I am linking to a paper of mine (‘Knowledge-Theoretic Properties of Strategic Voting’, co-authored with Eric Pacuit and Rohit Parikh) of possible relevance in the context of the just-decided elections and the importance of election season polling. Here is the abstract. (I am traveling and so unable to write a longer comment at this time).
Results in social choice theory such as the Arrow and Gibbard-Satterthwaite theorems constrain the existence of rational collective decision making procedures in groups of agents. The Gibbard-Satterthwaite theorem says that no voting procedure is strategy-proof. That is, there will always be situations in which it is in a voter’s interest to misrepresent its true preferences i.e., vote strategically. We present some properties of strategic voting and then examine – via a bimodal logic utilizing epistemic and strategizing modalities – the knowledge-theoretic properties of voting situations and note that unless the voter knows that it should vote strategically, and how, i.e., knows what the other voters’ preferences are and which alternate preference P′ it should use, the voter will not strategize. Our results suggest that opinion polls in election situations effectively serve as the first n–1 stages in an n stage election.
This is a technical paper and so unlikely to be readable to plenty of folks so I will try to provide a quick summary and discussion next week. The last sentence of the abstract though, should give you some indication of what its implications are and why they should be of interest to voters, politicians and pollsters alike.