VILLUPURAM, India—Indian politicians have a long tradition of wooing voters with promises of handouts like grain subsidies. But in this month's elections in the state of Tamil Nadu, politicians are plowing some new ground: They are promising to give away blenders, sheep, bus passes, gold necklaces and cable-TV hookups if they win.

Despite being one of India's better-performing states and its auto-industry hub, Tamil Nadu has its share of serious issues to debate this year, including how to halt corruption and fix electricity...