MARKHA VALLEY, India — Staring up at the steep and lifeless brown ridges looming over the valley, Gulzar Ahmad Dar, a boyish and chatty Kashmiri policeman, sighed at having drawn a short straw.

“What miserable luck I have,” he said, peering down the funnel of mountains toward the village of Markha, his destination, 22 grueling miles away. “But somebody had to get this place, no?”

Mr. Dar, 25, was the youngest in a group of five government employees randomly assigned by a computer to election duty in this exceedingly remote valley. The members of this polling team, like all the others across the country, were plucked from their day jobs and given the temporary but vital task of ensuring free and fair voting.

Voting ended Monday in the six-week exercise — the largest election in history — which included more than 800 million registered voters casting ballots in fetid slums and on palm-fringed beaches, from sultry, monsoon-drenched forests to the hostile windswept barrens of India’s craggy northern edge.