Antonio Mugica was in Boca Raton when an American presidential election really melted down in 2000, and he watched with shocked fascination as local government officials argued over hanging chads and butterfly ballots. It was so bad, so incompetent, that Mr. Mugica, a young Venezuelan software engineer, decided to shift the focus of his digital security company, Smartmatic, which had been working for banks. It would offer its services to what would obviously be a growth industry: electronic voting machines. He began building a global company that ultimately provided voting machinery and software for elections from Brazil to Belgium and...