Are there any states or countries whose Legislature uses a secret ballot in order to pass bills?
Not quite the same, but voice votes are anonymous. Congress uses them for routine matters and they’re official, unless someone challenges the result.
I consider it a middle step. It’s anonymous to the outside world (mostly) but not to those around you (like a party Whip). But yes, I would also be interested in knowing about voice votes.
Italy used to use them, but it was a bad idea. Members would say they planned to vote for a bill, and it would go forward because it had a majority of support lined up, and then would be defeated in the chamber on a secret ballot. And every member who had said they would vote for it would say afterwards that they had voted for it; must have been someone else who had reneged.
Made it very difficult to plan for legislation, and impossible for voters to hold their members to account.
I believe the Canadian parliament has a secret ballot to elect the Speaker of the House. This helps prevent the majority party from twisting arms to put a partisan person in the speaker’s chair. The speaker gets elected by members without the Prime Minister being able to dictate the choice. (Too much pressure can backfire)
As has been pointed it, it’s very bad for electoral accountability to not know how your representatives voted. I’m surprised anyone has ever used them in an electoral representative democracy.