shift/tip/tilt the balance of power
idiom
                                
              
          
                                                      : to cause a state or situation in which one country or group (such as a political party) has more power than a competing one                                      
              
                             
Their party's loss of two members shifted/tipped the balance of power in the legislature.
                                       The law tilts the balance of power towards corporations.
                         
                
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  Merriam-Webster unabridged




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