You can think of the model with people as beads on a string that allows an easy thought experiment to hypothesize what happens with different strategies.

Building the Model: Suppose that there are two answers to the debate (yes/no ). Assign ‘yes’ a positive value and ‘no’ a negative value. A high ‘yes’ value corresponds to strong conviction that ‘yes’ is the answer and vice-versa for 'no'. Fence-sitters would be right at ‘0’, with no conviction either way. As noted above, the debate position of a person is simply described by a number on the real line. Your models propose that if a listener has position ‘x’ then their response to position ‘y’ will be to gravitate towards y if |x-y| is small and be repelled away from y if |x-y| is large. (Local attraction but long-distance repulsion).

If you accept the model above, you can write down equations but a thought experiment works to some extent: imagine many beads randomly arranged on a line. Generally they pull and repulse each other, so suppose they are in equilibrium. (...if possible, see PhilGoetz's comment.) Then a “debater” placed anywhere along that line will have the effect of clustering nearby beads but scattering far beads away (an effect that increases with distance).

Using this thought experiment, you may determine that some kind of “collect” and “sweep” approach is best.