"The dinner with your fiancee or the meeting? I do these kinds of decisions every single day." - what decision?! If you scheduled something with someone to a certain hour and then you have other appointments, if the person does not arrive on time is not your fault and you've got to move on to the next appointment!
Taking the example of CocaKoala: you schedule a meeting, that is supposed to last 1h, to 4pm. So the meeting would take place from 4pm to 5pm. Then you'd schedule to have dinner with your fiancée at 6pm. Well, has the meeting supposedly finished at 5pm, you can get on time to this dinner. BUT if the person you're meeting with decides to only show up ate 6pm, all your later appointments will be ruined! I would never wait 2h for someone, especially if I have other appointments. And if you hope that someone will wait for you all that time either that person is too much patient with you or doesn't have anything else to do...
Btw if you make an arrangement, it's your responsibility to show up on time! Is not about how busy you or the other person are, is about respect!!
Best regards ;)