Why are gasoline prices going down? Because oil prices are:
Brent CrudeAll the reasons they went UP are still around - instability in the middle east, pinched domestic supply, increasing global demand, etc.
There's less worry about the ME because the war in Lebanon has ended, the Iranians have thumbed their noses at the west and the west appears to have backed down. The supply situation in the US has eased because the summer season is over, the hurricane season hasn't brought any major disruption (there were fears of a repeat of last year). The markets also expect a decline in US economic growth which will push US consumption lower.
In short, many of the worries that were elevating the oil price have gone away, at least temporarily.
The cynic in me says the republicans are telling the gas companies to drop their prices so they aren't an issue in the elections.
How would that affect the price the rest of the world is paying for crude oil?
Gasoline is made from oil. When oil goes up, gasoline goes up. Oil consumption has been rising rapidly for the last few years, which has put a lot of pressure on supply. The instability in the ME and elsewhere has increased fears that supply might be cut, and that has caused a rise in prices.
That's all market driven, and nothing to do with politics. No government has enough money available to dictate the price of oil, although plenty of governments can act to increase/decrease supply/demand. Oil companies charge the going rate, what they can sell the oil for to any other customer. (The rest of the world is paying a similar price for oil as well)
So the US government hasn't "told" anyone to reduce the price of oil, but their actions (not confronting Iran directly) have helped reduce the price. If the US decides after the elections to increase pressure on Iran, or even attack them, expect the price to go back up.