Andrew Gelman has an interesting graph showing governor approval rating set against state population:
The takeaway, basically, is that small states tend to be more approving of their governors. Why? Gelman has some theories: "In a large state, there will be more ambitious politicians on the other side, eager to knock off the incumbent governor; small states often have part-time legislatures and thus the governor is involved in less political conflict; small states (notably Alaska) tend to get more funds per capita from the federal government, and it’s easier to be popular when you can disburse more funds; large states tend to be more heterogeneous and so it’s harder to keep all the voters happy. As the graphs show, the pattern isn’t perfect, but it looks real to me." That's all possible. The other graph I'd like to see would map governor approval ratings against time in office. My understanding from folks who watch state politics more closely is that most governors start out extremely popular and then dip down towards earth after year two or three. It would be pretty easy to run a couple years of numbers and see if there's a strong correlation.
The takeaway, basically, is that small states tend to be more approving of their governors. Why? Gelman has some theories: "In a large state, there will be more ambitious politicians on the other side, eager to knock off the incumbent governor; small states often have part-time legislatures and thus the governor is involved in less political conflict; small states (notably Alaska) tend to get more funds per capita from the federal government, and it’s easier to be popular when you can disburse more funds; large states tend to be more heterogeneous and so it’s harder to keep all the voters happy. As the graphs show, the pattern isn’t perfect, but it looks real to me." That's all possible. The other graph I'd like to see would map governor approval ratings against time in office. My understanding from folks who watch state politics more closely is that most governors start out extremely popular and then dip down towards earth after year two or three. It would be pretty easy to run a couple years of numbers and see if there's a strong correlation. 
