I couldn't find this info anywhere. In order to give a +1 (and increase the counter), the person who votes must have a google account.
But the question is. Is it enough for the voter to have let's say, a gmail account, or the vote will be registered only if the voter has a google plus account?
You need a public Google profile to use the +1 button. At this time, the only way to create a public Google profile is to upgrade to Google+. Some users with legacy public profiles can use the +1 button without upgrading to Google+.
From the FAQ:
In order to use the Google +1 button, you need to have a public Google Profile visible to the world, which at a minimum includes the name you chose for the profile.