Most votes in legislatures are done by open ballot, often by calling of the rolls. Everybody's vote is very public. Since legislators work for us, it is important we know how they vote.

At the same time, secret ballots have a lot of virtues. People can vote their true intention, without fear of reprisals for their vote. Legislators are supposed to fear reprisal from their own voters, but not from other entities such as other legislators, political parties, donors etc. Many a time it's been the case that there was a result that was actually supported by the majority (sometimes a big majority) if you poll them in private, but which most are afraid to support in public.

To deal with that, in 2006 I proposed the use of cryptographic techniques to test secretly popular ideas which has many applications in legislatures and beyond. It's possible to create a mathematically secure system where people cast votes, but the votes can only be decrypted after a majority of the voters have voted "aye." Thus you could have a vote on legalizing marijuana (which most support in secret) and once a majority were in favour, it would be revealed and simultaneously become law, with no shame in having voted for it since now you're in the majority. People are afraid to be in the minority but they could fear it less.

A non-cryptographic way

Here's a way to do this without crypto. Pass out paper ballots, which come as a pair of nested envelopes. The inner envelope is actually pre-sealed with the elector's name inside. On the outside is the ballot, such as a boxes to check for yes/no. The elector takes their envelope and writes their choice on the outside, then puts it inside a plain outside envelope -- or alternately it just folds in half to hide the vote and it is placed in a ballot box.

For counting, the ballot box is opened in front of everybody. The outer inner envelope is extracted and the choices on it are tallied. If "yes" wins the day, the inner envelopes are opened, and the names of who voted yes or no are revealed.

If "no" is the winner, however, the envelopes are destroyed in front of everybody. Burned or put in a secure shredder or similar. The names are erased.

Impeachment conviction

This might be a good voting system for impeachment. Senators are very afraid, not just of voters, but of Trump and others in their party, of donors, of Fox News and other entities. They don't want to be part of a small group rebelling against Trump and his faction. That could lead to doom. But if they know that the rebellion will win, that a majority of them have joined it, more might sign on.

This could even be done in caucus. They could hold such a vote in caucus with whatever threshold they want. In particular, not just 17 GOP, but 26 of them, a majority. They could decide "If 26 of us vote to convict, then expect, but can't force all to convict. If 26 don't vote that way, then we expect, but can't force all to acquit." Or they could use 17 as the magic number, depending on what McConnell wants -- the logic being that "if we're going to do this, we might as well go all-in."

The counter to this is that Democrats want to force the Republicans to be public with their choice, hoping that those who support Trump will pay a price for it later. That's worthwhile -- but for now most are more afraid of Trump than they are of being punished for supporting him, and the insurrection, in the future.