You can choose. When you discard the Twins (or any other madness card), it goes to exile and all its madness abilities trigger. They are put on the stack at the same time, and because you control all the triggers, you can choose their order. The one on top will resolve first, letting you cast the card for its associated madness cost. If you don't, the card goes to the graveyard and all other madness triggers lose track of it, so you can't cast the card with them anymore.
Edit:
Sorry, just reread the madness rules, and my answer is a bit off. You can still chose, but there is only one trigger, the one associated with the madness abiliy exiling the card. The other madness abilities do nothing.
702.34a Madness is a keyword that represents two abilities. The first is a static ability that functions
while the card with madness is in a player’s hand. The second is a triggered ability that
functions when the first ability is applied. “Madness [cost]” means “If a player would discard
this card, that player discards it, but exiles it instead of putting it into his or her graveyard” and
“When this card is exiled this way, its owner may cast it by paying [cost] rather than paying its
mana cost. If that player doesn’t, he or she puts this card into his or her graveyard.”
You can choose. When you discard the Twins (or any other madness card), it goes to exile and all its madness abilities trigger. They are put on the stack at the same time, and because you control all the triggers, you can choose their order. The one on top will resolve first, letting you cast the card for its associated madness cost. If you don't, the card goes to the graveyard and all other madness triggers lose track of it, so you can't cast the card with them anymore.Edit:
Sorry, just reread the madness rules, and my answer is a bit off. You can still chose, but there is only one trigger, the one associated with the madness abiliy exiling the card. The other madness abilities do nothing.
702.34a Madness is a keyword that represents two abilities. The first is a static ability that functions
while the card with madness is in a player’s hand. The second is a triggered ability that
functions when the first ability is applied. “Madness [cost]” means “If a player would discard
this card, that player discards it, but exiles it instead of putting it into his or her graveyard” and
“When this card is exiled this way, its owner may cast it by paying [cost] rather than paying its
mana cost. If that player doesn’t, he or she puts this card into his or her graveyard.”
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)