Providence firefighters have set a second vote for Jan. 2 to decide whether to approve a modified settlement with the city that freezes pensions and makes other benefits changes. The firefighters union and retirees have already approved the settlement. But the union is holding another vote. Union head Paul Doughty told the Providence Journal on Monday that members want what he termed modest changes, including a clearer explanation of what the city pays into the system. He said he expects the changes to pass. The city negotiated settlements with police and firefighters as part of an effort to help avert bankruptcy. The city says the agreements reduce its unfunded pension liability by $178 million, from $903 million.