Just in case you thought something as simple as the manner in which a vote takes place is not consequential, consider the aborted attempt to take down Tom Craddick, the once and still Speaker of the Texas House of Representatives.
Unlike the United States House of Representatives, which is strongly organized around party lines, the Texas House has rules which allows for firm control by a well placed individual. The key mechanism is the fact that (1) votes for the Speakership are public and (2) the Speaker gets to select who gets on what committees and who chairs them. This puts rank and file members in a bind because they can be punished if they back the wrong candidate. Craddick has a reputation as someone who does not handle dissent very well, and has no qualms about punishing opponents. Since this makes House members nervous, they tend to be vague about who in fact they are going to vote for.
Nevertheless, an apparently autocratic leadership style led to a challenge to his leadership by two fellow Republicans, Brian McCall and Jim Pitts. Pitts was the eventual sole challenger, but his candidacy rested on a proposal that the votes for the Speaker be made public immediately. Pitts argued that either they be made public after committee assignemnts were made, or never. This obviously gives political cover to his supporters. Craddick supporters are arguing that member's constituents deserve to know immediately who their reps voted for, which may or may not be a good point, but Craddick certainly wants to know before making committee assignments or else he has no weapon to use to enforce support.
A move to have a secret ballot was defeated though, causing Pitts to withdraw his bid since there would be no cover for his supporters. Craddick was reelected overwhelmingly 121-27.
Only Democrats voted against him.
Now comes the fun part. Which commitee assignments will Pitts, McCall and the Democrats get?
Welcome to Texas politics.
Note: Though votes for the Speaker are public in the U.S. House, votes for party leader are secret, and held within the party caucus, which means that the leader of the majority party automatically becomes Speaker. And this is not an issue in either the Texas or U.S. since the head of each is elected by the general public.