I have installed the module that you mentioned and got the same error. It seems that even though the Vote Up/Down module allows you to give anonymous users permission to vote, internally, it does not support it and throws the specific error. I suspect - I'm guessing here - that they are using the user id to "save" what the logged-in user voted and when the user id is 0 (which means anonymous) an error is thrown.
Anyway, the way I see it, there are 2 main paths that you can follow in order to get the functionality that you want:
1) Have someone (= a drupal developer) modify the module for you. This way, you will be able to add the functionality, and even submit the changes it to the module's repository.
Pros: you help the community, you get a clean solution (depending on the developer's skill)
Cons: costly (I suspect), takes time, you get bad code and patch the problem (depending on the developer's skill)
2) Get the functionality through theming. Instead of enabling the module for anonymous users, you can just disable it, and through the node-nodetype.tpl.php file you can just show the image of the voting arrows to the anonymous users (you will have to use an if conditional to check if the user is logged in or not) and make the image point to a link like this:
This way the user will be redirected to the login form and then back to the node, but he will have to press the vote button again.
Pros: easy to implement, theme based solution = minimal interaction with code
Cons: it's really a work-around, not a solution, the user is not actually voting but he thinks he is voting (not really honest :P)