The concept of forcing the same card on multiple spectators dates back to the 1600s. For further information see Forcing the Same Card on Multiple Spectators.
The “Tossed-out Deck” combines this old idea with that of tossing a bound force deck into the audience for selections to be made. This was being done at least as early as the first decade of the twentieth century. Henry Hardin was using the idea with his marketed “Peerless Monte-Cristo Cards,” 1909.
T. Page Wright and William Larsen (Sr., although shown as “Jr.”), in a routine titled “Fantasies with Frames”, used an intricately prepared deck that included three banks of force cards; see The Sphinx, Vol. 26 No. 6, Aug. 1927, p. 192. While their aim was to force all three cards, they observed that if two spectators peeked at the same force card, the effect would still succeed. Note also their use of glued pairs of short and long cards, an idea that would develop into the Tele-matic Deck.
U. F. “Gen” Grant may have been the first to have three people peek at cards in a rubber-banded one-way force deck. Grant then removed three cards from the deck—the force card and two indifferent cards that lay on the top and bottom of the deck—and had each person verify that his card was among the three, à la “The General Card”. See “Lady Luck” in Phoenix, No. 181, Jul. 15, 1949, p. 723.
Orville Meyer contributed his synthesis, using a Tele-matic forcing deck, to Mental-wise, Vol. 2 No. 8, Mar. 1956, p. 2. Instead of showing a fan of three cards for confirmation, Meyer called off the names of three cards and had the three persons raise their hands if they had heard their card. This is likely where David Hoy got the idea. Curiously, the strength of this trick wasn't widely recognized until Hoy published it in his Bold and Subtle Methods of Dr. Faust, 1963, p. 25. He gave no history of the trick and his only change was to ask the three persons to affirm verbally that he had named their card, rather than having them raise their hands. Yet, the trick was for quite a time almost invariably identified as “Hoy's Tossed-out Deck”.