Figure 1

Example simulations of positive and negative influence. The conditional probabilities of $p(\dot{x}(t+1)|\dot{x}(t))$, $p(\dot{y}(t+1)|\dot{y}(t))$, and $p(\dot{x}(t+1)|\dot{y}(t))$ are fixed and unbiased. The only bias is from $\dot{x}(t)\to \dot{y}(t+1)$: $p(\dot{y}(t+1)=0|\dot{x}(t)=0)=P$ and $p(\dot{y}(t+1)=1|\dot{x}(t)=1)=P$. The influence from x to y is negative when $P<0.5$, as seen in (a)-(c). Similarly, the influence from x to y is positive when $P>0.5$, as seen in (d)-(f).