A broker may add spreads based on the spreads given by its liquidity providers. So just for fun, I want to know if there is any possibility that I can judge a broker’s service by evaluating its LPs? E.g. A broker has 3 highly qualified LPs, while B broker 5 low-quality LPs, is it fair to say A is much likely to be better than B?
Is this information publicly available? Or is this something only big brokers disclose? 
I don’t think the information is publicly available nor is the broker under any legal obligation to disclose its business model to you.
how would you know who the brokers liquidity providers really are? They dont have to tell you and if they are telling you it may not really be the case.
What If broker A has higher spreads, slower execution speeds and poor customer service but tell you they are routing your orders through Morgan Stanley and Goldman Sachs
Would you still trade with them even though broker B keeps your trades in house but is providing tighter spreads, faster execution speeds and exceptional customer service?