Every vote counts.
—platitude heard before every election (occasionally it’s even true)
Every vote counts, so vote early and often.
—cynical response to the first quote
Imagine that the U.S. Senate is about to vote on an important bill. It is known that there are more for votes than there are against votes, and so if all 100 senators show up, then the bill will pass. Let’s suppose there are A senators who are against the bill, and thus there are 100 – A senators who are for it, where A < 50. If A = 49, for ...