If you want to find people who still believe in “the American dream”—the magnetic idea that anyone can build a better life for themselves and their families, regardless of circumstance—you might be best advised to travel to Mumbai. Half of the Indians in a recent poll agreed that “the next generation will probably be richer, safer and healthier than the last.”

The Indians are the most sanguine of the more than 1,000 adults in each of seven nations surveyed in early September by the market-research firm YouGov for the London-based...