One question which faces every conclave and which plays an important role in every election is: do the cardinals want another pope in the same mold as the previous and who will continue the same basic policies, or do they want a pope who will break with the past and take the church on a new course? In answering this question, the cardinals go through two stages of inquiry, much of which actually occurs before the conclave.
First, they must make a careful and honest analysis of the previous popes work. One of the advantages of using cardinals to elect a pope and not bishops is that the cardinals are answerable to no one. Unless they desire to become pope themselves, there is no higher post for them to covet and so no great need for them to curry favor with someone else.
Thus, the fact that someone was made cardinal by the previous pope is no guarantee of him giving a glowing evaluation of that popes work. Much of what is said in public will certainly be positive and supportive; what is said behind closed doors, however, may be of an entirely different character. Cardinals who have passed the maximum age of eighty will also take part in conversations which occur before the actual conclave.
The second stage involves trying to determine, insofar as is possible, which features of the last pontificate derived from which aspects of the popes character. This is a necessary step if the cardinals are going to figure out what they want to look for or not look for when figuring out who should be their favored candidates for the next pope.
The current pope provides a good illustration of this process because he is unique in a number of ways for example, he was the first Polish pope and he was one of the youngest popes in long time. Aspects of John Paul IIs papacy which will receive close attention will include his indulgence of Opus Dei to the exclusion of other organizations (Jesuits, Franciscans, Dominicans, etc.), his close attention to young Catholics, his heavy involvement with European affairs, his insistence on a monarchial papacy where disagreement is treated like dissent, etc.
Cardinals will have to look at features like these and see if any of them can be attributed to his Polishness, his youth, his conservatism, etc. Another Polish pope is unlikely regardless of the circumstances, but if for example his preference for Opus Dei could be attributed to his Polish background and the cardinals wanted a change when it came to that issue, then it would be a mark against any Polish candidates.
Will the elector cardinals want the successor to Pope John Paul II to continue his policies or to mark a change? Thats a very difficult question to answer. They will almost certainly approve of a continuation of some policies, like the efforts to reach out to young people. Other policies, however, have created deep divisions within the Roman Catholic Church and this is not something that will receive a great deal of applause in private conversations.
Popes are often able to do a better job if they are able to understand and present both sides of an argument, even when they tend to agree with one side rather than the other. This has not been a common trait of John Paul IIs papacy on the contrary, he has often dismissed the other side as dissent from orthodoxy and rejected the very principle that there can be a loyal opposition within Roman Catholicism.