  We present a theoretical framework for evaluating effective interactions
between localized spins mediated by itinerant electrons in double-exchange
models. Performing the expansion with respect to the spin-dependent part of the
electron hopping terms, we show a systematic way of constructing the effective
spin model in the large Hund's coupling limit. As a benchmark, we examine the
accuracy of this method by comparing the results with the numerical solutions
for the spin-ice type model on a pyrochlore lattice. We also discuss an
extension of the method to the double-exchange models with Heisenberg and $XY$
localized spins.
