Sampling and polls
Terence Tao posted about small sampling and polls, and the somewhat non-intuitive fact that the margin of error of a poll only depends on the size of the sample and not at all on the size of the population being sampled; even if the latter quantity is quite small (e.g. 1,000 polled out of a population of 200,000,000) the margin of error may be quite good. An analogy:
Suppose one is in front of a large body of water (e.g. a sea or ocean), and wants to determine whether it is a freshwater or saltwater body. This can be done very easily: dip one’s finger into the body of water and taste a single drop. This gives an extremely accurate result, even though the relative proportion of the sample size to the population size is, literally, a drop in the ocean; the quintillions of water molecules and salt molecules present in that drop are more than sufficient to give a good reading of the salinity of the water body.
Alternatively: it's easy to see that for polling purposes the only relevant parameter of a population is its average opinion (in particular, its size is not relevant). If all you have is a phone that connects you to a random person in a population when you pick it up, then it is impossible to tell whether the population consists of a billion people evenly split between candidates A and B, or a thousand people evenly split between candidates A and B, or even whether the population consists of one person who flips a coin to decide whether to say A or B every time you call him.
Ron Rivest spoke on security in voting systems at a GBC-ACM function. There have been a couple of voting protocols proposed recently (Scantegrity II and Twin voting) which allow the integrity of an election to be independently verified by all (end-to-end verifiability), while simultaneously preventing any voter from proving how she voted. Importantly, software is only used for auxiliary purposes in these protocols and we need not trust the software at all. End-to-end verifiability would lend confidence to election results in a way which is simply impossible in current systems, and in a democracy we should demand no less than this degree of transparency.