Consider a simple 2-round voting scheme where the 1st round is a decision between two choices $A$ and $B$, and the second round is a decision between the winner of the 1st round and an existing choice $E$. The strategy for a voter can be seen as having three parts: the 1st round preference of $A$ vs $B$, 2nd round preference if $A$ wins, and 2nd round preference if $B$ wins.
Now this model is built with an assumption that the voter does not base their 2nd round strategy upon their voting in the first round. My lecturer casually mentioned that this, incorporating prior knowledge into voting strategy, would increase the number of components in the strategy from 3 to 5. Why is this? I have thought it out but can't come to any logical conclusion.
My second round strategy now has four components: $A$ won in the first round and I voted for $A$; $A$ won in the first round and I didn't vote for $A$; $B$ won in the first round and I voted for $B$: and $B$ won in the first round and I didn't vote for $B$.