Who decides which PHB variant rules are in play?

Question

The rules variants presented in the DMG are clearly there for the DM to decide upon.

Some of the variants in the PHB say that they are the DM's prerogative. For example, "Variant: Customizing Ability Scores" (PHB, p. 13) says:

At your Dungeon Master’s option, you can use this variant for determining your ability scores.

However, the "Variant: Encumbrance" section (PHB, p. 176) says:

Here is a variant if you are looking for more detailed rules for determining how a character is hindered by the weight of equipment.

As far as I can tell, there is no discussion of encumbrance in the DMG.

Does this mean that, RAW, individual players each decide whether or not they are using the encumbrance rule, and that a given game might have some players using the variant rule and others not?

(I realize that by Rule 0, A DM could decide that the variant rule was in play or not.)

Answer 1

The table

That is; all the players together make that decision. How that works exactly depends on the group and the game; some DMs will say "My game works like this and if you don't like that, don't join my game", but then some people will say "This is my house, I want to play like this, so if you don't want that, don't come here" and sometimes people hold a vote.

This is part of the general idea that playing an RPG is a social affair and some general rules and interactions are simply decided on by the players. The guys writing the manual won't be at your table, so they can't really tell you how to play. They can say "The DM decides" or "The person who owns the book decides" but in the end, it's easier for them to just be silent on the matter (or outright tell you to figure it out as a group).

So yeah, it's possible that some people in your group use the rule and others don't, it's also possible your group decides entirely one way or the other. As with all "What game are we playing?" questions, ask your group.

Answer 2

Session 0 is largely (in my experience) a "universe-defining" session. As such, for playability (and sanity among the DM and players), things like the encumbrance rule would be agreed upon by all to apply for the campaign. The DM could implement a rule by fiat, or leave it open to group agreement, but player-by-player rules would be untenable. In some cases, RAW falls short. The writers/editors/proofers/etc are, after all, only human and can miss details.