When Gillespie County Republicans conduct their primary in March, they will count votes in an ill-advised way: by hand, using scores of volunteers, without any machines.

Even if they can pull off their expensive, labor-intensive plan, they risk being sued by losing candidates or reprimanded by the state. And they may run up a huge bill of unnecessary costs.

“Hand-counting is a recipe for disaster,” said Bob Stein, a political science professor at Rice University and election administration exp...