Adjusting errors for c-hat AND model averaging

[amdurso]

Two fairly simple questions:

1) If c-hat is >1 (indicating overdispersion), in addition to reranking by QAIC, the exercise for Chapter 4 of the book recommends adjusting the standard errors by multiplying them by the square root of c-hat. Which standard errors are they referring to? of model estimates of p and psi? of the beta values? both?

2) When model averaging (i.e. summing the weights of models including a certain covariate), if the covariate is included in both p and psi, should the weight of that model count twice towards the overall? Example:

Model Name = Weight
psi(C1), p(.) = 0.2
psi(C1, C2), p(C1) = 0.2
psi(C2), p(C1) = 0.1

is the model averaged weight for C1 = (0.2 + 0.2 + 0.1) = 0.5 or (0.2 + 0.2 + 0.2 + 0.1) = 0.7?

Thanks,