How does the rational choice model help us understand the willingness of an individual to vote as well as whom she/he will vote for?
Downs and Riker come up with the calculus of voting, the formula, R=pB-C+D, where R is the probability that someone will vote, p is the probability of the vote “mattering”, B is the “utility” or benefit of vote, C is the cost of voting, and D is citizen duty.  Given that pB is usually 0, the equation becomes R=-C +D and in order for the R to be a positive value (which means a citizen will vote), we need civic duty to “outweigh” the cost of voting. 
The Rational Choice model has two competing views on how voters choose to vote.  One is proximity voting.  In this case, the voter chooses the candidate that they are the closest to in terms of where that candidate sits on a liberal/conservative line.  The other view is directional voting, which says the voter will vote for whomever is on their “side” of the scale.  For example, a Republican would vote for a Republican candidate even if they are closer to the Democratic candidate on the scale.