Anyone paying attention to politics and the courts over the last 20 years or so has heard of some variant of the term The Counter-Majoritarian Difficulty. Coined by Alexander Bickel the phrase reflects the anti-democratic nature of the judiciary. Put very basically, if our structure of government is based on the will of the majority (and it is for the most part) then having unelected judges overrule the legislation passed by the majority's representatives runs contrary to democracy.
The simple resolution is that the judges are not overruling the majority's decision on the basis of their own whims, but rather striking down laws that are opposed to the Constitution. Since the Constitution was passed by a supermajority and is the supreme law of the land, it takes precedence over any regular legislation. Therefore if a judge feels that some legislation goes against the Constitution, he is within his rights to declare that legislation unconstitutional. There is no more difficulty because we don't have unelected judges striking down statutes; rather it is the Constitution itself, which was also the will of the people, negating those statutes.
The problem with this answer is that the Constitution is hardly clear. Many, if not most, of its clauses are ambiguous and vague and require some element of human interpretation. If that is true, then we are back to square one. Say, for example, a judge decides that the Equal Protection Clause of the 14th Amendment requires a flat income tax, because a progressive tax treats people unfairly based on their income. Surely such a view is not self-evident in the text itself. But is the judge wrong? It is a plausible reading of that clause. But if we allow any plausible reading of a constitutional provision to overrule the will of the majority, then the Constitution becomes nothing more than a hook for unelected judges to impose their own personal policy preferences. They are overruling democratic legislation, not the Constitution. The Counter-Majoritarian Difficulty rears its ugly head again.
One solution to this problem is for judges to have a methodology. Embedded in our system of courts is the concept of precedent. Precedent takes two forms: vertical and horizontal. Vertical precedent requires that a lower court accept the decisions of a higher court as binding. So the Court of Appeals in bound by the decisions of the Supreme Court no matter how wrong-headed the decision might be. Horizontal precedent is how the court's own precedents affect its future decisions. The Supreme Court is bound by its own precedent in the sense that it considers its earlier decisions weighty, but it can overrule those precedents if it wanted to do so. While the exact nature of horizontal precedent is hotly debated, it basically serves as a presumption of correctness if a similar case arises in the future.
Almost everyone accepts that precedent is binding on the courts in some sense. Precedent limits judicial discretion by requiring judges to deal with earlier decisions on the subject. So using my above example, since the Supreme Court has ruled that wealth classifications are reviewed under rational basis scrutiny (meaning the classification is constitutional as long as the court can provide a rational basis for the distinction, which it almost always can do), any judge who wants to render certain aspects of our tax code unconstitutional will have a very difficult time jumping the hurdle of precedent.
While precedent does serve a constraining function, some believe other methodologies work better. One of the justifications for Originalism (a methodology of constitutional interpretation that requires interpreting texts according to their original meaning) is that it points judges to an objective guidepost and therefore minimizes discretion. If the term "Equal" did not include wealth classifications in 1866, then the Constitution's original meaning did not prohibit a progressive tax code. Judges must square their decisions with objective historical analysis and that limits discretion greatly.
Whether this idea is true or not can be debated a different day. The fact is, however, that a methodology does serve as a means of constraining judicial discretion. A methodology requires the judge to take into consideration a number of extra factors, and those factors limit the possible outcomes. So Originalism and precedent do limit the number of judicial outcomes.
The common denominator between precedent and Originalism is that they both process-based constraints. We limit judicial discretion by forcing judges to take into consideration other factors besides the actual text itself. Methodologies (which includes precedent) imposes restrictions on how judges decide cases. It focuses on process. But there is another means of preventing judicial overreach: we could appoint the type of judges who wouldn't overreach. We could focus on the judge's character rather than how he would decide cases.
Traditional morality the last few centuries can be broken down into two distinct strands. Consequentialism, made famous by Jeremy Bentham, requires a moral agent to act in a way that has positive consequences. The most famous form of consequentialism, Utilitarianism, requires doing actions that increase overall utility. The opposing theory is Kantian Deontological Ethics, which focuses on duties and obligations. We must do acts that are required by a duty and refrain from acts that contravene an obligation.
The theme between these two moral theories is that they focus on actions rather than on the person. We must commit acts that have favorable consequences or are in concert with a duty. An alternative theory, Aristotelian Virtue Ethics requires that a person must act according to how a virtuous person would act. A virtuous person is one who possess a number of virtues.
How does this apply to the constitutional questions? Over the last few years Lawrence Solum has pushed the idea that constitutional theory should take into consideration Virtue Ethics. In his article The Aretaic Turn in Constitutional Theory Solum argued that when appointing judges, rather than looking at their methodologies, we should look for certain judicial virtues and avoid judicial vices. His list of virtues include judicial temperance, judicial courage, judicial temperament, judicial intelligence, and judicial wisdom. Judges who obtained these virtues should be confirmed. Judges who do not or have the countervailing vices should not be confirmed irrespective of methodology or ideology.
Interestingly we have a precedent for such a view. Even since I've become exposed to legal theory I've always been bothered by the lack of methodology in Halacha. There are rules of evidence like presumptions and precedent has a very important role, but there aren't any methodologies similar to Originalism of which I am aware. How do we avoid the problem of judicial overreach, which would be Poskim imposing their personal policy views on the population?
Yisro gave us the answer. In Shemos Perek 18 he tells Moshe that he must appoint judges. What type of judges should he appoint? In 18:21 he lists four judicial virtues: "אַנְשֵׁי-חַיִל יִרְאֵי אֱלֹהִים, אַנְשֵׁי אֱמֶת--שֹׂנְאֵי בָצַע" which can roughly translated as "men of accomplishment, G-d fearing people, men of truth, people who despise money." Basically Moshe should look for people who fear G-d and cannot be bribed. Such judges are less likely to be influenced by the litigants and will offer an honest judgment.
I can't say that Yisro was worried about judicial overreach in the same sense as Bickel, his list of virtues can serve as a starting point in the right direction.