The case of a defeated New Mexico candidate arrested in a politically motivated shooting spree has turned a spotlight on an issue that has been evolving in the United States: whether people with criminal convictions are eligible to run for public office.

Solomon Peña overwhelmingly lost a bid for the New Mexico statehouse as a Republican and is accused of paying four men to shoot at the homes of four Democratic officials. He had denied his loss and made baseless claims that the November election was “rigged” against him, even though he received just 26% of the vote against the longtime Democratic incumbent.