Open-source software can be inspected by anyone. Increasing the number of eyes looking at source code increases the likelihood that subtle bugs will be unearthed. No company can bring as many eyes to bear as the Web can, so open-source software tends to be more robust and secure than closed-source software.
It's bad enough that vulnerabilities in consumer-grade software cost consumers and businesses millions, perhaps billions of dollars every year. The consequences of vulnerabilities in the software that controls our voting machines, or that counts the votes, could be the integrity of our elections.
For once, let's not wait for a disaster to occur. This is not a hard problem. Let's address it.