You can also do it with a defaultdict:
year_person = {2000: 'Linda', 2001: 'Ron', 2002: 'Bruce', 2003: 'Linda', 2004: 'Bruce', 2005: 'Gary', 2006: 'Linda'}
from collections import defaultdict
d = defaultdict(list)
for k, v in year_person.items():
d[v].append(k)
print dict(d)
>>> {'Bruce': [2002, 2004], 'Linda': [2000, 2003, 2006], 'Ron': [2001], 'Gary': [2005]}