By Isla Binnie
ROME (Reuters) - Twenty-year-old Francesco Incorvaia, a sociology student from Rome, was just the kind of voter Matteo Renzi had spent years trying to win over.
Italy's youngest ever prime minister had changed labor laws in a bid to reduce one of Europe's highest youth unemployment rates, handed cash to low earners and proposed constitutional amendments to streamline lawmaking and boost an ailing economy.
But Incorvaia and millions of other young Italians walked into voting booths at a referendum on Sunday and effectively threw him out of office, handing him a stinging defeat that left him no choice but to resign.
"At least this way there is an idea that the people can still have some say, without leaving too much power in the hands of people who don't care about us," Incorvaia said, standing outside his university department in Rome.
According to a survey by research firm Quorum for SKyTG24, about 80 percent of voters aged between 18 and 34 opposed Renzi's proposal to shrink the upper house Senate and claw back power from regional administrations -- a tsunami of opposition from a generation that is rewriting the political map in Italy.
Despite his youthful vim, Renzi, who was 39 when he took the premiership almost three years ago, came to be seen as part of the creaking old establishment he pledged to revamp.
With Renzi pledging to step down, the younger generation's preferred anti-establishment 5-Star Movement has called for early elections and said it is ready to govern.
M5S campaigned hard against Renzi's constitutional reform proposal, on the grounds it would remove democratic checks and balances, and it was clear many young people were also expressing their support for 5-Star in voting it down.
"Lots of people in the 5-Star Movement are young, so they seem like a new start compared to the 80-year-olds in the other parties," said Veronica Bagaglini, 20, a student from near Rome.
Rising support for 5-Star has sent shivers through financial markets because the movement has promised to call a referendum on Italy's membership of the euro.
It rivals Renzi's Democratic Party as the most popular party in opinion polls and would be favorite to win elections under the current system, which may be changed as mainstream parties seek to keep them out of power.
Young voters helped propel 5-Star into power in the municipalities of Rome and Turin this year. Overall, voters under 35 years of age represent about a fifth of the electorate.
"For me the victory of the 'No' vote is above all an important signal, it signals that the people are tired of enduring the policies of austerity (and) neoliberal politics of Renzi's government and the previous governments," said "Students for No" campaign representative Federica Ciarlariello.
Many first-time voters in Sunday's referendum grabbed the chance to register their frustration with mainstream politicians, including Renzi, who have presided over what, for them, has been a lifetime of economic stagnation.
"There is a school near here where there were mice, the ceilings fell in, and the toilets didn't work," Incorvaia said.
Prospects beyond school remain bleak.
A new law Renzi passed to make it easier for private companies to fire workers was meant to encourage employers to hire. But the law only applies to new hires, while changes to the pensionable age by a previous government mean their older colleagues now stay in the workforce longer than before.
Today, Italians under 35 earn 26.5 percent less than their contemporaries 25 years ago, while income for the over-65s has risen 24.3 percent, according to research firm Censis.
The 'Yes' vote prevailed only in provinces where youth unemployment is below the national average of 36 percent, according to the Info Data unit of Il Sole 24 Ore newspaper.
"There has been an unprecedented and perverse trick, a transfer of resources over time that has literally knocked out millennials economically," Censis said.
Using an Internet-based model of direct democracy, 5-Star has cemented its support base among younger voters by pitching honesty and integrity as more valuable than the experience of parties sullied by decades of scandal.
"Corruption is everywhere in Italy, and it needs to be tackled," said Rome student Bagaglini. She said it was difficult to believe that even 5-Star could make a difference, then added: "But why not?"
(Editing by Mark Bendeich and Philippa Fletcher)