It's not entirely true to say that the Tor relay controls the bandwidth on the client side. There are two values in the TORRC that that help limit how much bandwidth is consumed: RelayBandwidthRate and MaxAdvertisedBandwidth. This isn't the decider for the bandwidth that you advertise.
This article covers how bandwidth is measured on the Tor network.
Originally, the directory authorities would just use whatever bandwidth estimate you claimed in your relay descriptor. As you can imagine, that approach made it cheap for even a small adversary to attract a lot of traffic by simply lying. In 2009, Mike Perry deployed the "bandwidth authority" scripts, where a group of fast computers around the Internet (called bwauths) do active measurements of each relay, and the directory authorities adjust the consensus bandwidth up or down depending on how the relay compares to other relays that advertise similar speeds.
This a portion of the much larger and detailed article. I think your answers are in there.