Which type of opinion should someone consult to understand why a particular Supreme Court justice agreed with the Court's ruling on a case?

Views of denied appeals. The Supreme Court receives about 10,000 petitions a year. The Justices use the "Rule of Four" to decide if they will take the case. If four of the nine Justices feel the case has value, they will issue a writ of certiorari. This is a legal order from the high court for the lower court to send the records of the case to them for review. When all is said and done the Supreme Court will hear about 75-85 cases a year. This tells us that most petitions are denied. The Justices of the Supreme Court are most likely to take cases that will affect the entire country, not just the individuals involved. They want to clarify legal issues that are important to as many people as possible, so they take cases that will have a large constitutional impact, or that answer important legal questions that affect the whole nation.