different dialects, all times of Shabbos etc.

Why and how did this evolve?

Answer 1

There's no such thing as "an accepted Halachah" - it's just a figure of speech. Whatever is accepted by someone is rejected by someone else.

Halachah is always offered, but not accepted. A single Rabbi, can state that he rules it so or so, but nothing turns automatically into Halachah until people start practicing it. And we judge it, pretty much, statistically.

Rambam wrote his Mishnah Torah but it was not widely accepted immediately, so the writing does not turn it into Halacha. HaTur wrote the 4 Turim but it wasn't accepted, but when R' Karo copied it, it became "the de-facto" Halachah pretty arbitrary, it could be the other way around, as it happened to many other good Seforim.

So it is a matter of a "luck" whether a ruling will or will not be accepted by the wide audience or the other Rabbis (that rule wide audiences).

Answer 2

You're not [probably] like what I'm gonna say but it must be said:
Judaism is all about following Rabbis and their "subjective truths" and not about following [some kind of ] "the absolute objective truth". Here are the reasons why the Halachah looks as it is:

1. Unlike the science that's goal is to find the empirical truth (as we don't care who discovered the formula or proved a theorem as long as it works), in Judaism, we follow the opinions of single Rabbis implying that that's the truth.

2. Besides the belief that the Rabbis are guided by the Ruach Hakodesh (the Rabbies deny themselves) there's no way of the empirical testing the validity of any argument. So, theoretically, a Rabbi can utter any ruling without anyone being able to refute it. Here's a simple test for you: find a Machloket in the Gemmorah and see if you can refute the opposite resolution of a dispute (the factual Halachah). If you can't it is just as valid as the actual one.

3. There are hundreds of ruling Rabbis, and there's no pre-defined way of who we follow in what questions. This is the way of the Talmud: in one Halachah, we follow R"A, in another R"Y, or Rabbah or Chahamim (anonymous) or Ravinah or R"Ashi or whatever (some try to set rules post-factum though). Who did Rambam follow? How did the Mechaber decide on the three to rule by Majority - is there such a principle in our Halachah? How did Mishnah Berura decide on his sources - who he follows?

4. The punchline - whoever thinks that the purpose of learning Torah (and Halachah as you ask) is about finding the truth is wrong. It is all about "engaging in learning Torah" (as we say the Beracha "לעסוק בדברי תורתך"). To prove that is enough to remind you that the Sanhedrin was [presumably] functioning till the late Amoraim and ALL the disputes of the Talmud could be easily ruled in court, but they didn't use that tool, they preferred the disputes and inconsistencies, and personification of the Halachah instead of unifying and streamlining it.

(Did you see any Gdol Hador trying to unite other Gdoylim to prevent disputes or the opposite? (Here in Israel we have a joke about a Photoshopped virtual "Mizrach" where different Gdoylim (like R' Ovadia and R' Elyashiv and R' Kanyevsky and R' Auerbach Z"L) sit together by one table - which is only good for Kapparot on Rosh Hashonah).) So they all inherently endorse the diversity and variety of Rabbis and opinions, for it gives us the opportunity to continue that approach further.

Therefore we end up with a fabulous, legendary and incredible culture of following [arbitrary] traditions. There's no logical reasonable explanation and necessity of most of the current Mishnah Berurah or Shu"A. For example, women wobble Lulav with/without Berachah - can we refute if it was prohibited? Women don't put Teffilin - can we refute if they were obligated (Based on R' Akiva in Eruvin 98-99)?

But, as I said in #4, cheer up, if we're given the reward just for mere engaging in all those fights and disputes, and if that's the G-d's will - that's just fine, as the final Rashi in the Ecclesiastes - "מה שתוכל עשה ולבך לשמים"!!

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Some afterthoughts:

1. _{The Rabbis that deal with Halachic rulings, pretty much all of them are (unfortunately for me) are very inconsistent and non-systematic, following the format of our Scriptures and the Rabbinical books (Mishnah and Gemmorah) that are also very much inconsistent and non-systematic.}

   • _{Take for example the way of commanding the Mitzvot in the Torah: First, there's no clear understanding of what substitutes a Mitzvah in the Torah, Second, there's no fixed formula for a Mitzvah: some are direct (Don't murder), some indirect (Bney Israel will not eat גיד הנשה), some are given in single (honor your parent)some in plural (fear your parent), some detailed (Lost and Found) some only hinted (Works on Shabbos), some only once (Teffilin) some numerous times, some before Matan Torah (פרו ורבו) and some after etc.}

   • _{The Mishnah and the Gemorah follow the same vagueness, having no clear system of principles of how the Halachah is ruled (some tried to formulate it post-factum but it is not widely accepted). Sometimes it follows one Rabbi sometimes another - just a matter of chance.}

   • _{Take for example Rambam's Mishnah Torah. Each Mitzvah is phrased differently, bringing different sources, sometimes citing whole Gemmorahs and sometimes not relying on the Gemmorah at all. There's not even a clear definition of what a Mitzvah is, as for example in Hilchos Krishma he starts with: "Twice a day [we] read Krishmah", not mentioning it's a Mitzvah at all, but 3 lines further he states "it is a Mitzvah to remember the Exodus at night", not mentioning that actually it is not a Mitzvah at all (he doesn't count it in his 613)}

_{And the list goes on and on.}