Non-veto wielding nations have tried for years to reform the U.N.'s post-World War II power structure with little success.
The treaty, which took effect in 2014, builds on efforts to protect women and girls from violence since the 1990s. Some nations say they oppose it based on sovereignty concerns.
The European Union and eight other nations condemned Saudi Arabia, demanding that it cooperate with a U.N.-led investigation into Jamal Khashoggi's brazen murder.
Even in a country with a tradition of hosting international organizations, one-third of all voters preferred to put the promise of "Swiss law first" ahead of global cooperation.
The centerpiece of the European Union's new rules, and what makes them relevant for international organizations, is the policy of accountability, experts say. Data handlers must be able to demonstrate compliance and delete data if asked.