Investigate the cabinlist on ET. That gives you an idea about what rooms were occupied. I have to tell you that the cabinlist isn't fully reliable, cause we don't know all the right cabinallocations. Some of them are rather a guess. You will see that many rooms were unoccupied, but it isn't sure that they were indeed unoccupied during the voyage.
It is really hard to tell which cabins were unoccupied, especially if you consider that some are not known yet and are unlikely to ever be known and that passengers changed cabins, and who knows who changed to what cabin.
Approximately 40% of all first class cabins were not occupied. I can tell you for sure though, that cabins B82, 88, 90, 92 were not occupied.
Bedroom steward Etches, in my opinion, made it pretty clear that the rooms Daniel mentioned were vacant. Guggenheim shared B-84 with Victor Giglio and didn't need the entire suite. If Guggenheim had wanted an extra cabin for his valet, he would have used one of the smaller inside cabins. The nearest cabin of this sort was B-86, which was occupied by Alexander Cairns, the Carter valet
The most reliable life-saving devices on Titanic were those empty cabins. Not one person who was not aboard died as the result of the ship sinking. No, I'm not trying to be funny. It is a serious matter that has been avoided for 90 years--why were so many cabins empty?
Most books pass it off as a result of the coal strike. This explanation defies logic. Lots of smaller passenger ships were tied up and idle because of the strike. The removal from service of a substantial portion of the passenger fleet should have created demand for berths in excess of what Titanic could supply. Yet, the ship sailed with empty cabins. Why?
That is an intriguing question. I suppose part of it may have been due to the coal strike. People who might have traveled to the U.K. may have been inclined to travel to places not effected by it. That's what I would do.
Another factor for some would be the fact that this was a maiden voyage, which was not always popular to begin with...at least among seasoned travelers who were well aware of the fact that new vessels always had some bugs still in them which could make for an unpleasant crossing.
As to those who might otherwise have been traveling but declined to do so...well...that makes for some interesting fodder for speculation. Interesting question Dave.
Also consider passenger load was effected by the seasons, and that the high season was still a month away. May - September ships usually sailed with a full compliment of passengers. You will notice that generally maiden voyages are timed to allow ships to miss entirely the leaner winter season. Olympic's maiden voyage was in June, Majestic in May, Queen Mary and Aquitania in May, the United States in July. Certainly their are exceptions such as Lusitania and Mauretania. Their maiden crossings in the fall of 1907 readily spring to mind as does Homeric in Feb. 1922. Something would be amiss had Titanic made it to July and sailed half full. In addition I believe I recall reading that the return crossing was much better booked.
Mike H. makes an interesting point. Potential passengers may have been elsewhere and boarding ships from other European ports not affected by coal strikes.
However, at this time passengers may well have been avoiding "The Olympics". During her maiden voyage the Olympic almost crushed a tug. Three months later she was significantly wounded and required an extensive renovation that resulted in her missing three round trips and in February of 1912 she lost a propeller blade. This may all have helped to wilt her popularity of her first few months in service. I haven't got specific statistics, but in some late 1911 or early 1912 trips Olympic carried a total of 400 passengers throughout all her classes.
On April 3, 1912, a week prior to Titanic's departure, Olympic sailed from Southampton. She arrived in New York on April 10, with the exact same complement of 1st class passengers, that Titanic would have on April 14, 1912 -- 324 (including Nourney, who transferred from 2nd).
It wasn't just Titanic that was so under filled, it was Olympic as well. Perhaps it wasn't just those ships, perhaps all other ships still in service were also experiencing a lack of passengers.