Masses of FIlipinos support Duterte because they demand immediate change, and they believe that killing their way to prosperity is a legitimate option at this point. The Philippines had been a basket case since the 70s when Marcos began turning the country into a dictatorial despot, and after 40 years of economic regression, the people think that meaningful change can be achieved within a presidential term (six years). The preceding president, Noynoy Aquino, actually did a commendable job of steering the country in the right direction after four decades of backwardness, achieving the country's first-ever investment grade credit rating and turning business outsourcing as a major industry. But despite the data suggesting the country was finally improving, Filipinos everywhere still believed the president was a failure, and so they voted in a radical autocrat who now risks reversing all the country's recent economic gains. 40 years of poverty and corruption cannot be erased within six years, but don't tell that to Filipinos.
When you have millions of uneducated people who are as clannish, machismo, impatient and idealistic as Filipinos, the group consensus can be a horrible sight to behold.