halacha - Halachic significance of the plurality of Jews living in Israel

I once heard that if Israel has the largest Jewish population, it has a significant effect on certain Halachot.

What are the criteria for this, and what halachot are affected? (Shmita is the one most cited)

According to JewishVirtualLibrary, that seems to now be the case, or is it? (links hidden in the word 'JewishVirtualLibrary')

Answer

It's actually if Israel has the majority of the world's Jewish population, not just a plurality. The figures in your second link have 42.5% in Israel vs. 57.5% outside of it - so we're not quite there yet. (There is also, of course, the difficulty of determining who is a halachic Jew, ואכמ"ל.)

Anyway, Yovel (and Shemittah, according to some posekim) depends not only on the majority of the Jews being in the Land of Israel, but also on their living in their designated tribal territories (Rambam, Hil. Shemittah ve-Yovel 10:8). With almost no one knowing which tribe they're from, though, that's not really possible before Moshiach comes, barring major improvements in DNA analysis.