WASHINGTON--Public employee unions survived a threat to their power in nearly half the country Tuesday as the Supreme Court deadlocked on a lawsuit designed to abolish their ability to require compulsory dues in more than 20 states.

The 4-4 vote is the most dramatic consequence yet of last month’s death of Justice Antonin Scalia. His comments at January arguments suggested he would have voted to overrule a 1977 precedent allowing public employee unions to collect mandatory dues from represented workers if authorized by state law.