"Will have" refers to an event in the future that precedes some other event in the future. "By the time the police arrive, I will have hidden the evidence." At some point in the future the police will arrive. Before that time, but still after the present time, I will hide the evidence.
"Would have" refers to a past hypothetical. It is used when you want to say that an event didn't happen, but that in some alternate universe where conditions where different, it did happen. (Okay, that's an odd wording, but I'm struggling how to express the idea without using the words "would have". To say, "would have" refers to something that would have happened ..." probably doesn't help. :-) Like, "If Sally had passed the test, she would have gotten the job." Sally didn't pass the test and didn't get the job, but if she had passed the test, then she would have gotten the job. "Jack would have won a fair contest." Jack lost the contest, but if it had been fair, he would have won. (Or perhaps there never was any contest, but if there had been a fair one, he would have won. Depends on context.) The condition doesn't necessarily have to be spelled out in a simple IF/THEN construct. You could say, "Mr Smith died before I was born. I would have liked to have known such a man." In this case the condition is clear from the context: if our life-spans had overlapped. It could certainly be more subtle.
I'm struggling to think of any other use of "would have". If another poster here thinks of one, please feel free to shout it out.
You could not use "would have" instead of "will have" in the above paragraph, because (a) there is no condition on Jack selecting the living quarters, and (b) even if there was, "would have" is used for past events, not future events.
Best Answer
When it's possible to say "they said they will", the will can be changed to its past tense (would) because said is past tense. Although "they say they will" may also reference something said in the past, you cannot use would instead of will because would will take on a different definition ("used to give advice").
Context indicates that will could've been used both times, but it seems like the author chose to change one to avoid sounding repetitive.
Will Means Still
When can will be used? When it's something that still is likely to happen. If you think about it this way, the "future at the time when the author was writing this article" is the same as the "future at the time when the survey was conducted". (It's reasonable to assume everyone's still planning to do what they said, since the survey is probably recent.)
You can't use will if: