It is important to remember however that it is standard practice to give confidence intervals assuming only random error--NOT systematic error such as would come from underrepresentation of people with cellphones or imperfections in deciding who a "likely voter" is.
Random error is what prevents you from getting sixes exactly 1/6 of the time when you roll perfectly balanced dice. Systematic error would happen if the die is loaded.
That does seem contradictory. If the 50th percentile is above 270, then by definition the probability of being above 270 is > 50%. I think the 279 is a typo since the other 3 numbers and the mention of a threshold effect in the text are all consistent with each other but not with 279.
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Random error is what prevents you from getting sixes exactly 1/6 of the time when you roll perfectly balanced dice. Systematic error would happen if the die is loaded.