MAYABUNDER, India—The midday sun was blazing when Biswajit Roy, a middle-aged Indian high-school teacher, gingerly pulled himself, and two voting machines, into a modified dugout canoe.

His mission: Traverse crocodile-infested mangrove swamps, cross a stretch of open sea and then hike through a jungle to the remote village of Hanspuri so its 261 voters could cast ballots in India's national elections.

"When...