I don't work at Bungie.
Theoretically it is supposed to increase stability, however I did some tests with a Ghelion's Demise before and after selecting the rodeo perk and I wasn't able to discern any change in the amount of recoil or the recoil pattern.
I know this isn't exactly the most scientific answer as i'm just giving you my observations, but yeah.
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That's exactly how I tested it