Why did the US credit rating downgrade in 2011 decrease US government bond yields? I'm not sure how bond yields were decreased by the  US credit rating downgrade in 2011. Since the credit rating is down, shouldn't the yields increase since the US government wants to attract more bond buyers?
My guess is this is a coincidence. That is, the effect of the credit rating agencies was either approximately zero, or if it was substantial and negative, that this was swamped out by other factors.
If bond ratings have a causal effect on yields, that effect is usually for smaller issues and smaller issuers where the market depends on the rating agencies for critical information. For the big issuers the banks are well informed on the issuer and need the rating agency less.
For example, consider the paper The relationship between credit default swap spreads, bond yields, and credit rating announcements (JBF 2004). When they look at CDS spreads, which are mostly for bigger issuers, they find:

By pooling all observations we find a significant (at the 1% level)
increase in the CDS spread well in advance of a downgrade event. In
the case of reviews for downgrade and negative outlooks there is a
significant (at the 1% level) increase in the CDS spread during the 30
days preceding the event. CDS spreads increase by approximately 38 bps
in the 90 days before a downgrade, by 24 bps before a review for
downgrade, and by 29 basis points before a negative outlook. When
observations are pooled there are no significant changes in CDS spread
during the 10 business days after any type of negative event.

I interpret this as saying that bond markets seem to react to the information on these larger issuers that the credit rating agencies are also using to change their ratings and at the same time they are considering those changes. However, the actual rating change, the information in that rating, and the reasoning behind it doesn't matter much. What holds for large corporate issuers is going to be even more true for a large issuer like the US government.
However, there is alternative evidence from the sovereign market in Europe. Credit rating agency downgrades and the Eurozone sovereign debt crises (JFS 2016):

This paper studies the reaction of the Euro's value against major
currencies to sovereign rating announcements from Moody's, S&amp;P and
Fitch CRAs during the Eurozone debt crisis in 2010–2012 based on event
study methodology combined with GARCH models. We also analyze how the
yields of French, Italian, German and Spanish government long-term
bonds were affected by CRA announcements. Our results reveal that CRA
downgrades, watchlist and outlook announcements had no impact on the
value of the Euro currency but increased exchange rate volatility.
At the same time, downgrades as well as negative outlook
announcements increased the yields of French, Italian, and Spanish
bonds and even affected the German bond's yields. This shows that
the monetary union has led to a breakdown of the consequences of the
rating shocks between currency value and sovereign bond yields. The
reason is that part of the rating shock is absorbed by an internal
repricing of sovereign bonds.