Players can't take actions once Magus of the Balance's ability begins to resolve until it's done resolving. If any abilities trigger during this process, they're put onto the stack after it's done resolving.

When Magus of the Balance's ability resolves, first the player whose turn it is chooses an appropriate number of lands they control (which may be zero if that player doesn't control more lands than the player who controls the fewest). Then each other player in turn order does the same, knowing choices made by previous players. Finally, all of the chosen lands are sacrificed simultaneously. Players repeat this process for cards in hand and creatures they control, except while choosing cards in hand, players won't know the identity of cards chosen by the previous players.

If a player has zero cards in hand, controls no lands, or controls no creatures, other players will have to discard their entire hand, sacrifice all of their lands, or sacrifice all of their creatures, as appropriate.