If a city council votes to allow their police department to carry and use guns, and later a cop shoots and kills an innocent bystander, is it the city council's fault? No it is not. The city council voted for the police to use guns appropriately and judiciously. The council didn't vote for the police officer to misuse guns.
Joe Biden, along with 76 other US senators voted for the Authorization For Use Of Military Force Against Iraq Resolution Of 2002. That was not a vote for war.
Biden and the other senators voted the AUMF resolution with this main subhead: "Support For United States Diplomatic Efforts." Below that subhead and in the following section, the Senate voted to:
"Strictly enforce through the United Nations Security Council all relevant Security Council resolutions regarding Iraq and encourages him in those efforts; and
Obtain prompt and decisive action by the Security Council to ensure that Iraq abandons its strategy of delay, evasion and noncompliance and promptly and strictly complies with all relevant Security Council resolutions regarding Iraq.
Enforce all relevant United Nations Security Council resolutions regarding Iraq."
"[Support President Bush's] reliance by the United States on further diplomatic or other peaceful means alone either (A) will not adequately protect the national security of the United States against the continuing threat posed by Iraq or (B) is not likely to lead to enforcement of all relevant United Nations Security Council resolutions regarding Iraq; and acting pursuant to this joint resolution is consistent with the United States and other countries continuing to take the necessary actions against international terrorist and terrorist organizations, including those nations, organizations, or persons who planned, authorized, committed or aided the terrorist attacks that occurred on September 11, 2001." (see Congress.gov link below for entire AUMF resolution)
A little background is in order. Saddam Hussein, in an ill-advised bluff, gave the world at the time the impression that he had "the weapons to defend Iraq and the Arab nation" and greater weapons development capacity than Iraq actually had.
Iraq was cooperative on what inspectors called "process"—allowing inspectors access to suspected weapons sites, for example—it was only marginally cooperative in answering the questions surrounding its weapons programs.
On November 8, 2002, the UN Security Council adopts Resolution 1441. The resolution declares that Iraq "remains in material breach" of past resolutions and gives Iraq a "final opportunity to comply with its disarmament obligations" set out by Security Council resolutions stretching back to the end of the 1991 Persian Gulf War.
Remember too that "Iraq's era under President Saddam Hussein was notorious for its severe violations of human rights. Secret police, state terrorism, torture, mass murder, genocide, ethnic cleansing, rape, deportations, extrajudicial killings, forced disappearances, assassinations, chemical warfare, and the destruction of southern Iraq's marshes were some of the methods Saddam and the country's Ba'athist government used to maintain control. The total number of deaths related to torture and murder during this period are unknown, but generally estimated to be around 250,000".
"Human Rights Watch and Amnesty International issued regular reports of widespread imprisonment and torture."
The vote AUMF vote by Biden and others voted for resolution that was prefaced by a sting of 23 whereas statements including:
Whereas the efforts of international weapons inspectors, United States intelligence agencies, and Iraqi defectors led to the discovery that Iraq had large stockpiles of chemical weapons and a large scale biological weapons program, and that Iraq had an advanced nuclear weapons development program that was much closer to producing a nuclear weapon than intelligence reporting had previously indicated;
Whereas Iraq, in direct and flagrant violation of the cease-fire, attempted to thwart the efforts of weapons inspectors to identify and destroy Iraq's weapons of mass destruction stockpiles and development capabilities, which finally resulted in the withdrawal of inspectors from Iraq on October 31, 1998.
As the New York Times reported, "Ever focused on bipartisan consensus, Mr. Biden joined forces with [Republican Senator Richard] Lugar to produce alternative language that would give Mr. Bush narrower authority. The resolution authorized military action specifically for the purpose of dismantling a weapons of mass destruction program, and it emphasized "the importance of international support," Mr. Biden and Mr. Lugar said at the time."
Biden later acknowledged, the AUMF did not work as he had hoped. "It was a mistake to assume the president would use the authority we gave him properly," he said on NBC’s "Meet the Press" in 2005.