Well since we have to teach them to count and they do appear to have some form of language, they could just split themselves into a line and count off.
They would need poll watchers of some kind though, to be sure the count was done fairly.
They also live in smaller communities than people do, so I wouldn't imagine this would be a great solution for a whole nation of dolphins. But it would work for a large pod.
Interestingly what a chuckle fuck is exactly what I thought when I read this article.
One of my older siblings favorite turns of speech.