The Six Nations champions had a virtually full strength panel to choose from and opted to use Madigan's versatility to allow Darren Cave to travel as specialist backup at centre among a collection of backs who can cover multiple positions.
While Ireland can call up a replacement halfback within 48 hours if Conor Murray or Eoin Reddan are unable to play, an injury on the eve of a game would leave them relying on a player who has little or no experience at No 9.
"There's a degree of risk no matter what you do and we just feel it's something we can manage with the cover that we have got," Schmidt said.
"I'd like to think it's calculated, I'd like to think we've given it as much thought as we could and we just felt that it allowed us a little bit more flexibility further out."
While some coaches have opted to bring two hookers, Schmidt followed Australia's Michael Cheika in gambling at halfback.
However the Wallabies fallback option, Matt Giteau, has played there at international level.
Schmidt said he did not originally think he would go down the same route, but said Madigan was among a number of players he talked to about potentially covering different positions.
"He has done a lot of individual training. He hasn't trained within the team that much but in the last week he's started to slot in and do a little bit with the team as well," Schmidt said.
"It was always in the back of our minds, I spoke to Ian about it last season so it's not suddenly something. Ian did some work on it in the offseason and he's been quietly preparing himself for that potentially to happen."
Schmidt said tighthead prop Tadhg Furlong, a surprise pick after making his debut last weekend, has done some good work at loosehead to provide cover at another vulnerable position, while leaving out Andrew Trimble was one of the toughest calls.
"I think we spent six hours on Sunday and for some of those hours Andrew Trimble was coming to the World Cup with us and for some he wasn't. That's how tight it was," Schmidt said of the Ulster winger whose season was wrecked by injury.
"Time just ran out for him."
Ireland face France, Italy, Canada and Romania in Pool D at the World Cup. Their first match is against the Canadians on the second day of the tournament.
Squad:
Forwards: Rory Best, Sean Cronin, Tadhg Furlong, Cian Healy, Jamie Heaslip, Iain Henderson, Chris Henry, Jack McGrath, Jordi Murphy, Sean O'Brien, Paul O'Connell (captain), Peter O'Mahony, Mike Ross, Donnacha Ryan, Richardt Strauss, Devin Toner, Nathan White.
Backs: Tommy Bowe, Darren Cave, Keith Earls, Luke Fitzgerald, Robbie Henshaw, Paddy Jackson, Dave Kearney, Rob Kearney, Ian Madigan, Conor Murray, Jared Payne, Eoin Reddan, Jonathan Sexton, Simon Zebo.
