One way to check vote integrity now gaining adoption is the Risk-Limiting Audit (RLA) which brings mathematical rigor and adaptability to post-election auditing.
Risk-Limiting Audit (RLA): A Smart Way to Check Vote Integrity

Smartmatic's blog about electronic voting

One way to check vote integrity now gaining adoption is the Risk-Limiting Audit (RLA) which brings mathematical rigor and adaptability to post-election auditing.