...Assuming someone has made duplicate reservations and actually ticketed them, if they cancel one or more of the reservations, does Amtrak even have the ability to keep them from boarding if they have a ticket for a canceled reservation?
Once the ticket has been printed, then a refund or voucher credit is only issued when the physical ticket is returned. If the ticket is used for travel, then no refund is possible. So, cancelling a ticketed reservation and then using the ticket anyway means no refund or voucher credit.
Exactly, but if it was used for travel it would not be refunded. What I am stating is what if someone had 3 different reservations, ticketed all 3, then decided to cancel 1 or more of them, and then use of of those canceled tickets to board. I doubt many would try, but it is potentially one way to get around the duplicate reservation rule.
Alan might be able to confirm (or not), but once the three tickets are printed, then, like airline boarding passes, things are pretty firm. I don't think that Amtrak could easily cancel a ticketed reservation, unless for a specific space, like a sleeper room. Besides, all three tickets could conceivably be used if there happened to be three people in a household that shared the same name (I know a household that used to have two - mine). Just having the same name and address and even credit card does not mean the tickets are positively for the same person.
However, for the most common reason to multi-book trips - business travel with a floating return time - having printed tickets for all the options is way too cumbersome. Business travellers do not want to deal with returning paper tickets and handling vouchers that have to be turned in for future reservations. They want purely electronic reservations that auto-credit when cancelled or just left unused. So, they would use a means to accomplish that without giving the duplicate reservations cops at Amtrak cause to cancel reservations. I don't do it myself (honesty is one of my failings), but it can be done.