In the UK, parliamentary votes are usually public, so that MPs remain accountable for their actions. Since 2009, votes to choose the Speaker of the House of Commons have been taken by secret ballot. I am curious as to why this vote is done in secret.
The rule was introduced in 2001, following the 2000 election of Michael Martin. That election took place "by means of a conventional parliamentary motion with recorded votes on an amendment for each candidate". Due to the large number of candidates, the repeated ballots took 6 hours. The process was also politically charged, with party whips lobbying MPs to vote for specific candidates, and Martin's election was controversial, since it broke with the tradition of alternating the role between the two main parties.
The new rules, introducing an exhaustive secret ballot, were intended to speed up the process and make it less political.
"In a significant departure, MPs will vote in a secret ballot, away from the eyes of the whips. A secret ballot also ensures that MPs will not be forced into voting for the most popular candidate out of a fear that their lack of support might be punished by the new Speaker in future debates." — Daily Telegraph, 20 May 2009
I suspect, but have not yet found a smoking gun, that the answer lies in the previous election in 2000:
This was the last Speaker election to be conducted by means of a conventional parliamentary motion with recorded votes on an amendment for each candidate. With an unusually large number of candidates, a significant number of MPs spoke in favour of switching to a less time-consuming procedure, but Sir Edward Heath, who was presiding in his capacity as Father of the House, declined to allow a vote on this issue.
The repeated ballots took nearly six hours. Each candidate gave their own speech of submission to the will of the House, having each been nominated and seconded by Members in separate speeches. Martin was the front runner going into the ballot and was never in any danger of losing during the election, winning every ballot by at least 76 votes.
As a result of this election, the rules for electing a Speaker were changed the following year to a use a secret and exhaustive ballot. This procedure was first used in the Speaker election of 2009.
On the other hand, I can't tell if there was actually any improvement:
At the election of Speaker Bercow in 2009 proceedings started at 2.30pm and there were three rounds of voting with the Speaker-elect taking the chair at 8.30pm.