I’ve noticed that Kriyat Ha-Torah works differently in Reform and Conservative synagogues. The aliyot are shorter. I heard that this is because they work on a three year cycle, rather than an annual one. How does that work? Also, what is the source for using a three year cycle, and what are the benefits?
While I do not love this system, I am familiar with it. Most of the weekly parshas are divided into three roughly equal sections. A few special ones (Haazinu comes to mind) are not divided and always read whole, probably due to their short length. The Torah cycle still starts with Bereishit each year on Simchat Torah, but almost every Shabbat morning aliyah is shortened (weekdays, festivals and roshei hadashim are unaffected). The weeks that they fall on match the standard parsha expected for either Eretz Yisrael or for the diaspora, "doubling" the weekly parsha as needed according to the calendar except it is often not a real doubling as you will see.
If one is trying to match it up to the conventional breaks marked in a Chumash, on the first year of the cycle, it will start at the beginning of the parsha, but Cohen will end sooner, Levi will start shifted forward, etc. until you get to shvee/maftir at roughly the 1/3 point. The new stopping points are standardized and can be found in a luach intended for a Conservative synagogue. They usually fall on what would be a paragraph break in English or a similar conceptual ending (e.g. "Ani Hashem" or similar). This file lists all the breaks in detail if you want to study them and see if there are any errors in my description.
For the second year of the cycle, the reading and Cohen Aliyah will start at the 1/3 point where it had ended one year before and go to the roughly 2/3 point. For the third year, it will start at 2/3 and go to the end, with maftir then being the same as the traditional one.
It is often said that the entire Torah gets read out-of-order over the course of three years with this system, but that is not strictly true. Because the calendar often causes us to combine certain parshiot (e.g Mattot and Masei), there will usually be at least one "second parsha" that does not get read during the three year cycle.
I do not have a source of how the Conservative movement reasoned that this was an acceptable system to use, but I believe its benefits are purely to accommodate the Torah reader and the congregants. You will often find the Torah reader moving at a slower pace in a Conservative synagogue because there are simply 2/3 fewer syllables to say on any given week. This is easier to speak correctly out loud than the rapid style that I have seen in many Orthodox synagogues, and it is also easier for the congregation to follow, who may have a lower level of Hebrew-reading ability, having learned it as children after public school rather than in a Orthodox day school setting. The elapsed time of the Torah reading may be slightly less and that may accommodate impatient congregants too, but I find that the total elapsed time does not really seem that different, given the adjusted reading rate and the time that it takes for other aspects of an aliyah.