Just what it says in the title. What if Crown Prince Rudolf didn't make a murder/suicide pact and continued to live? How would Rudolf's survivinal change the course of the Austro-Hungarian Empire? His political views were supposedly liberal but would that be enough to save the Empire? I read in Twilight of the Habsburgs by Alan Palmer that he supported centralization within the Austrian half of the Duel Monarchy, with the creation of unified Liberal and Conservative parties, I assume similar to those in the UK. Would this help or hinder the Empire? Would it be possible to implement? Would WWI still happen? What about the succession? He had one daughter, Archduchess Elisabeth Marie, had supposedly infected his wife, Princesse Stephenie of Belgium, with a venial disease and was considering divorce/annulment of the marriage at the time of his death. So would we see Princess Stephenie being set aside for the matter of Succession? if so who would the Crown Prince marry? If not, would he see this supposedly liberal man change the succession laws to allow his daughter to become Crown Princess and eventually Empress-Queen, emulating their famous ancestor Maria Theresa?
There's an awesome mini series in English about Rudolf; it's called
The Crown Prince, made in 2006. It's definitely a little idealistic and includes a completely fictional subplot involving Rudolf going around Vienna in normal garb, meeting a young Jewesss girl and falling for her, as well as some cameos by Prince Wilhelm of Prussia (IE Kaiser Bill), but it's actually very good and let's you get into the mind of Rudolf, his relationship with parents, and his beliefs. It's split into two parts, both 1 1/2 hrs long, but it's really good.
Anyways, as for the actual Crown Prince...
He was definitely a liberal in the classic Westminister sense; he support expanded industries, railroads, and technology. During his time as crown prince, there was a school law passed that essentially allowed children to leave school at 12 in order to help their parents in the fields, or to get a job, ect. I'm not sure what his views were vis a vis the status of the empire as a dual monarchy: he definitely did not like Prime Minister Taafe, and despised his Iron Ring which dominated the Austrian Parliament for over decade, and was essentially a "conservative" party, although it was merely a loose clique united around Taafe that included clericals, Slavs, and the agrarian land owners.
Another issue is indeed the Archduchess Stephanie and the venereal disease. Rudolf had contracted syphilis (how he caught it I don't know, but it seems he was a frequent visitor of brothels, had mistresses before the Baroness Mary Vetsera). By the time he committed suicide, he was getting sick. His doctors were advising him that the climate in winter was not good for him, and that he needed time to recuperate and rest abroad, either in Corfu or the Azores, but Rudolf never did so; he constantly craved his father's approval and never got it because Franz Josef was old fashioned, conservative, and all about the military, while his son was an intellect and wanted a share in the government that Franz Josef was never willing to give him, as he believed he was too immature.
Rudolf also clashed with Stephanie; again while he was much like his mother, being both idealistic, liberal, and impulsive, Stephanie was basically the kind of woman whom would've been Franz Josef's perfect type had she been born forty years earlier: she was religious, reactionary, and traditional. She lived a typical life as Crown Princess, she lived to host dinners and socialize, while Rudolf did not. I've heard he actually appealed to the Pope shortly before his suicide for a possible divorce or annulment, but the Pope gave no answer and informed Franz Josef, who was appalled. He essentially told Rudolf to grow up and basically mend his marriage.
Because we know so little about Rudolf, I don't know how he would be if he actually become Emperor, if he would change the succession laws. He loved his daughter dearly, but would he want to put the burden of reigning a multiethic empire upon her shoulders? If he saw potential in her, perhaps he would work to set aside the law; after all, Hungary had reigning Queens in the past, and there is Maria Theresa for precedent. It's hard to tell how she would reign, too. Her life is somewhat documented, but a lot of her life choices were due to the empire collapsing, like her being known as the "Red Archduchess" and being a socialist.
For Rudolf, we need some two big changes before even touching political stuff.
A) Keep him out of the brothels, or at least away from whoever gave him syphilis. There's no cure for it in this time period; all the doctors did for Rudolf was suggest time in a warmer climate. They also provided him with copious amounts of morphine to alleviate the pain and discomfort. The first pain killer essentially synthesized from opium poppy, it was hailed as a miracle cure and by the 1880s was used for all kinds of aches and pains, and was even in cough syrup and liberally prescribed, if not simply buyable at the chemist. Rudolf can't lead Austria or solve it's structural issues if he's hooked on morphine or in the late stages of syphilis; get him a mistress early in life, someone like Mary Vetsera, but pragmatic and encouraging of his pursuits, preferably a lady who belongs to the high nobility, or at very least the rising business class.
B) Get him a different wife. He basically got married because of Franz Josef nagging. He could've picked her at random for all we know, for we know he went to Belgium, spent one day with her, then proposed. The marriage was postponed because she hadn't reached puberty. The Empress Sisi was also no fan of Stephanie, she reportedly called her a clumsy oaf and "a stupid elephant." Rudolf is sort of restrained because he is of course a Habsburg and is expected to make an equal marriage, and there are far fewer reigning Catholic dynasties than there were thirty years before, although marriages into deposed dynasties were still considered equal (Archduke Charles marrying Zita of Bourbon-Parma, for instance). Ideas that come to mind:
Mercedes of Orléans,
Maria Immaculata of Bourbon-Two Sicilies,
Maria Alexandrovna of Russia Marie d'Orléans to name jusr a few princesses near his age range. Maria Alexandrovna may be a bit out there, but I recall one of Tsar Paul's daughters married into the Habsburg dynasty in the late 18th century, although she died in childbirth...