Political Cartoons

Interesting but unanswerable socioeconomic question:

High gas prices will raise voter turnout by making people angry, but there's likely a marginal counterweight to that because driving to the polls is more expensive. Vice-versa for low gas prices, where it'll depress voter turnout, but as a marginal boost to turnout, driving to the polls is very cheap.

If you could somehow hold enough statistically independent trials of nationwide elections to measure this at different prices (I'd assume sampling from real elections has too many confounding variables even accounting for things like PPP, fuel efficiency, etc.), I wonder what the graph would look like of gas prices' effect on turnout. I imagine it would be a rise followed by a saturation followed eventually by a falloff as people actually start to riot (assuming you just kept increasing it indefinitely). Moreover, is there any point on the left of the curve (gas price is the x-axis and turnout is the y) where the effect of the drive being cheap actually outweighs the anger over prices? In this dream experiment, you can assume free gas is on the table, and we can even cross into the negatives and have gas stations paying you to get gas if we want.