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I wonder how much of an effect on the value of Steem the Steem dollar has? I can't imagine it's that much since it's so far down the must on coinmarket cap compared to Steem.

I don't know as well. I just discovered that the witnesses kind-a control the SBD value. However, how that actually works, I don't know since every witness can set different values and how a common is derived is for me still unknown, as the proper understanding how the witnesses can indeed control SBD values. In the recent history we saw SBD jumping to 7US$ and coming down almost as quickly. I guess, the witnesses did not play role there. After that jump, SBD stayed slightly above 1US$; just yesterday or 2 days ago I read some witnesses reports on their adjustments to the Steem value that is used to calculate the rewards, that is apparently the only value they can control, so they do not control the Steem value in our internal market as they (obviously) do not control the Steem value on external markets. Quite a complex thing to understand without having all the implemented algorithms and formulas on the table.

The SBD part is not as straight forward to get your head around. My understanding of the goal for the witnesses is maintain a value of parity with the US dollar. There is a few ways they can do this. Setting the interest rate is one.
The Steem value on the other hand is controlled by the markets but also subject to any changes in the rate of new Steem creation.

Correct, the idea is to have SBD pegged to US$. How to do this? Indeed interest rates. In addition, witnesses can also set a discount to Steem value used for calculating the rewards. It becomes even more complex, because this Steem value is not the internal market or external market Steem value, or at least not the same parameters. https://steemit.com/sbd/@timcliff/attention-sbd-converters-please-read-important-information-about-sbd-steem-conversions