Right now, votes in both US houses have been made into a currency = cash via lobby, and also by offshore transfers, or even via bagmen.
In the UK each party must vote as the party leader directs, or in a free vote where each person can choose freely.
In the USA there is some degree of party voting, but this visible vote can be seen and the response to a lobbyist $$ or bagged $$ and the payor knows how he voted and can act to discipline the member of the house or senate. This is a degree of departure from democratic ideals. Yes, I know bribes are outlawed, but there are ways, quid-pro-quo actions.
I wonder if there can be 2 votes, one by hand and the other secret, to give deniability and the member can vote his mind in the secret one. The secret one wins, and the show of hands is for show?