The headline on this obituary for R' Eliyashiv ("A One Man Supreme Court") got me thinking - why do we invest so much power in precedents set by individual rabbis, as great as they may be, but not in court rulings? Courts usually look to individual rabbis' prior rulings when deciding a case, rather than individual rabbis looking at previous court cases to determine how they should rule. Why is that?
First Rabbnic courts do look to previous decisions by other courts for guidance in their decisions. You will note on the Rabbinute's page regarding testing to be Dayyan that one is tested specifically on Piskei Din. Piskei Din of which 18 volumes are available free online, are the previous rulings of the High Rabbinical court of Israel. Regarding the Teshuvot of Rav Eliashiv in particular, in his sefer Kovetz Teshuvot, according to the seforim blog, they are simply culled from Piskei Din from the years Rav Eliashiv sat on the court. Likewise many works of Teshuvot by great Rabbis are their recorded decisions from times that they sat on Batei Din. So part of the answer is that they do rely upon previous court decisions for precedent. However, and this is of equal importance, precedent plays a very minimal part in Beit Din process. Secifically the Shulchan Arukh in Choshen Mishpat 10:1 and 10:2(as well as other places), state that one should not rely too heavily on precedent, but rather should treat each case as it's own entity.
I believe there are two, closely related, reasons for why we look to written rabbinical decisions for halachic precedence, but we do not look to previous court decisions.
The first reason is that, generally speaking, a court does not issue a detailed explanation of how they came to their decision. Such an explanation is essential for using the decision as a precedent. Real-world cases are, almost without exception, extremely complex, and even apparently minor details can have a major impact on the final decision. Thus, even when two cases appear to be very similar, without knowing the exact details of the case and the reasoning used by the rabbis on the court, there is no way to make use of a court decision as a halachic precedent.
A second factor that makes it problematic to use court decisions as precedent is that a court may reach a final decision without the judges actually agreeing on the reason. For example, a court may find John Doe liable for damages to his neighbor, but the judges, while agreeing on the final judgement, need not necessarily agree on the reasoning. So, again, without a clearly presented explanation of how and why they came to their conclusion, there is no way to make use of the precedent.