WASHINGTON — Senate Republicans today failed in their bid to overturn a new rule making it easier for unions to organize workers in the airline and railroad industries.

The Senate voted 56-43 against a GOP resolution that would have prevented the Obama administration from enforcing the rule.

The new rule, approved by the National Mediation Board in May, changes how votes are counted in union representation elections. It allows employees to unionize if a majority of those voting support the union.

Under the old rule — in place for more than 75 years — a majority of all workers in a unit had to favor union representation. That meant workers choosing not to vote were treated as "no" votes.

Advocates say the change makes elections more democratic and brings airlines and railroads in line with other industries, where the outcome is decided by majority vote.

But Republicans called it political payback to unions and argued that such a dramatic change in the way votes are counted should rest with Congress, rather than a politically appointed board.