Players can't gain life.
At the beginning of your upkeep, Witch Hunt deals 4 damage to you.
At the beginning of your end step, target opponent chosen at random gains control of Witch Hunt.
Spells and abilities that would cause a player to gain life still resolve, but the life-gain part has no effect.
Abilities that trigger whenever a player gains life can’t trigger and effects that would replace gaining life with another effect won’t apply because it’s impossible for players to gain life.
If an effect sets a player’s life total to a specific number and that number is higher than the player’s current life total, that part of the effect won’t do anything. (If the number is lower than the player’s current life total, the effect will work as normal.)
To choose a target at random, all possible legal targets must have an equal chance of being chosen. There are many ways to do this, including assigning each possible legal target a number and rolling a die.
The target is chosen at random as you put the last ability on the stack. Players can respond to this ability knowing who the target is.
If you control Witch Hunt, you are not a legal target. If there are no legal targets available, the ability is removed from the stack and you retain control of Witch Hunt.