Had you asked me the question posed by the Biur Halacha quoted in the previous post, I would have given a simple answer (or to be more accurate, denied the premis of the question). True, if you do the melacha of an entire week in one day you reduce the odds of chilul Shabbos from 7/7 to 1/7, but that tactic assumes that chilul Shabbos is calculated based on the overall weekly (monthly? yearly?) basis. Who says that is the case? Perhaps each day must be looked at individually. The fact that chilul Shabbos can be avoided in future days based on actions taken today is irrelevant and need not be taken into consideration, especially given that the additional action done today is itself further chilul Shabbos. I can even imagine practical ramifications to this question. If someone is sick and must be mechalel Shabbos one week, may one engage in greater chilul Shabbos if it would potentially speed up recovery and eliminate the need for chilul Shabbos next week, or should one observe as much of Shabbos as possible and worry about next week when it comes? I am not really sure of the answer and don't see why the former position is unquestionably right. Happily for me I received an e-mail from someone in response to the previous post that offered a sevara along the same lines as my own, so apparently my knee-jerk reaction to the question is shared by others.
The Biur Halacha does not offer this answer but does present an elegant bit of lomdus. On any given day, the only work that is permissable is work necessary to remain alive -- pikuach nefesh. We asked: why be mechalel Shabbos every day when one can do all work needed one day a week? The answer is that one is not in fact mechalel Shabbos every day! Since Shabbos may be violated for the sake of pikuach nefesh, the work done is not chilul Shabbos. Only doing more work than necessary for pikuach nefesh would be chilul Shabbos, and therefore no preparations for future days may be made.
I certainly take nothing away from the M"B's answer, but am curious as to whether my sevara is off base and if it is, why. The next question I think will get us closer to a better understanding. The assumption behind the halacha is that each day has an equal chance as any other of being the real Shabbos and based on this uncertainty we must adopt a strict position and treat every day as the potential real Shabbos. But, asks the Magen Avraham, why should this be so? We know that in halacha there is a principle of bitul b'rov, i.e. a minority can be ignored in favor of a majority. If there are 9 stores selling kosher meat and 1 store selling treif meat, a piece of meat found on the street may be assumed kosher given the 9/10 probability that this is correct. Here too, given that 6/7 of every week must be days of chol and not Shabbos, why not say that any given day is chol based on the principle of rov? To be continued, bl"n.