Martin Gilens and Benjamin page published an article that uses data to come to this conclusion about the public's influence on American policy:
"The central point that emerges from our research is that economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while mass-based interest groups and average citizens have little or no independent influence."
Iskander De Bruycker and Marcel Hanegraaff authored a recent study, focusing on the EU, in which they "demonstrate that interest groups with more economic resources are generally more influential, but only if their policy positions are congruent with a public majority." Sorry this one is paywalled. Such is the state of academic publishing. :(
[0] https://archive.org/details/gilens_and_page_2014_-testing_th...
[1] European Journal of Political Research , Volume 63 , Issue 1 , February 2024 , pp. 26 - 44 DOI: https://doi.org/10.1111/1475-6765.12582