While resolving Polygraph Orb's last ability, your opponent chooses a card to be discarded without revealing it, chooses a creature to be sacrificed, or chooses to do neither. Then that player discards that card, sacrifices that creature, or loses 3 life. Your opponent can always choose to lose 3 life, even if they have cards to discard or creatures to sacrifice.

In a multiplayer game, each opponent in turn order makes their choice once, then all of the actions occur simultaneously. Opponents will know choices made by earlier opponents when making their choices, although a card chosen to be discarded this way isn't revealed until it's discarded.

In a Two-Headed Giant game, Polygraph Orb's last ability causes both opponents to sacrifice a creature, discard a card, or lose 3 life.

If you can't exile enough cards to meet or exceed the required mana value, you can't choose to collect evidence at all.

Once you've announced that you're casting a spell, players can't take actions until you've finished doing so. Notably, opponents can't try to remove cards from your graveyard to stop you from collecting evidence.