  We investigate dual mechanisms for interacting particle systems. Generalizing
an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we
show that a simple linear transformation leads to a moment duality of suitably
rescaled processes. More precisely, we show how dualities of interacting
particle systems of the form $H(A,B)=q^{|A\cap B|}, A,B\subset\{0,1\}^N,
q\in[-1,1),$ are rescaled to yield moment dualities of rescaled processes. We
discuss in particular the case $q=-1,$ which explains why certain population
models with balancing selection have an annihilating dual process. We also
consider different values of $q,$ and answer a question by Alkemper and
Hutzenthaler.
